WO2010138696A1

WO2010138696A1 - System and method for passive range-aided multilateration using time lag of arrival (tloa) measurements

Info

Publication number: WO2010138696A1
Application number: PCT/US2010/036368
Authority: WO
Inventors: Ryan Haoyun Wu
Original assignee: Sensis Corporation
Priority date: 2009-05-27
Filing date: 2010-05-27
Publication date: 2010-12-02
Also published as: WO2010138696A9

Abstract

The present invention improves the performance of existing secondary surveillance radar (SSR) transponder multilateration (MLAT) systems using a Time Lag of Arrival (TLOA) measurement. The present invention correlates TCAS interrogation messages and reply messages, which are transmitted on different frequencies, to determine TLOA measurements that are used with TDOA MLAT to achieve higher positioning accuracy and greater surveillance coverage than conventional MLAT systems. The present invention applies to any MLAT system including surface MLAT, Wide-area MLAT, active MLAT, passive MLAT, range-aided MLAT, non-range aided MLAT, Precision Runway Monitoring (PRM) MLAT, and any other MLAT system based on receiving SSR transponder signals. The present invention also applies to Mode-S transponder signals and ATCRBS transponder signals.

Description

SYSTEM AND METHOD FOR PASSIVE RANGE-AIDED MULTILATERATION USING TIME LAG OF ARRIVAL (TLOA) MEASUREMENTS

FIELD OF THE INVENTION

The invention relates to improving secondary surveillance radar (SSR) transponder rnultilateration (MLAT) systems to achieve higher positioning accuracy, greater surveillance coverage and lower system cost.

BACKGROUND OF THE INVENTION

The prior art listed herein include the Traffic Collision Avoidance System (TCAS) US standard and Air Collision Avoidance System (ACAS) international standard technologies, the MLAT technologies, and two studies utilizing TCAS for the purpose of achieving ground and air aircraft positioning purposes.

The following items describe TCAS system prior art:

RTCA DO- 185 A"Minimum Operational Performance Standards for Traffic Alert and Collision Avoidance System II (TCAS II) Airborne Equipment"; - RTCA DO- 181 C "MINIMUM OPERATIONAL PERFORMANCE

STANDARDS FOR AIR TRAFFIC CONTROL RADAR BEACON SYSTEM/MODE SELECT (ATCRBS/MODE S) AIRBORNE EQUIPMENT"; and

"Introduction to TCASS II version 7", FAA, DOT, November 2000. A summary of the TCAS system prior art is provided in the following:

TCAS I is mandated in US on aircraft with 10 to 30 seats, although TCAS II may be installed instead. TCAS II is mandated in US and Europe on all commercial turbine-powered transport aircraft with more than 30 passenger seats (or Maximum take-off weight, MTOW above 33000 pounds ~ 15000kg). ACAS II (TCAS II v.7) is mandated in Europe on all commercial turbine powered transport aircraft with more than 19 passenger seats (or MTOW above 5700kg).

TCAS I is the first generation of collision avoidance technology. It is cheaper but less capable than the modern TCAS II system, and is mainly intended for general aviation use. TCAS I systems are able to monitor the traffic situation around a plane (to a range of about 40 miles) and offer information on the approximate bearing and altitude of other aircraft. It can also generate collision warnings in the form of a "Traffic Advisory" (TA). The TA warns the pilot that another aircraft is in near vicinity, announcing "traffic, traffic", but does not offer any suggested remedy; it is up to the pilot to decide what to do, usually with the assistance of Air Traffic Control. When a threat has passed, the system announces "clear of conflict". TCAS II is the second generation of TCAS, used in the majority of commercial aviation aircraft. It offers all the benefits of TCAS I, but will also offer the pilot instructions to avoid danger, known as a "Resolution Advisory" (RA). The suggestive action may be "corrective", suggesting the pilot change vertical speed by announcing, "descend, descend", "climb, climb" or "Adjust Vertical Speed Adjust" -. By contrast a "preventive" RA may be issued which simply warns the pilots not to deviate from their present vertical speed, announcing, "monitor vertical speed" or "maintain vertical speed". TCAS II systems coordinate their resolution advisories before issuing commands to the pilots, so that if one aircraft is instructed to descend, the other will typically be told to climb — maximising the separation between the two craft. As of 2006, the only implementation that meets the ACAS II standards set by ICAO is

Version 7.0 of TCAS II.

Mode-S TCAS operations per ICAO Annex 10 V4 will now be explained. An TCAS target interrogates Mode-S targets using top or bottom omni antennas with interrogation equivalent power of 54 dBm. A Mode-S transponder is with nominal MTL of - 74 dBm. Such that the nominal TCAS interrogation-reply maximum target separation is about 30 nmi. A directional antenna is recommended for ATCRBS operations only.

An TCAS target acquires and establishes "valid targets" by monitoring DF 11 and DF 17 squitters. An TCAS target obtains Mode-C altitude information of valid targets by monitoring the AC filed of DFO and DF4 replies of the targets of interest or by interrogating (UFO) the targets once per 10 sec. An TCAS target identifies "intruders" as the valid targets that have altitude within 10,000 ft of own altitude. An TCAS target interrogates (UFO, 16 AQ=I) intruders for range and range rate at an initial rate of once per 5 seconds. An TCAS targets identify "immediate threats" as the intruders with potential threat level (TAU) less than 60 seconds. An TCAS target interrogates immediate threat targets with a rate of once per second and non immediate threat targets with a rate of once per 5 seconds or at least once per 5 second depend on altitudes. A valid ground target (ground status is set) is still being interrogated periodically for its ground status by an TCAS target to insure timely acquisition when airborne. An TCAS target when is on the ground still interrogates targets but is with a limited interrogation power equivalent to 3 nrni in range. Radar solicits only DF4 replies by sending UF4 interrogation messages such that SSR and TCAS operations are distinguishable. A transponder (Mode-S or ATCRBS) shall never detect more than 280 TCAS interrogations (Mode-S and ATCRBS combined) in a one-second period from all TCAS interrogators within 30 nmi.

The following item describes MLAT prior art:

U.S. Patent No.7,170,441, Target Localization Using TDOA Distributed Antenna. This invention is a system and method of locating a target using a distributed antenna. The antenna consists of several receiving elements in known locations. At least one of the receiving elements is also a transmitter and transmits an interrogation signal to a target. The return signal from the target is received by a plurality of receiving elements and the target's position is calculated using the time of arrivals of the reply signal and the round trip delay between the transmission of the interrogation signal and the reception of the subsequent reply signal. The following item describes an airborne navigation positioning system based on

TCAS systems utilizing fixed TCAS transponder and location database to allow aircrafts to multilaterate their position similar to DME/DME operation:

"GPS Supplemental Navigation Systems for Use During the Transition to a SoIe- Means-GPS National Airspace System", Demoz Gebre-Egziabher, Sherman C. Lo, J. David Powell, Per Enge, Department of Aeronautics and Astronautics, Stanford University.

The following item describes a ground-based surveillance system utilizing TCAS interrogator as land of ground radar:

"AIR SURVEILLANCE FOR SMART LANDING FACILITIES IN THE SMALL AIRCRAFT TRANSFORATION SYSTEM", Eric J. Shea, MSEE Thesis, April 2002, Virginia Polytechnic Institute and State University, Blacksburg, VA.

Conventional MLAT systems receive data link (DL) messages to determine the position or location of the emitter without utilizing interrogation messages or information regarding a non-cooperative interrogator (which does not include the RU itself). Current multilateration (MLAT) system rely upon active interrogations to provide target range estimates for aiding TDOA MLAT calculations to achieve desired positional accuracy at far- field (target far from ground sensors) regions. Two types of conventional passive MLAT measures for passively sensing target positions involve frequency and signal strength measurements. These measures are known to be unreliable for precise positioning but are generally good for enhancing performance.

For a received signal strength (RSS) passive MLAT enhancement, the antenna-gain- compensated received signal strength indicates the path loss such that the propagation distance of the transmitted signal is known if the transmitting power is known and the signal is not obstructed or corrupted by multipath and Doppler induced fading. Normally only a rough magnitude of RSS is consider useable due to the aforementioned conditions which are often encountered. For a doppler frequency shift (DFS) measurement enhancement, the difference between the received and transmitted signal carrier frequency indicates the doppler shift due to a target's tangential velocity (range rate) to the RU such that the range rate or the time- derivative of range to the target can be measured by measuring doppler shift. However, precise measurement of doppler shift is difficult to measure due to the uncertainty in the exact transmitting frequency and requirement of a stable frequency reference at the receiver end.

What is needed is a system and method to provide more accurate target positions than can be obtained by conventional passive MLAT systems and to enable the coverage area range to be extended for passively multilaterating target positions.

SUMMARY OF THE INVENTION

According to a first aspect of the present invention, there is provided a method of multilaterating a transmitter position, comprising the steps of receiving a first message transmitted by a first transmitter in a first frequency range at each of at least three time synchronized remote receiving units (RUs), time stamping a time of arrival (TOA) of the first message at each of the RUs, and transmitting the received first message and the TOA data from each of the at least three RUs to a central processor, where the central processor uses the TOA data of the received first message to determine time difference of arrival (TDOA) measurements. The method further comprises the steps of receiving a second message transmitted by a second transmitter in a second frequency range at each of the RUs, time stamping a TOA of the second message at each of the RUs, transmitting the received second message and the TOA data from each of the RUs to a central processor, where the central processor uses the TOA data of the received second message to determine time difference of arrival (TDOA) measurements, associates the first message with the second message, determines the difference between the time of receipt of the first message at the second transmitter and the time of transmission of the second message that is associated with the first message by the second transmitter, creates a Time Lag of Arrival (TLOA) measurement using the TOA of the first message, the TOA of the second message that is associated with the first message, and the difference between the time of receipt of the first message at the second transmitter and the time of transmission of the second message that is associated with the first message by the second transmitter, and determines a position of the first transmitter and the second transmitter using at least the TLOA measurement and TDOA measurements. In one embodiment of the present invention, the associating of the first message with the second message is performed within a predetermined time period by determining that the first message is an interrogation message and the second message is a reply message in response to the interrogation message. In another embodiment, the TLOA measurement is determined by the following equation: TLOA₁ == t₂ — ti - td where: t₂ is the time of arrival of the second message transmitted by the second transmitter at an RU, t_\ is the time of arrival of the first message transmitted by the first transmitter, and t_d is the difference between the time of receipt of the first message at the second transmitter and the time of transmission of the second message that is associated with the first message by the second transmitter.

In one embodiment, the second frequency range is different from the first frequency range. In another embodiment, the second frequency range is identical to the first frequency range.

In one embodiment, the difference between the time of receipt of the first message transmitted by the first transmitter at the second transmitter and the time of transmission of the second message by the second transmitter is transmitted in a third message received by one or more of the RUs. In another embodiment, the difference between the time of receipt of the first message at the second transmitter and the time of transmission of the second message by the second transmitter is included in the second message transmitted by the second transmitter. In yet another embodiment, the difference between the time of receipt of the first message at the second transmitter and the time of transmission of the second message by the second transmitter is a fixed value.

In one embodiment, the step of determining the position of the first transmitter and the second transmitter further comprises using vertical position information of at least one of the first transmitter and the second transmitter. In another embodiment, the step of determining the position of the first transmitter and the second transmitter further comprises using Angle of Arrival (AOA) information of at least one of the first transmitter and the second transmitter.

In one embodiment, the step of determining the position of the first transmitter and the second transmitter further comprises using position track information of at least one of the first transmitter and the second transmitter. In another embodiment, the step of determining the position of the first transmitter and the second transmitter further comprises using range information of at least one of the first transmitter and the second transmitter.

According to a second aspect of the present invention, there is provided a method of enhancing multilateration of aircraft position using three or more remote receiving units, comprising the steps of receiving a first message transmitted by a first aircraft in a first frequency range at each of at least three time synchronized remote receiving units (RUs) in a geographic region, time stamping a time of arrival (TOA) of the received first message at each of the RUs, and transmitting the received first message and the TOA data from each of the RUs to a central processor, wherein the central processor uses the TOA data of the received first message to determine a time difference of arrival (TDOA) measurement. The method further comprises the steps of receiving a second message transmitted by a second aircraft in a second frequency range at each of the RUs, time stamping a TOA of the second message at each of the RUs, and transmitting the received second message and the TOA data from each of the RUs to a central processor, where the central processor uses the TOA data of the received second message to determine a time difference of arrival (TDOA) measurement; associate the first message with the second message, determine the difference between the time of receipt of the first message at the second aircraft and the time of transmission of the second message that is associated with the first message by the second aircraft, create a Time Lag of Arrival (TLOA) measurement using the TOA of the first message, the TOA of the second message that is associated with the first message, and the difference between the time of receipt of the first message at the second transmitter and the time of transmission of the second message that is associated with the first message by the second aircraft; and determine a position of the first aircraft and the second aircraft using at least the TLOA measurement and TDOA measurements.

In one embodiment, the method further comprises the step of decoding aircraft altitude data from at least one of the first message and the second message. In one embodiment, the first frequency range includes 1030 MHz. In another embodiment, the first message is a TCAS interrogation message. In one embodiment, the second frequency range includes 1090 MHz. In another embodiment, the second message is a TCAS reply message. In one embodiment, the difference between the time of receipt of the first message at the second aircraft and the time of transmission of the second message that is associated with the first message by the second aircraft is a fixed value. In another embodiment, the step of associating the first message with the second message is performed within a predetermined time period by determining that the first message is an interrogation message and the second message is a reply message in response to the interrogation message.

In one embodiment, the step of determining that the first message is an interrogation message and the second message is a reply message in response to the interrogation message further comprises using a UF message type and a MODE-S address of the interrogated aircraft decoded from the first message and a DF message type and MODE-S address of the interrogated aircraft decoded from the second message.

In one embodiment, the TLOA measurement is determined by the following equation: TLOA₁ = t₂ - ti - td where: t₂ is the time of arrival of the second message transmitted by the second aircraft at an RU, ti is the time of arrival of the second message transmitted by the first aircraft at an RU, and t_d is a known aircraft transponder's reply delay time.

In one embodiment, the step of determining the position of the first aircraft and the second aircraft further comprises using vertical position information derived from the MODE C altitude information of at least one of the first aircraft and the second aircraft. In another embodiment, the step of determining the position of the first aircraft and the second aircraft further comprises using Angle of Arrival (AOA) information of at least one of the first aircraft and the second aircraft. In yet another embodiment, the step of determining the position of the first transmitter and the second transmitter further comprises using position track information of at least one of the first aircraft and the second aircraft. In still another embodiment, the step of determining the position of the first aircraft and the second aircraft further comprises using range information of at least one of the first aircraft and the second aircraft. According to a third aspect of the present invention, there is provided a method of

TCAS-aided multilateration of aircraft position using three or more remote receiving units, comprising the steps of receiving 1030 MHz transmitted interrogation messages at each of at least three time synchronized remote receiving units (RUs) from a first aircraft that is TCAS- equipped of a plurality of aircraft in a geographic region, time stamping a time of arrival (TOA) of the 1030 MHz transmitted interrogation messages from the first aircraft at each of the RUs, receiving and time stamping a time of arrival (TOA) of a 1090 MHz transmitted reply messages from a second aircraft of the plurality of aircraft at each of the RUs, decoding aircraft altitude data from at least one of the 1030 MHz transmitted interrogation messages and the 1090 MHz transmitted reply messages at one or more of the RUs, and transmitting the received 1030 MHz transmitted interrogation messages, the 1090 MHz transmitted reply message, TOA data and decoded aircraft altitude data from each of the RUs to the central processor, where the central processor determines TDOA measurements using TOA data, associates the received 1030 MHz transmitted TCAS interrogation messages transmitted by the first aircraft and the 1090 MHz transmitted reply messages, creates a Time Lag of Arrival (TLOA) measurement using the associated 1030 MHz transmitted interrogation messages and 1090 MHz transmitted reply messages; and determines a position of the first aircraft and the second aircraft using at least the TLOA measurement, TDOA measurements and decoded aircraft altitude data.

In one embodiment, the TLOA measurement is determined by the following equation: TLOAi = t₂ - ti - td where: t₂ is the time of arrival of the second message transmitted by the second aircraft at an RU,

U is the time of arrival of the second message transmitted by the first aircraft at an RU, and t_d is a known aircraft transponder reply delay time.

According to a fourth aspect of the present invention, there is provided a method of TCAS-aided multilateration of aircraft position and velocity using three or more remote receiving units, comprising the steps of receiving 1030 MHz transmitted interrogation messages at each of at least three time synchronized remote receiving units (RUs) from a first aircraft that is TCAS-equipped of a plurality of aircraft in a geographic region, time stamping time of arrival (TOA) data of the 1030 MHz transmitted interrogation messages at each of the RUs, receiving and time stamping time of arrival (TOA) data of 1090 MHz transmitted reply messages from a second aircraft of the plurality of aircraft at each of the RUs, and decoding aircraft altitude data from at least one of the 1030 MHz transmitted interrogation message and the 1090 MHz transmitted reply message at one or more of the RUs. The method further comprises the steps of transmitting the received 1030 MHz transmitted interrogation messages, the 1090 MHz transmitted reply messages, TOA data and decoded aircraft altitude data from each of the RUs to the central processor, where the central processor determines TDOA measurements using TOA data and associates the received 1030 MHz transmitted interrogation message and the 1090 MHz transmitted reply message, creates one or more Time Lag of Arrival (TLOA) measurements using the associated 1030 MHz transmitted interrogation messages and 1090 MHz reply messages, combines the TDOA measurements of 1090MHz transmitted interrogation messages by the second aircraft, the TDOA measurements of the 1030 MHz transmitted reply messages by the first aircraft and the TLOA measurements of the first aircraft and the second aircraft are within a predetermined time window into a super measurement set, and determines a position of the first aircraft and a position and a velocity of the second aircraft using at least the TLOA measurements, TDOA measurements and decoded aircraft altitude data.

In one embodiment, the TLOA measurement is determined by the following equation:

TLOA₁ = X₂ - ti - td where: t₂ is the time of arrival of the second message transmitted by the second aircraft at an RU, t_\ is the time of arrival of the second message transmitted by the first aircraft at an RU, and t_d is a known aircraft transponder reply delay time. According to a fifth aspect of the present invention, there is provided a method of deriving a position and at least one of a MODE-S address and a MODE-A ID of a TCAS transmitter comprising the steps of estimating positions of a plurality of aircrafts in a geographic region using at least one of 1090 MHz TDOA MLAT, range-aided MLAT, and ADS-B, forming target position tracks for the plurality of aircrafts in the geographic region, receiving and time stamping TOA data of a UF- 16 TCAS interrogation message from the TCAS transmitter at one or more receiving units (RUs), and decoding a MODE-C altitude and one of the MODE-S address and the MODE-A ID of the TCAS transmitter from the UF- 16 TCAS interrogation message. The method further comprises the steps of transmitting the received UF- 16 TCAS interrogation message, TOA data, MODE-C altitude, and one of the MODE-S address and MODE-A ID from the at least one RU to a central processor, wherein the central processor associates the TCAS transmitter with a formed target position track using at least one of the MODE-S address, MODE-A ID and MODE-C altitude and deriving the position of the TCAS transmitter at the time of interrogation based on the associated formed target position track and the TOA data of the UF- 16 TCAS interrogation message. According to a sixth aspect of the present invention, there is provided a method of deriving a position and at least one of a MODE-S address and a MODE-A ID of a TCAS transmitter comprising the steps of estimating positions of a plurality of aircraft in a geographic region using at least one of 1090MHz TDOA MLAT, range-aided MLAT, and ADS-B, forming target position tracks for the plurality of aircraft in the geographic region, receiving and time stamping TOA data of a 1030MHz transmitted TCAS interrogation message from the TCAS transmitter at at least three(3) RU, and transmitting the received TCAS interrogation message and TOA data from each of the RUs to a central processor, where the central processor determines TDOA measurements, determines the position of the TCAS transmitter using the TDOA measurements and associates the TCAS transmitter with a formed target position track using the determined position of the TCAS transmitter and the formed position tracks, determines at least one of the MODE-S address and the MODE-A ID of the TCAS transmitter from the MODE-S address and MODE-A ID of the associated formed target position track, and derives the position of the TCAS transmitter at time of interrogation based on the associated formed target position track, the determined position of the TCAS transmitter using 1030MHz TDOA measurements and the TOA data of the TCAS interrogation message.

According to a seventh aspect of the present invention, there is provided a method of deriving a Time Lag of Arrival (TLOA) measurement comprising the steps of receiving a first message transmitted by a first transmitter at a first receiver, time stamping a Time of Arrival (TOA) of the first message at the first receiver, receiving at a second receiver a second message transmitted by a second transmitter that receives the first message prior to the transmission of the second message from the second transmitter, time stamping a TOA of the second message at the second receiver, determining the difference between the time of transmitting the second message by the second transmitter and the time of receiving the first message at the second receiver, and determining the TLOA measurement using the TOA of the first message at the first receiver, the TOA of the second message at the second receiver, and the difference between the time of transmitting the second message by the second transmitter and the time of receiving the first message at the second receiver.

TLOA₁ = t₂ - t₁ - t_d where: t₂ is the time of arrival of the second message transmitted by the second transmitter at a receiver, ti is the time of arrival of the first message transmitted by the first transmitter at a receiver, and t_d is the difference between the time of receipt of the first message transmitted by the first transmitter at the second transmitter and the time of transmission of the second message by the second transmitter.

In one embodiment, the positions of the first receiver and the second receiver are different. In another embodiment, the positions of the first receiver and the second receiver are the same. In yet another embodiment, the first receiver is the second receiver.

BRIEF DESCRIPTION OF THE DRAWINGS

For a fuller understanding of the nature and objects of the invention, reference should be made to the following detailed description of a preferred mode of practicing the invention, read in connection with the accompanying drawings in which: Fig. 1 illustrates one method of obtaining a new measurement using the TLOA- assisted multilateration system of the present invention;

Fig. 2 shows an example of one embodiment of the TLOA-assisted multilateration system of the present invention;

Fig. 3 is an example of a Mode-S target interrogated by a TCAS target; Fig. 4 illustrates the pulse trains of a 1030 MHz interrogation message and a 1090

MHz Mode-S message; Fig. 5 illustrates one example of a TCAS target interrogating a Mode-S aircraft being received by four RU's;

Fig. 6 illustrates the solution curves of a TLOA measurement in two-dimensions using one embodiment of the TLOA-assisted multilateration system of the present invention; Fig. 7 illustrates the wide area coverage provided by the TLOA-assisted multilateration system of the present invention;

Fig. 8 illustrates a typical TCAS II equipage for an aircraft and nominal antenna coverage for TCAS II equipped aircraft;

Fig. 9(a) illustrates the "hearable" regions for an RU to receive a TCAS transmission; Fig. 9(b) illustrates the replier coverage per TCAS interrogator using a minimum separation of 3 nrni between aircraft using the TLOA-assisted multilateration system of the present invention;

Fig. 9(c) illustrates the minimum separation for Precision Runway Monitoring (PRM); Fig. 10 illustrates unambiguous and ambiguous TLOA message pair association using the TLOA-assisted multilateration system of the present invention;

Fig. 11 illustrates the probability of ambiguous TLOA message pairs;

Fig. 12 illustrates the theoretical position error of TDOA MLAT and TLOA-assisted MLAT for TCAS and Mode-S targets using one embodiment of the TLOA-assisted multilateration system of the present invention;

Fig. 13 illustrates the theoretical position error of TDOA MLAT and TLOA-assisted MLAT for TCAS and Mode-S targets using decoded aircraft altitude in one embodiment of the TLOA-assisted multilateration system of the present invention;

Fig. 14 illustrates the theoretical position error of TDOA MLAT and TLOA-assisted MLAT for aircraft surface operations for areas having good GDOP using one embodiment of the TLOA-assisted multilateration system of the present invention;

Fig. 15 illustrates the theoretical position error of TDOA MLAT and TLOA-assisted MLAT for aircraft surface operations for areas having bad GDOP using one embodiment of the TLOA-assisted multilateration system of the present invention; Fig. 16 illustrates another embodiment of the TLOA-assisted multilateration system of the present invention; and

Fig. 17 depicts the positions of one or more RUs, a TCAS target and a Mode-S target for the generalized formulation of TLOA and TDOA for determining the position of the TCAS target and the Mode-S target using one embodiment of the TLOA-assisted multilateration system of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides a novel passive multilateration (MLAT) system and method for determining the position of a target using one or more Remote Units (RUs) that has performance equivalent to a conventional Range-aided MLAT that transmits interrogations to assist in the determination of target position. In one embodiment, the position of Mode-S targets is determined using one or more RUs without interrogation but with position accuracy equivalent to that of active Range-aid MLAT systems. A passive aircraft beacon transponder signal receiver, such as an RU, is capable of

TCAS-aided MLAT operation since no interrogation is required from the RU. However, it does require the presence of an ADS-B or non ADS-B equipped TCAS interrogator in the coverage area and requires the target to be within the TCAS interrogator's interrogation range, which has a nominal range of 40 nautical miles (nmi). It also requires both the interrogation and reply message to be received by the RUs.

The present invention utilizes the TCAS system in a different manner than the existing MLAT system discussed in the Background section. The present invention does not require any ground transmitters and does not require any additional interrogation messages to be transmitted than are currently present in the airspace during normal operations. The system and method of the present invention only requires the RUs to receive and process both uplink messages and downlink messages, which may be transmitted on different frequencies. The uplink messages may include interrogation messages and the downlink messages may include interrogation reply messages.

Conventional MLAT systems estimate target positions by measuring multiple Time of Arrivals (TOAs) of the received messages on the 1090MHz band and form Time Difference of Arrival (TDOA) equations for solving the target positions. In order to solve target's x y z position at least 4 RUs are required to establish at least 3 TDOA equations such that a DFO/16 (i.e. Mode-S Downlink Format 0 or 16 or TCAS DF) target position can be solved. Given a 1030MHz band receiving capability, a UFO/16 (i.e. Mode-S Uplink Format 0 or 16 or TCAS UF) target can also be solved in a similar fashion if provided with 4 or more RUs receiving the UFO/16 message. While the above operation may provide dual-link target positioning capability, the accuracy may be poor due to poor GDOP when targets are outside the constellation of RUs. A typical method to combat this is to interrogate targets to obtain ranges to target from round-trip delays. Such ranges are obtained for aiding with the MLAT calculation for better accuracy. Suppose range interrogation is not feasible or not preferable, other mitigation methods need to be included to improve the accuracy. The performance provided by the system and method of the present invention is achieved by aiding the conventional MLAT' s TDOA measurements with a new type of measurement, Time Lag of Arrival (TLOA). TLOA is the time lag between the time an RU receives a TCAS interrogation message and the time an RU receives the TCAS reply message transmitted in response to the TCAS interrogation message. New TLOA measurement equation can be determined for RUs once correlations between TCAS interrogations and TCAS replies are established. The addition of the TLOA measurement of the system and method of the present invention provides more accurate positions than can be obtained by passive MLAT systems and enables the range of the coverage area of the MLAT system to be extended. The TLOA measurements are established passively and are used with the TDOA measurements provided by the MLAT system so that no active range interrogation is required for calculating a target position. TLOA measurements can also be combined with other MLAT measurement types including range measurements and Angle of Arrival (AoA) measurements, in addition to TDOA measurements for further improving the performance. More specifically, in one embodiment, for TCAS equipped vehicles and aircraft, and aircraft and vehicles equipped with Mode-S transponders, a system and method is disclosed to improve the positional accuracy without interrogating targets in the far fields. In the present invention, at least a subset of the ground RUs are required to be able to receive, decode, and timestamp UF-O and UF- 16 TCAS messages in the 1030MHz frequency band as well as all SSR messages in the 1090MHz band in order to facilitate the new MLAT algorithm. The system of the present invention uses both 1090MHz and 1030MHz bands, monitoring and correlating the Traffic Collision Avoidance System (TCAS or internationally known as the Airborne Collision Avoidance System or ACAS) messages transmitted between TCAS equipped aircraft (e.g. TCAS interrogator) and Mode-S transponder equipped aircraft (e.g., Mode-S responder) to determine the position of Mode S responder targets, as shown in Fig. 1. In this embodiment, the RUs receive both 1090 MHZ TCAS DF messages and 1030 MHz TCAS UF messages, which are not used by RUs in existing multilateration (MLAT) systems, and associate the interrogation messages transmitted in the 1030 MHz TCAS UF messages with the reply messages transmitted in the 1090 MHz TCAS DF messages to form an additional target measurement, thereby achieving greater accuracy than can be achieved in existing passive MLAT systems.

The principle of TCAS-aided MLAT of the present invention is applicable for determining the position of any type of radio frequency (RF) wireless communication system. For example, the principle of TLOA-TDOA positioning of the present invention applies to any RF wireless communication systems that use an interrogation-reply sequence of transmissions, such as TCAS operations, which are observed by another party, such as at least three ground transceivers (i.e., RUs).

Fig. 2 illustrates the minimum components and operation of the generalized TLOA- assisted multilateration. In Fig. 2, a TLOA measurement is obtained by an observer node (k) on two communicating nodes (i and j). Nodey sends a message at to to node i. Node i receives the message and send a reply message after td seconds. Node k receives both messages and measures the difference in the arrival time of the two messages and the measured difference is the TLOA measurement (t₂-ti) that can supplement any positioning algorithm or validate any position estimates on the three nodes. The TLOA measurement results in equation (1):

TLOA - C = ^(x_k - X₁)² + (y_k - y,)² + (z_k - z,.)² + ^x₁ - X_jf + <y, - yrf + (Z₁ - Z_j)²

-fa* - *j)² + (y_k - yj)² + (z_k - ^Zj)²

The above equation is used to help solve any positioning estimation or multilateration problem on any of the position component(s) of the node i,j, and k. In the case where position component(s) are solved through other means, the TLOA measurement provides valuable redundancy which is used to further improve the position accuracy or is used to validate the solution to further the integrity of the solution.

For example, Fig. 1 illustrates the process of obtaining a new measurement in one embodiment of the present invention. In Fig. 1, the TCAS equipped aircraft transmits a TCAS UF (interrogation) message to an aircraft under interrogation , and the interrogated aircraft replies to the TCAS UF message with a TCAS DF (reply) message. Both the TCAS UF interrogation message and the TCAS DF reply message are received by at least three RUs. In accordance with international standards, if the TCAS UF interrogation message is a

UFO (short ACAS interrogation), the TCAS UF interrogation message contains the Mode-S aircraft's (i.e., the interrogated) Mode S address. If the TCAS UF interrogation message is a UF 16 (long ACAS interrogation), the TCAS UL interrogation message includes three message types: a resolution message, an ACAS Broadcast message, and an RA broadcast. In addition to the interrogated Mode-S aircraft's Mode S address, the Resolution message and ACAS Broadcast contain the interrogating TCAS equipped aircraft's Mode S address, and the RA broadcast message contains the Mode-A ID and Mode-C altitude of the interrogated Mode-S aircraft. The TCAS DF reply message is a DFO or a DF 16, which always contains the interrogated Mode-S aircraft's Mode-S address and encoded Mode-C altitude.

After receiving the TCAS UF interrogation messages and TCAS DF reply messages, the RUs are able to associate the two messages from among all of the messages received by the RU using the unique address of the Mode-S aircraft (i.e., interrogate). Once the association is established, a Time Lag of Arrival (TLOA) measurement is calculated. TLOA is the time lag between when an RU receives the UFO/ 16 message from the TCAS interrogator target and when an RU receives the associated DFO/ 16 message from the Mode- S replying target.

For system to acquire a TLOA measurement, the RUs must be capable of receiving, time stamping, and decoding at least the UF0/UF16 and DF0/DF16 messages on the 1030 MHz and 1090 MHz band respectively.

Fig. 3 illustrates an example where target i is a Mode-S target to be interrogated by a TCAS equipped targety and RUi receives both the TCAS UF and TCAS DF messages between the target i and targety. Note that the RU that receives the TCAS UF messages needs not to be the RU that receives the corresponding TCAS DF messages and can be different. For convenience we use the same RU in the formulations. At to seconds, targety sends out an UFO or 16 interrogation message addressed to target i. At t_/ seconds, the ground monitoring RUi receives the UFO or 16 message. Target i receives the UFO or 16 message and then sends out a DFO or 16 reply message with its own address after t_d seconds, and at t₂ seconds, the RUi receives the DFO or 16 message. Upon receiving the UFO or 16 message addressed to target i, the RUi opens an associating window waiting for the arrival of the solicited DFO or 16 message. If the DFO or 16 message arrives without ambiguity a TLOAi is created as TLOA₁ =t₂ - t_x - t_d where t_d is the known transponder delay time which is specified in RTCA DO 161-C. In the present invention, the 1030 MHz interrogation message is time stamped using the rising edge of Pl P2 pulses similar to the time stamping of the 1090 Mode-S messages using the message preamble, as shown in Fig. 4. The accuracy of the time stamp on the 1030 MHz message is approximately equivalent to that of the 1090 MHz message since the maximum rising time of the edges of interrogation and reply pulses are identical according to specification (i.e., 0.1 micro seconds).

As explained above, an RU may provide a TLOA measurement per TCAS communication between an interrogating TCAS interrogator and an interrogated Mode-S target. Such TLOA as a function of two unknown target positions (x,-, yι, z,) and (XJ, y_j, zj) can be added to the existing TDOA MLAT formulations to improve accuracy. The TLOA equation for Fig. 5 is formulated as

(t₂ - t_x - t_d) - C = ^(X_x - X₁)² + (Y_x - y_t)² + (Z₁ - Z₁)² + J(χ_t - X_j)² + {_yi - _yjγ + (z,. - _Zjf

- ,J(X₁ - X_j)² + (Y_x - y_j)² + (Z_x - Z_j)² or

TLOA_x ^■ C = dist(tgt₍ → tgt_j → RU_x ) - dist(tgt_! -» RU₁ ) where C is the Speed of Light in atmosphere and dist(A→ B→ C) means the sum of distances of point A to point B, and point B to point C. Hence, for an N-RU system a total of 2N- 1 measurements can be established for solving the unknown positions of target i and j. These measurement equations include: N-I TDOA equations for the UFO target; and N-I TDOA equations for the DFO target; and 1 TLOA equations for the UFO/DFO targets (by any RU). So for the four RU MLAT system shown in Fig. 5, in addition to the 6 TDOA equations, the TLOA equation provides the redundancy and ability for obtaining more accurate solutions and extending the coverage area of the MLAT system as well. For the detailed derivations of the TLOA-TDOA MLAT for Fig. 5, please refer to the Section entitled "Generalized TLOA-TDOA MLAT MLE and CRLB Formulations" at the end of this specification.

In the above example, the DFO/ 16 message contains not only the Mode-S target's address, but also its Mode-C altitude (the AC field in DFO/16), so the vertical position of the target can be derived and treated as a known value such that the 2N- 1 equations are used for solving five (5) unknown parameters instead of six (6). A system of only three (3) RUs is capable of solving target positions since in such system five (5) equations are sufficient for solving five (5) unknown parameters. The same approach applies to UF/DF 16 type messages of TCAS operations. The only difference in UF/DF 16 operation is that the interrogation message contains additionally either the interrogator's Mode-S address or its Mode-A ID and altitude information such that the altitude of the interrogator can be known either indirectly by looking it up from a recently received altitude report using its Mode-S address as the key or directly by using the reported altitude. In either case since altitudes of the both targets are known, the remaining 4 unknowns can be solved redundantly using only three (3) RUs.

Fig. 6 provides a visualization of a TLOA measurement by fixing one target's parameters at a time and explaining the geometry in a two-dimensional sense. Due to the high-dimensional nature of TLOA (five (5) parameters) it is difficult to physically describe the solution surface formed by the measurement as what can be done for the TDOA (where the measurement forms a hyperbolic surface of solution space) and range-aided (where measurement forms a spherical surface of solution space) measurements. In Fig. 6, the solution curves of a TLOA measurement are illustrated in a two-dimensional sense. In Fig. 6, the outer circle "E" represents the ellipse of Mode-S target i's TLOA measurement and fixing the position of TCAS target j's position on which points satisfies:

A + B = (constant of TLOA - fixed C).

The line intersecting the outer circle "E" represents the hyperbola of TCAS target j's TLOA measurement and fixing the position of Mode-S target i's position on which points satisfies: A - C = (constant of TLOA - fixed B).

The effect of TLOA on the solutions of the positions of target i andy can be understood through the concept of a penalty or cost given by the solution curves. Given a TLOA OfRU₁, if one first estimates a position of the TCAS target y and then tries to determine the position of the Mode-S target i, the possible positions of target i indicated by the TLOA is the ellipse with foci on the RUi and the TCAS target j, as shown in Fig. 6. Solutions for the position of target i that are farther away from the ellipse generate greater penalties, thereby creating a limiting effect on the solution to obtain more reasonable solutions with lower penalties or costs (similar to the effect of range-aided MLAT, where a circular solution curve is created that limits the solution space). On the other hand, if one first estimates the position of the Mode-S target i, the possible positions of the TCAS target y indicated by the TLOA is the hyperbola with foci on the RUi and the Mode-S target i. Similarly solutions of target j farther away from the hyperbola will create greater penalties such that the solutions are limited to a more reasonable space. So the present invention can be understood such that the effect of a TLOA on the solution space is to introduce additional penalties so that solutions are limited to a more reasonable solution space and accuracy is improved. The system and method of the present invention can be referred to as a "passive, range-aided" system and method based on the solution space limiting effects brought by the range-sum elliptical curve (curve of A + B = constant) and the range-difference hyperbolic curve (curve of A - C = constant) of TLOA that is obtained passively by monitoring TCAS communications.

In summary, the TLOA-aided or Passive Range-aided MLAT operation shall yield solutions containing at least:

TCAS interrogator's position (x,-, y_t, z_;); and Mode-S target's position (XJ, y_j, zj), its Mode-S address, and its Mode-C altitude, where Z_j is derived from Mode-C altitude.

If only UF/DF O messages are received, the Mode-S address and Mode-C altitude of the interrogating TCAS target cannot be obtained directly. However, the address and Mode- C altitude may be obtained by correlating, either in the solution space or measurement space, the current interrogation-event solution of the TCAS interrogating target with an earlier interrogation-event solution of the same TCAS target during which the TCAS target was acting as a TCAS interrogatee that was replying to an interrogation by another TCAS target (i.e., interrogator). If Mode-C altitude is acquired for the TCAS target, an additional iteration may be performed to solve target positions using the Mode-C altitudes of the TCAS target and the Mode-S target. In this case, as in the UF/DF 16 message operations, four (4) parameters instead of five (5) are to be solved such that better position accuracy can be expected.

In the method of the present invention, solving target positions involves an iterative cost-minimization process. To perform position estimation using an iterative method, the initial estimates of the target positions should be as close to the solution as possible. If a three dimensional solution is to be solved, the three dimensional solution will need at least four (4) RUs for calculating a closed-form solution. However, if the target's vertical position is either known or assumed, the three dimensional solution will only need a minimum of three (3) RUs. Direct closed-form solutions solving both target positions using TDOA and TLOA equations are helpful but not required.

When a target is interrogated by more than one TCAS interrogator in a short period of time and more than one TLOA measurement is formed from such interrogations, the position accuracy of the interrogated target can be further improved by solving the TDOA and TLOA equations jointly by assuming a constant velocity of the interrogated target. In this case, the position of the interrogated target is modeled as an initial starting position plus movements which are just the elapsed time multiplied by the velocity. When more than two interrogators (i.e., two or more TLOAs) are available, the positions and velocity of the target can be solved redundantly to obtain higher accuracy. The correctness of a joint solution relies on the assumption of constant velocity, therefore the time limit for combining interrogation events for a fast-maneuvering target is shorter than the time limit for combining a cruising target.

The present invention can be referred to as TCAS-aided MLAT, TLOA-TDOA MLAT, TLOA-aided MLAT or passive range-aided MLAT. Some of the advantages of TCAS-aided Multilateration according to the invention are: it does not require any interrogation or transmission, i.e. it is passive, which is suitable for high-density environment that would not welcome additional ground interrogations; - it only requires 1030 MHz and 1090MHz receiving capabilities — it receives a

TCAS interrogation message (UFO/16) and a reply message (DFO/16) to create a Time Lag of Arrival (TLOA) measurements; and it estimates the positions of the TCAS interrogating and replying targets based on the TLOA and conventional TDOA measurements, achieving improved surveillance accuracy over conventional TDOA MLAT and extending the coverage area of MLAT systems by using the TLOA measurement. A direct comparison of TDOA MLAT, TDOA Range-aided MLAT and TDOA TCAS-aided MLAT (the present invention) is presented in Table 1.

Table 1

For a TLOA to be measured, a TCAS communication needs to occur first and at least an RU needs to be able to receive the TCAS communication. More specifically, for a TLOA to be measured, the Mode-S target needs to be within the coverage of the TCAS interrogating target (nominally up to 30 to 40 nmi), the targets need to be within each other of at most 10,000 ft in altitude (TCAS does not interrogate targets vertically separated by 10000 ft or more); and the targets need to be within an RUs's listening range (nominally up to ~250 nmi depend on MTL (minimum threshold level) and the direction of TCAS antenna).

For example, using the above criteria and assuming the coverage radius of TCAS is 30 nmi, if one TCAS equipped target is within 15 nmi from a system center, all of the Mode- S equipped targets within 15 nmi from the system center and within 10,000 ft of the altitude of the TCAS target will be within the area covered and the present invention will be able to measure a TLOA for each of the Mode-S equipped targets. For Mode-S targets outside of 15 nmi from the system center, any Mode-S targets that are within 30 nmi distance and 10,000 ft altitude of a TCAS target will also be within the area covered, if both the Mode-S target and the TCAS target are within the maximum radio range of the RU (normally up to 250 nm). An example of the wide-area coverage provided by the TLOA of the present invention is shown in Fig. 7.

Fig. 8 illustrates the typical TCAS II equipage, in which a top directional TCAS/TCAS antenna and an omni bottom TCAS/TCAS antenna are included. According to original specification, the TCAS target should be equipped with a top omni-directional antenna 10 and a bottom omni-directional antenna 20. The nominal antenna coverage for the omni-directional antennas is shown in Fig. 8. Directional antennas are only recommended for ATCRBS whisper-shout operations and are optional for Mode-S TCAS operations so that ground RUs have less difficulty capturing transmitted TCAS interrogation messages. However, the current recommendation for TCAS II version 7 (equivalent to ACAS II) operations suggests that the top antenna should be a directional antenna which will make detecting the interrogation message more difficult when the directional antenna transmitting the TCAS interrogation message is not facing the RUs. The use of directional antennas will impact the number of interrogations and reply that can be associated properly since the

TLOA operation will work with directional antennas if the UFO/ 16 transmission covers both the Mode-S target and the required receiving RUs. Many TCAS installations now include directional antenna for the bottom TCAS antenna in their system for improved azimuth performance. The purpose of adopting directional antenna is to provide additional azimuth positions of targets to aid pilots with identifying potential threats more easily. Specifically, the directional antenna is used for estimating azimuth positions of targets to provide Horizontal Resolution in addition to present Vertical Resolution to the pilot.

While TCAS interrogations can be transmitted omni-directionally, in practice a sectorized transmission is preferred to reduce azimuth ambiguity. A typical TCAS sectorized antenna is composed of a passive antenna array of 4 elements and transmissions are separated into four sectors - forward, rear, left, and right. The typical horizontal beamwidth is 90 ±10 degrees and the vertical beamwidth is at least -15 ~ +15 degrees. The transmission power on each sector and the top and bottom are also different, the typical power are 52, 48, 43, and 34 dBm respectively for top forward, top rear, top left and right, and bottom omni directional interrogations. The limiting effect brought by directional TCAS interrogations need to be considered carefully. Fig. 9(a) illustrates the "hearable" region in which an RU receives the TCAS interrogation transmitted by a TCAS directional antenna. Since the nominal maximum glide slope of 4.5 degrees is much smaller than the half vertical beam width of TCAS directional antenna, an RU is able to receive the interrogation by an approaching TCAS aircraft regardless of top or bottom antenna. For overflying TCAS aircrafts, the "hearable" region is governed by the 15 degree boundary line illustrated in the figure such a deaf cone is formed on top of the RU due to the narrow vertical beam width of the TCAS interrogation transmitted by a TCAS directional antenna. Notice that TCAS targets that are 25 nmi away from an RU can be heard by the RU (with antenna pointing at the RU and within maximum range) since most flights are assigned with altitudes no greater than 40,000 ft.

Tables 2 and 3 provide details of coarse 1030 receiving coverage in terms of range from RU to interrogator. Assuming Friss Path Loss = 92.697 + 20 loglO{dist in km} at 1030 MHz, the maximum range with respect to Tx power and MTL levels are shown in Tables 2 and 3.

Table 2

If one then considers coverage in terms of number of repliers per interrogator, the following applies. Using 3 nmi as a minimum separation between two aircrafts, and assuming linear landing and departure routes, at maximum capacity and minimum separation, the replier coverage per TCAS interrogator is shown in Fig. 9(b). The coverage shown in Fig. 9(b) is based on the following facts: minimum separation per PRM operation is shown in Fig. 9(c) maximum Arrival/departure capacity per airport is 50 AC/hr or 72 sec/ AC; - nominal 747 landing speed: 155-161 mph or 69-72 m/s or -25 sec/nmi for landing; nominal arrival glide slope is 3° (max 4.5°); departure climb slope varies from 200ft/nmi (1.9°) to 1800 ft/nmi (16°); and nominal climb slope is 3.5° - 7°. The minimum separation based on capacity and landing speed is then 72 sec/ AC * nominal speed 72 m/s - 5184 m = 2.8 nmi. This confirms that the PRM 3 nmi separation is feasible.

In one embodiment of the present invention, the association or correlation of UFO and DFO for a Mode-S target can be achieved based on the density of the TCAS operations being limited per the ICAO specification, which states that TCAS is designed such that "a victim transponder will never detect more than 280 TCAS interrogations in a one-second period from all TCAS interrogators within 30 nmi" (ICAO Annex 10 V4). For TLOA operated within a 15 nmi range, the maximum TLOA value occurs when the TCAS interrogator and the Mode-S interrogate are at a distance of 30 nmi from each other on the edge of the coverage area. In this case, the lag between the 1030 MHz TCAS interrogation and the 1090 MHz reply message pair to determine the TLOA have a separation of 185 microseconds. For wider coverage where targets are outside of the 15 nmi radius the maximum TLOA may be 60 nmi or 370 microseconds when the RU, the TCAS interrogator, and the Mode-S target are on the same line or the TCAS interrogator is in the middle and is 30 nmi closer to RU than is the Mode-S target, as shown in Fig. 9(a). In this example, to calculate the probability of having a potential erroneous association between a UFO and a DFO message due to ambiguity, one may conservatively assume that the ambiguity in associating an UFO with its solicited DFO occurs when two TLOA messages pairs start to overlap. As illustrated in Fig. 10, detection of overlap of two TLOA pairs can be declared when two or more DFOs with the same solicited address are received within 185 microseconds (for 15 nmi coverage; for greater than 15 nmi coverage it is 370 microseconds) after the UFO. The probability of having an ambiguous association of a TLOA given K interrogations per second per transponder can be approximated as the probability of picking a number 'N' between 1 and 5405 (for 15 nmi coverage; for greater than 15 nmi coverage it is 2703) more than once among K trials where N is the number picked in the first trial.

The number of overlap or ambiguous TLOA message pairs is a function of the density of the TCAS interrogation messages in the coverage area. The probability of overlap or ambiguous TLOA message pairs is depicted in Fig. 11. The maximum (i.e. the worst) probability of having an ambiguous TLOA is 0.1 given the maximum K value of 280 in accordance with the ICAO specification. As shown in Fig. 11, since the overlap probability is moderately low, a filtering logic is implemented to discard a TLOA whenever the risk of having an ambiguous TLOA is detected and the remaining unambiguous TLOAs are sufficient for the system and method of the present invention to achieve the improved surveillance accuracy over conventional TDOA MLAT and extended coverage area of MLAT systems without trying to resolve the ambiguous TLOAs.

In one embodiment of the method of the present invention, a plurality of time- synchronized ground RUs are deployed in a network, at least one of the RUs receives and timestamps a TCAS interrogation message (i.e., 1030 MHz Mode-S Uplink Format message), at least three RUs receive and timestamp a Mode-S reply message (i.e., 1090 MHz Mode-S Downlink Format message), the RUs transmit the received messages to a central processor, the central processor groups messages that are from the same transmission event into a cluster and associates a TCAS interrogation event cluster to its corresponding TCAS replying event cluster. The central processor then calculates the time-difference of arrivals (TDOAs) and the time-lag-of-arrival (TLOA) for a pair of associated clusters and calculates the position of the TCAS interrogating target and the position of the TCAS replying target using the TDOAs, TLOA, and available barometric altitude information decoded from the TCAS reply and interrogation messages. In this embodiment, associating a TCAS interrogating-event cluster with a TCAS replying-event cluster includes the steps of selecting a TCAS-interrogation-event cluster as a reference cluster and selecting TCAS-replying-event clusters that contain the same replying- party address and have arrival times within a certain time window of the earliest arrival time of the TCAS-interrogation messages of the reference cluster as candidate companion clusters. If there is only one candidate companion cluster, the candidate companion cluster is declared as the companion cluster and the companion cluster and the reference cluster are associated. However, if there are two or more candidate companion clusters, as the simplest measure, no companion clusters will be declared and no association is formed. In another embodiment of the method of the present invention, a plurality of time- synchronized ground RUs are deployed in a network, at least one of the RUs receives and timestamps a TCAS interrogation message (i.e., 1030 MHz Mode-S Uplink Format message), at least three RUs receive and timestamp a Mode-S reply message (i.e., 1090 MHz Mode-S Downlink Format message), the RUs transmit the received messages to a central processor, the central processor groups messages that are from the same transmission event into a cluster and associates a TCAS interrogation event cluster to its corresponding TCAS replying event cluster. The central processor then calculates TDOAs and the TLOAs for a pair of associated clusters, groups pairs of associated TCAS-interrogation-replying clusters that are addressed to the same replying-party and are within a certain time window into a super cluster set, and calculates the position of the TCAS interrogating target and the position and velocity of the TCAS replying target using the TDOAs, TLOAs, and available barometric altitude information decoded from the TCAS reply and interrogation messages.

The following section provides accuracy analyses of the system and method of the present invention for different scenarios. For these analyses, the accuracy is defined as the lower error bound of the TLOA-TDOA Maximum Likelihood position estimator, which is shown with the accuracy of traditional TDOA position estimator for comparison. For details about the calculation of the error bound and the formulation of the position estimator please refer to the Section entitled "Generalized TLOA-TDOA MLAT MLE and CRLB Formulations" at the end of this specification.

In the following analysis, the sources of measurement error are assumed as zero-mean Gaussians and are defined in the following:

1030 and 1090 message receiving timing error std = 8 ns (Range: 8ns if RefTran; 15 ns if GPS; worst 35ns); Mode-S transponder turnaround time uncertainty std = 109 ns (Range: 24 if no-bias - 109 with maximum bias perceived as additive noise);

Mode-S target Z (Mode-C altitude) measurement error std = 8.8 meters (Range: 2.2 if 25 ft step; 8.8 if 100ft step;); and

TCAS target Z (Mode-C altitude) measurement error std = 8.8 meters or 10,000 Meters (Range: 2.2 if 25 ft step; 8.8 if 100ft step; -infinite if not available).

In these analyses, the error std of TCAS target's Z measurement includes the following two assumptions: that 8.8 meters is used for the Mode-S target Z measurement error when the altitude of TCAS interrogator is obtained from Mode-C altitude; and that 10,000 meters is used for the Mode-S target Z measurement error when the altitude is not available. Normally the Mode-S address and Mode-C altitude of the TCAS target can not be obtained directly from the interrogation message but can be obtained by correlating prior 1090 MHz messages transmitted by the same TCAS target. The correlation can be done by using TDOA and position gating techniques through either corrected TDOA measurements or Mode-S target tracks. If no Mode-C altitude can be obtained for the TCAS target, an extremely high error std is assigned such that any given z value is deemphasized greatly.

On the other hand, the Z error std of the Mode-S target is assumed to be 8.8 meters because the Mode-C altitude information is available in the Mode-S reply message. Here a 100ft Mode-C quantization step is assumed, therefore a quantization error of 8.8 meters is expected.

Fig. 12 illustrates the theoretical positioning error of a TCAS interrogator (e.g. TCAS target) and a Mode-S replier (e.g. Mode-S target) where the Mode-S target's Mode-C altitude is available and the TCAS target's Mode-C altitude is not available. A square 4-RU constellation is used in which the RU baseline is ~10,000 ft which is the length of typical runway and the location of the RUs are plotted as dots in the upper graph. The lower-left corner RU is selected as the reference RU and as the RU providing TLOA measurement. The upper graph depicts the trajectory (on x-y plane) of the TCAS target and the Mode-S target. The error is plotted along the time axis corresponding to a point in the trajectories. The lower graphs depict the expected accuracy or position error in meters over time (horizontal axis) where the dotted curves represent the accuracy of conventional TDOA MLAT and the solid lines represent the accuracy of the TLOA-TDOA MLAT. For the TCAS target, the TLOA measurement significantly reduces the position error spikes, such as the approximately 1000 meter error spike around time 160, as shown in the middle graph. For the Mode-S target, the TLOA measurement significantly reduces the position error over a majority of the time period, as shown in the lower graph.

Fig. 13 illustrates the theoretical positioning error of a TCAS target and a Mode-S target where the MODE-S target's Mode-C altitude available and the TCAS target's Mode-C altitude are available. In this case great improvements are shown in the Mode-S target position accuracy utilizing TLOA measurement, as shown in the lower graph. The TCAS target's position accuracy is relatively unaffected by the TLOA measurement as shown in the middle graph. Improvements in TCAS target's position accuracy can also be observed mostly for regions that suffer from bad traditional TDOA geometries (e.g., bad GDOP) where targets and RUs tend to line up.

As shown in Figs. 12 and 13, the TLOA-TDOA (TCAS-aided) MLAT system and method of the present invention provides a significantly improved accuracy over conventional TDOA only MLAT for the TCAS target and the Mode-S target.

In another embodiment, the TLOA-TDOA (TCAS-aided) MLAT system and method of the present invention is utilized to improve the position accuracy of a conventional TDOA only MLAT system for ground operations. Figs. 14 and 15 illustrate the impact of the present invention on surface operations. There is no significant difference for the position of the TCAS target and the Mode-S target in areas having good RU geometry (i.e., good GDOP region which is the region enclosed by the RUs in Fig. 14 and Fig. 15). However, results demonstrate a significant improvement in target position error when a target moves outside of regions having good RU geometry (i.e., bad GDOP region which is the region outside the RU constellation enclosure as shown between time 100 to time 300 in Fig. 15) while not degrading the good GDOP region performance using the TLOA measurement of the present invention for ground operations. Note that a transponder turnaround time of 109ns is assumed (maximum uncertain bias in the form of noise). In a real world situation on the surface this bias should not be treated as noise, which will result in bias solutions with lower standard deviations. Even though observations on the turnaround bias conclude that for most of the transponders the bias is small and can be tolerated, estimating the bias as a bounded parameter is retained to guarantee unbiased results. In summary, the performance of TLOA- TDOA or TCAS-aided MLAT of the present invention is significantly better than the conventional TDOA MLAT.

In another embodiment of the present invention, the TCAS target of opportunity is ADS-B equipped such that its positions can be derived from ADS-B position tracks and need not to be solved from the TLOA-TDOA equations.

Yet another embodiment of the present invention incorporates TLOA measurements with TDOA measurements, AOA measurements, linear target motion modeling, time diversity, and optionally the energy and frequency domain measurements to aid with determining target position, if available.

This embodiment of the present invention assumes the altitudes of the TCAS interrogator and the replying target are available and solves the horizontal positions and velocities of the TCAS target and the Mode-S target such that a total of 8 parameters ([X₁, yi, Vχi, V_yi, X₂, y₂, v_x2, Vy₂]) are estimated, as shown in Fig. 16. The position and velocity are solved by forming sufficient measurement equations across a short period of time within which the velocities are approximately constant. Since each successful TCAS interrogation of opportunity provides three measurement equations (one TLOA and two AOA equations), a collection of at least three such interrogations of opportunity provides sufficient data to solve the problem. Note that if the altitude of the interrogator is not known such that the vertical location and velocity need to be estimated, at least four such interrogations of opportunity are required to solve the problem.

Optionally, the energy domain measurement (received signal strength) is used for providing second-level measurements to aid with the position and velocity estimations. The signal strength measurements indicate the coarse range such that can be incorporated into the measurement equations. In another option, the frequency domain measurement (Doppler shift) is used for providing second-level measurements to aid with the velocity estimations. The frequency shift measurements indicate the coarse range rate such that can be incorporated into the measurement equations.

In another embodiment of the present invention, TLOA-aided MLAT is used to provide more accurate positions for ATCRBS equipped targets. The construction of a TLOA measurement relies on the correct association of the interrogation messages to the corresponding reply message. However, the association of interrogation and reply messages for ATCRBS is more difficult because ATCRBS interrogations are not addressed. Therefore, additional techniques need to be developed to accomplish the TLOA measurements for ATCRBS targets.

Since TCAS equipped targets are typically equipped with a Mode-S transponder, the present invention tracks the interrogating targets to identify the source of an ATCRBS TCAS Whisper-Shout interrogation. Based on the receiving power of the ATCRBS Mode-C interrogation and suppression pulses and the position and heading of the interrogator under track, its Whisper-Shout interrogation power and interrogation quadrant can be estimated such that a reactive volume can be identified in which potential ATCRBS targets may reply to the interrogation. A coarse check based on the coarse 2D position solution of the ATCRBS TCAS Mode-C reply is implemented to gauge the likelihood of the correlation between the reply and the interrogation. Such likelihood can be constructed based on the coarse position of the ATCRBS target with respect to the reactive volume and on the time of reply with respect to the time of interrogation. To further reduce false association due to FRUIT (False Reply Unsynchronized in Time), observation over a longer period establishes a correlation of the replying target with the interrogator using the semi-random pattern of interrogations. Only replies that conform to the interrogation pattern of an TCAS interrogator are considered for association to reduce the false association rate. Though better association performance is achieved for associating the TLOA measurements for ATCRBS targets, greater latency is also experienced in this embodiment of the system and method of the present invention.

In another related embodiment of the present invention, a 1030 MHz sounder is used to transmitl030 MHz interrogations at pre-negotiated times, which are known to the RUs. The 1030 MHz sounder is a transmit only device that mimics the role of a Secondary

Surveillance Radar or a TCAS interrogator and transmits at a fixed known location and at known transmission times enabling the formation of a TLOA equation between the sounder unit, a interrogated target and an RU receiving the target replies to be accomplished without requiring RUs to receive the interrogation signal from the sounder unit and without requiring the sounder unit to receive target replies. A periodical pseudo-random ATCRBS whisper shout & Mode-S all-call interrogation sequence can be factory set and triggered at runtime based on common time source, such as GPS. The location of the sounder unit is also made known to the RUs. Since the transmitting time and location are exactly known to the RUs, there is no need for the sounder unit to receive target replies such that the communication bandwidth between a sounder unit and a RU can be minimized or even eliminated if desired. Benefits of the 1030 MHz sounder embodiment include:

1. The sounder is positioned detached from the RU, such that security of military operations is guaranteed by de-correlating the operation units from transmission units. The sounder units can be simple and compact, so as to be easily mounted on vehicles (including UAV), buildings, or set up in remote locations. Note that interrogations sent from detached and far-located sounder units may be considered ambient such that the receiving events can be considered passive.

2. No or extremely low communication bandwidth between a sounder unit and an RU.

3. The sounders can work with traditional 1090 MHz receivers (no interferometry) to provide target surveillance if 2 or more units are interrogating the same target. Note that a low-bandwidth communication link between a RU and a sounder unit is required if Mode-S all call interrogations are not allowed such that roll-call interrogations need to be scheduled and the schedules need to be delivered to the sounder unit. If the sounder unit is mobile, it's positions also need to be transmitted to the RUs or the central processor periodically.

In another embodiment of the present invention, the position of a TCAS target at the time of interrogation is derived from its position track data instead of being solved from the TLOA-TDOA MLAT position estimation. In this embodiment, the steps of the algorithm are as follows: 1. The system determines the address of at least one Mode-S TCAS equipped targets by decoding the received messages and estimating their position fixes using one of the following methods: a. TDOA MLAT (using 1030 MHz or 1090 MHz measurements), b. Range-aid TDOA MLAT, or c. ADS-B report.

2. The system forms target position tracks from the target position fixes obtained in step 1.

3. The system receives, decodes, and timestamps UF-O or UF- 16 TCAS interrogation messages from interrogating targets (say, target Tl, T2, etc...) at one or more RUs.

4. The system estimates the positions of the targets Tl, T2, etc... using the timestamp information base on the MLAT technique of step Ia.

5. The system decodes the address of the TCAS target from the UF message when ever available. If the TCAS target's address is not provided in the UF message, the system determines the TCAS target's addresses by correlating the target position metrics, which include the MLAT positions, Mode-C altitude information, TDOA information, and timestamp information.

6. The system propagates the position of TCAS target's position at time of interrogation based on its address, message arrival time, and position track. 7. The system receives, decodes, and timestamps a DF-O or DF- 16 TCAS reply from a replying target (say, target Rl) at one or more RUs. 8. The system determines which known TCAS target is the interrogator of the TCAS reply of target Rl of step 7 based on Rx-Tx time logic and the AP field of the UF&DF-0/16 messages.

9. If an TCAS target, target Ti, is found, the system determines the TLOA based on the time of receiving the UFO or UF 16 interrogating message, the time of receiving the DFO or DF 16 message, and the positions of receiving RUs.

10. The system calculates the position of target Rl by solving MLAT equations formed by: a. TDOA measurements derived from the timestamps of step 7, and b. the TLOA measurements of step 9, and c. Mode-C altitude of step 5.

GENERALIZED TLOA-TDOA MLAT MLE AND CRLB FORMULATIONS

Problem Layout

The generalized Time Lag of Arrival (TLOA) aided Time Difference of Arrival (TDOA) Multilateration (MLAT) formulation is provided. Derivations include the layout of the Maximum-likelihood estimator (MLE) and the calculation of Cramer-Rao Lower Bound (CRLB). The following calculations make reference to the situation shown in Fig. 17.

For N ground receiving remote unit (RUi, ..., RU_N), At most N-I TDOA equations can be formed upon receiving the interrogation from u :

(t_xx -I_2x)C = ^(X_x -Uf ₊ (Y_x -v)² ₊ (Z_x - w)² -^X₂ -u)² + (Y₂ -v)² + (Z₂ - wγ

(*_π -t_m)C = 4(X_x -Uf ₊ (Y_x -Vf ₊ (Z_x - w)² - 4(X_N -U)² + (Y_N -vγ ₊ (Z_N - wγ

At most N-I TDOA equations can be formed upon receiving the reply from x :

(t_X2 -I₂₂)C = ^(X_x -x)² + (Y_x -y)² + (Z_x -z)² -4(X₂ -X)² + (Y₂ -y)² + (Z₂ -zf

One TLOA equation can be formed upon receiving interrogation and corresponding reply messages:

(t_n - t_n - t_d )C = 4(X_t - x)² + (Y₁ - y)² + (Z₁ - zf + 4(x - u)² + (y - v)² + (z - w)²

- 4(X₁ - U)² + (Y₁ - V)² + (Z_t - w)² i e {l, 2, ..., N}

where C is the speed of light in standard atmosphere. Note that the reference RUj of the TLOA equation can be any of the receiving RUs and for convenience i = 1 is to be selected for the formulation later on. Also notice the dependency between two TLOA equations. For this example, since

(/•a ~~

- t_u - t_d)C - (t ₂₂ - t_2X -t_d)C TLOA of RU₂ can be derived from the TLOA of RUi and the TDOAs of RUi and RU₂ of interrogation and reply messages. Likewise a TLOA of both RUl and RU2 can be derived from the sum of the TLOA of RUl and a DF/UF TDOA of RUl and RU2. These variations of TLOA formulation are mathematically equivalent or interchangeable because of the mathematical dependency among them. The problem of solving the unknown position of [u, v, w] [x, y, z] is the problem of solving the above maximum 2N- 1 TDOA and TLOA equations. To solve the above problem, MLE is to be used by assuming measurement error terms as the difference between the measurement value (left-hand side of the above equations) and the functional value at a solution (right-hand side of the above equations). Weighted least-squares approximation of the MLE is further used by assuming the error terms are zero-mean Gaussians. Next the formulation of the error and its covariance are determined.

Error Covariance

Assume measurement errors are resulted from the following sources:

1030 MHz TCAS interrogation receiving timing error at RU_J: nu 1090 MHz Mode-S reply receiving timing error at RU;: n_\2

Mode-S Transponder Turnaround Time (Delay) uncertainty: ri_d Mode-S target Mode-C vertical position error: n_z TCAS target Mode-C vertical position error: n_w Further assume the error sources are independently Gaussian distributed with zero mean and standard deviations with value range indicated in the next paragraph. Denote the Gaussian error as: n,, ~ N(0,σ^)

n_d ~ N(0,σ_d ²) n_z ~ N(0,σ_z ²)

and the independency implies:

E{n_n,n_β) = 0; E(n_n,n_j2) = 0;

£(«π>%) = °;

E(n_n,n_d) = 0; E{n_i2,n_d) = 0; E(n_n,n_z) = 0; E{n_n,n₂) = 0; E(n_n,n_w) = 0; E(n_i2,nJ = 0; E(n_d,n_z) = 0; E(n_d,n_w) = 0; E(n_w,n_z) = 0;

The nominal values of the timing error standard range are from 8 ns to 35 ns depending on the synchronization technique used and the actual SNR of the message. Nominal values of Mode-S transponder delay uncertainty standard ranges from 24 ns to 109 ns depending on the severity of the bias uncertainty. Nominal values of the vertical position error standard of Mode-S replying target is either 2.2 meters or 8.8 meters depending on whether the altitude is encoded with a 25ft step size of a 100ft step size. Nominal values of the vertical position error standard of TCAS interrogating target is either 2.2 meters, 8.8 meters, or a very large value (such as 10,000 meters) depending on whether the altitude is encoded with a 25ft step size of a 100ft step size when it is available, or when the altitude information can not be obtained.

Based on above error source assumptions, a measurement error vector, e , which is jointly Gaussian, can be defined as

where z is the measurement of z and w is the measurement of w.

The covariance of measurement error, R = E(e,e ) , can be derived as sub matrices as

where R_uu is the covariance between interrogation TDOA terms and a N-I by N-I matrix with elements:

R_ux is the covariance between interrogation and reply TDOA terms and a N-I by N-I matrix with elements :

R_ux(n,m) = 0

R_xx is the covariance between reply TDOA terms and a N-I by N-I matrix with elements:

R_xx(n,m) = -J ^σi²2 + ^σ«+l,2 n = m

' 12 n ≠ m

R ^VL_rL_r is the variance of the TLOA and R_LL = <J_d ² + er 'f1,,1 + ^τ σ^<J,l²,2 R_uL is the covariance between interrogation TDOA terms and the TLOA and a N-I by 1 matrix with elements:

RΛn,l) = -σ_n ²

R_xL is the covariance between reply TDOA terms and the TLOA and a N-I by 1 vector with elements:

RAn,l) = σ_n ²

R_zz is the variance of the z error and R_zz = σ₂ ²

R_uz and R_xz are covariance between TDOA terms and z and are N-I by 1 zero vectors.

R_Lz is the covariance between TLOA and z and is zero.

R_mv is the variance of the w error and R_mv = σ² _v

R_uw and R_x^, are covariance between TDOA terms and z and are N-I by 1 zero vectors.

R_Lw and R^ are the covariance between w and TLOA and z respectively and are zeros.

If the timing error are identified such that n_n = n_jΛ = n_j2 = n_l2 = n_t , the covariance matrix can be simplified as

2σ; <— σ, - σ, O O t I σ, → 2σ - σ, O O

2σ; <- σt O O

R = f

→ 2σ,² σ O O

O O O • •• O O

O O O ^{• • ■} O O O σ Cost Function

The Weighted Least-squares cost function, F, to be minimized with respect to the solution is defined as:

F = e R^~ e = e W_e in which the process of minimizing F is equivalent to the process of maximizing the likelihood function

of the MLE.

Utilizing Newton's method to minimize F, a new solution can be found based on any current solution. Let η = [u, v, w, x, y, z]^τ denote the solution vector and Newton's method gives a new solution by

- =H^~ι —G where G is the Gradient vector of F and H is the Hessian matrix of F.

Fisher Information matrix and CRLB The Fisher Information Matrix (FIM) is derived because it is necessary for calculating the Hessian matrix and also necessary for deriving theoretical lower bound of the error covariance of the solution vector. The FIM, / , is defined as

J = (Ve^iT¹ (Ve) and the Cramer-Rao Lower Bound (CRLB) of the solution is the inverse of FIM as

B= t

Root-Mean-Square Error

The root-mean-square (RMS) position error can be derived from CRLB since the diagonals of CRLB indicates the lowest-possible error variances of the position solution parameters.

If V_ is denoted as the diagonals of the CRLB matrix the 2DRMSE of interrogator (u ) = ^V₁ + V₂ ; the 3DRMSE of interrogator (u ) = ^F₁ + V₂ + V₃ the 2DRMSE of replier (x ) = ^F₄ + F₅ ; and the 3DRMSE of replier (x)

Initial Estimate of the Solution Vector Newton's method requires an initial solution as a starting point for iterating on the new solutions. It is desirable for the initial solution to be as close to the final solution as possible to guarantee a correct convergence. In order to provide the initial solution, target positions are solved first by the closed-form solution approach based on interrogation and reply TDOA measurements, respectively. It will be understood that various modifications and changes may be made in the present invention by those of ordinary skill in the art who have the benefit of this disclosure. All such changes and modifications fall within the spirit of this invention, the scope of which is measured by the following appended claims.

Claims

What is claimed:

1. A method of multilaterating a transmitter position, comprising the steps of: receiving a first message transmitted by a first transmitter in a first frequency range at each of at least three time synchronized remote receiving units (RUs); time stamping a time of arrival (TOA) of the first message at each of the RUs; transmitting the received first message and the TOA data from each of the at least three RUs to a central processor, wherein the central processor uses the TOA data of the received first message to determine time difference of arrival (TDOA) measurements; receiving a second message transmitted by a second transmitter in a second frequency range at each of the RUs; time stamping a TOA of the second message at each of the RUs; transmitting the received second message and the TOA data from each of the RUs to a central processor, wherein the central processor uses the TOA data of the received second message to determine time difference of arrival (TDOA) measurements; associating the first message with the second message; determining the difference between the time of receipt of the first message at the second transmitter and the time of transmission of the second message that is associated with the first message by the second transmitter; creating a Time Lag of Arrival (TLOA) measurement using the TOA of the first message, the TOA of the second message that is associated with the first message, and the difference between the time of receipt of the first message at the second transmitter and the time of transmission of the second message that is associated with the first message by the second transmitter; and determining a position of the first transmitter and the second transmitter using at least the TLOA measurement and TDOA measurements.

2. The method of claim 1, wherein associating the first message with the second message is performed within a predetermined time period by determining that the first message is an interrogation message and the second message is a reply message in response to the interrogation message.

3. The method of claim 1 , wherein the TLOA measurement is determined by the following equation:

TLOA₁ = t₂ - ti - t_d where: t₂ is the time of arrival of the second message transmitted by the second transmitter at an RU, tj is the time of arrival of the first message transmitted by the first transmitter, and td is the difference between the time of receipt of the first message at the second transmitter and the time of transmission of the second message that is associated with the first message by the second transmitter.

4. The method of claim 1, wherein the second frequency range is different from the first frequency range.

5. The method of claim 1 , wherein the second frequency range is identical to the first frequency range.

6. The method of claim 1 , wherein the difference between the time of receipt of the first message transmitted by the first transmitter at the second transmitter and the time of transmission of the second message by the second transmitter is transmitted in a third message received by one or more of the RUs.

7. The method of claim 1 , wherein the difference between the time of receipt of the first message at the second transmitter and the time of transmission of the second message by the second transmitter is included in the second message transmitted by the second transmitter.

8. The method of claim 1, wherein difference between the time of receipt of the first message at the second transmitter and the time of transmission of the second message by the- second transmitter is a fixed value.

9. The method of claim 1, wherein the step of determining the position of the first transmitter and the second transmitter further comprises using vertical position information of at least one of the first transmitter and the second transmitter.

10. The method of claim 1, wherein the step of determining the position of the first transmitter and the second transmitter further comprises using Angle of Arrival (AOA) information of at least one of the first transmitter and the second transmitter.

11. The method of claim 1 , wherein the step of determining the position of the first transmitter and the second transmitter further comprises using position track information of at least one of the first transmitter and the second transmitter.

12. The method of claim 1, wherein the step of determining the position of the first transmitter and the second transmitter further comprises using range information of at least one of the first transmitter and the second transmitter.

13. A method of enhancing multilateration of aircraft position using three or more remote receiving units, comprising the steps of: receiving a first message transmitted by a first aircraft in a first frequency range at each of at least three time synchronized remote receiving units (RUs) in a geographic region; time stamping a time of arrival (TOA) of the received first message at each of the RUs; transmitting the received first message and the TOA data from each of the RUs to a central processor, wherein the central processor uses the TOA data of the received first message to determine a time difference of arrival (TDOA) measurement; receiving a second message transmitted by a second aircraft in a second frequency range at each of the RUs; time stamping a TOA of the second message at each of the RUs; transmitting the received second message and the TOA data from each of the RUs to a central processor, wherein the central processor uses the TOA data of the received second message to determine a time difference of arrival (TDOA) measurement; associating the first message with the second message; determining the difference between the time of receipt of the first message at the second aircraft and the time of transmission of the second message that is associated with the first message by the second aircraft; creating a Time Lag of Arrival (TLOA) measurement using the TOA of the first message, the TOA of the second message that is associated with the first message, and the difference between the time of receipt of the first message at the second transmitter and the time of transmission of the second message that is associated with the first message by the second aircraft; and determining a position of the first aircraft and the second aircraft using at least the TLOA measurement and TDOA measurements.

14. The method of claim 13, further comprising the step of decoding aircraft altitude data from at least one of the first message and the second message.

15. The method of claim 13, wherein the first frequency range includes 1030 MHz.

16. The method of claim 15, wherein the first message is a TCAS interrogation message.

17. The method of claim 13, wherein the second frequency range includes 1090 MHz.

18. The method of claim 17, wherein the second message is a TCAS reply message.

19. The method of claim 13, wherein the difference between the time of receipt of the first message at the second aircraft and the time of transmission of the second message that is associated with the first message by the second aircraft is a fixed value.

20. The method of claim 13, wherein associating the first message with the second message is performed within a predetermined time period by determining that the first message is an interrogation message and the second message is a reply message in response to the interrogation message.

21. The method of claim 20, wherein determining that the first message is an interrogation message and the second message is a reply message in response to the interrogation message further comprises using a UF message type and a MODE-S address of the interrogated aircraft decoded from the first message and a DF message type and MODE-S address of the interrogated aircraft decoded from the second message.

22. The method of claim 13, wherein the TLOA measurement is determined by the following equation: TLOAi = t₂ - ti - td where: t₂ is the time of arrival of the second message transmitted by the second aircraft at an RU, ti is the time of arrival of the second message transmitted by the first aircraft at an RU, and t_d is a known aircraft transponder's reply delay time.

23. The method of claim 13, wherein the step of determining the position of the first aircraft and the second aircraft further comprises using vertical position information derived from the MODE C altitude information of at least one of the first aircraft and the second aircraft.

24. The method of claim 13, wherein the step of determining the position of the first aircraft and the second aircraft further comprises using Angle of Arrival (AOA) information of at least one of the first aircraft and the second aircraft.

25. The method of claim 13 , wherein the step of determining the position of the first transmitter and the second transmitter further comprises using position track information of at least one of the first aircraft and the second aircraft.

26. . The method of claim 13 , wherein the step of determining the position of the first aircraft and the second aircraft further comprises using range information of at least one of the first aircraft and the second aircraft.

27. A method of TCAS-aided multilateration of aircraft position using three or more remote receiving units, comprising the steps of: receiving 1030 MHz transmitted interrogation messages at each of at least three time synchronized remote receiving units (RUs) from a first aircraft that is TCAS-equipped of a plurality of aircraft in a geographic region; time stamping a time of arrival (TOA) of the 1030 MHz transmitted interrogation messages from the first aircraft at each of the RUs; receiving and time stamping a time of arrival (TOA) of a 1090 MHz transmitted reply messages from a second aircraft of the plurality of aircraft at each of the RUs; decoding aircraft altitude data from at least one of the 1030 MHz transmitted interrogation messages and the 1090 MHz transmitted reply messages at at least one of the RUs; transmitting the received 1030 MHz transmitted interrogation messages, the 1090 MHz transmitted reply message, TOA data and decoded aircraft altitude data from each of the RUs to the central processor, wherein the central processor determines TDOA measurements using TOA data and associates the received 1030 MHz transmitted TCAS interrogation messages transmitted by the first aircraft and the 1090 MHz transmitted reply messages; creating a Time Lag of Arrival (TLOA) measurement using the associated 1030 MHz transmitted interrogation messages and 1090 MHz transmitted reply messages; and determining a position of the first aircraft and the second aircraft using at least the TLOA measurement, TDOA measurements and decoded aircraft altitude data.

28. The method of claim 27, wherein the TLOA measurement is determined by the following equation:

TLOAi = t₂ - ti - td where: t₂ is the time of arrival of the second message transmitted by the second aircraft at an RU, ti is the time of arrival of the second message transmitted by the first aircraft at an RU, and t_d is a known aircraft transponder reply delay time.

29. A method of TCAS-aided multilateration of aircraft position and velocity using three or more remote receiving units, comprising the steps of: receiving 1030 MHz transmitted interrogation messages at each of at least three time synchronized remote receiving um^'ts (RUs) from a first aircraft that is TCAS-equipped of a plurality of aircraft in a geographic region; time stamping time of arrival (TOA) data of the 1030 MHz transmitted interrogation messages at each of the RUs; receiving and time stamping time of arrival (TOA) data of 1090 MHz transmitted reply messages from a second aircraft of the plurality of aircraft at each of the RUs; decoding aircraft altitude data from at least one of the 1030 MHz transmitted interrogation message and the 1090 MHz transmitted reply message at one or more of the

RUs; transmitting the received 1030 MHz transmitted interrogation messages, the 1090

MHz transmitted reply messages, TOA data and decoded aircraft altitude data from each of the RUs to the central processor, wherein the central processor determines TDOA measurements using TOA data and associates the received 1030 MHz transmitted interrogation message and the 1090 MHz transmitted reply message; creating one or more Time Lag of Arrival (TLOA) measurements using the associated 1030 MHz transmitted interrogation messages and 1090 MHz reply messages; combining the TDOA measurements of 1090MHz transmitted interrogation messages by the second aircraft, the TDOA measurements of the 1030 MHz transmitted reply messages by the first aircraft and the TLOA measurements of the first aircraft and the second aircraft are within a predetermined time window into a super measurement set; and determining a position of the first aircraft and a position and a velocity of the second aircraft using at least the TLOA measurements, TDOA measurements and decoded aircraft altitude data.

30. The method of claim 29, wherein the TLOA measurement is determined by the following equation:

31. A method of deriving a position and at least one of a MODE-S address and a MODE- A ID of a TCAS transmitter comprising the steps of: estimating positions of a plurality of aircrafts in a geographic region using at least one of 1090 MHz TDOA MLAT, range-aided MLAT, and ADS-B; forming target position tracks for the plurality of aircrafts in the geographic region; receiving and time stamping TOA data of a UF- 16 TCAS interrogation message from the TCAS transmitter at at least one RU; decoding a MODE-C altitude and one of the MODE-S address and the MODE-A ID of the TCAS transmitter from the UF- 16 TCAS interrogation message; transmitting the received UF- 16 TCAS interrogation message, TOA data, MODE-C altitude, and one of the MODE-S address and MODE-A ID from the at least one RU to a central processor, wherein the central processor associates the TCAS transmitter with a formed target position track using at least one of the MODE-S address, MODE-A ID and MODE-C altitude; deriving the position of the TCAS transmitter at the time of interrogation based on the associated formed target position track and the TOA data of the UF- 16 TCAS interrogation message.

32. A method of deriving a position and at least one of a MODE-S address and a MODE- A ID of a TCAS transmitter comprising the steps of: estimating positions of a plurality of aircraft in a geographic region using at least one of 1090MHz TDOA MLAT, range-aided MLAT, and ADS-B; forming target position tracks for the plurality of aircraft in the geographic region; receiving and time stamping TOA data of a 1030MHz transmitted TCAS interrogation message from the TCAS transmitter at at least three(3) RU; transmitting the received TCAS interrogation message and TOA data from each of the RUs to a central processor, the central processor determining TDOA measurements, determining the position of the TCAS transmitter using the TDOA measurements and associating the TCAS transmitter with a formed target position track using the determined position of the TCAS transmitter and the formed position tracks; determining at least one of the MODE-S address and the MODE-A ID of the TCAS transmitter from the MODE-S address and MODE-A ID of the associated formed target position track; and deriving the position of the TCAS transmitter at time of interrogation based on the associated formed target position track, the determined position of the TCAS transmitter using 1030MHz TDOA measurements and the TOA data of the TCAS interrogation message.

33. A method of deriving a Time Lag of Arrival (TLOA) measurement comprising the steps of: receiving a first message transmitted by a first transmitter at a first receiver; time stamping a Time of Arrival (TOA) of the first message at the first receiver; receiving at a second receiver a second message transmitted by a second transmitter that receives the first message prior to the transmission of the second message from the second transmitter; time stamping a TOA of the second message at the second receiver; determining the difference between the time of transmitting the second message by the second transmitter and the time of receiving the first message at the second receiver; and determining the TLOA measurement using the TOA of the first message at the first receiver, the TOA of the second message at the second receiver, and the difference between the time of transmitting the second message by the second transmitter and the time of receiving the first message at the second receiver.

34. The method of claim 33, wherein the TLOA measurement is determined by the following equation:

TLOAi = X₂ - ti - t_d where: t₂ is the time of arrival of the second message transmitted by the second transmitter at a receiver, ti is the time of arrival of the first message transmitted by the first transmitter at a receiver, and t_d is the difference between the time of receipt of the first message transmitted by the first transmitter at the second transmitter and the time of transmission of the second message by the second transmitter.

35. The method of claim 33, wherein the positions of the first receiver and the second receiver are different.

36. The method of claim 33, wherein the positions of the first receiver and the second receiver are the same.

37. The method of claim 33, wherein the first receiver is the second receiver.