CN113589346B - GDOP minimum value calculation method for system layer and user layer under constraint condition - Google Patents

GDOP minimum value calculation method for system layer and user layer under constraint condition Download PDF

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CN113589346B
CN113589346B CN202110892840.3A CN202110892840A CN113589346B CN 113589346 B CN113589346 B CN 113589346B CN 202110892840 A CN202110892840 A CN 202110892840A CN 113589346 B CN113589346 B CN 113589346B
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minimum value
matrix
geometric
user layer
constraint condition
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CN113589346A (en
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滕云龙
汪忠来
刘影
孙鼎
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University of Electronic Science and Technology of China
Yangtze River Delta Research Institute of UESTC Huzhou
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Yangtze River Delta Research Institute of UESTC Huzhou
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/35—Constructional details or hardware or software details of the signal processing chain
    • G01S19/37—Hardware or software details of the signal processing chain
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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  • Radar, Positioning & Navigation (AREA)
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Abstract

The invention discloses a method for calculating a GDOP minimum value of a system layer and a user layer under constraint conditions, which is applied to the technical field of navigation and aims at the problem that the traditional method suitable for calculating the GDOP theoretical minimum value (or mathematical minimum value) of a multimode receiver is not suitable for calculating the GDOP minimum value under the constraint conditions.

Description

Method for calculating GDOP minimum value of system layer and user layer under constraint condition
Technical Field
The invention belongs to the technical field of navigation, and particularly relates to a technology for calculating a minimum value of a geometric precision factor (GDOP).
Background
With the continuous improvement and development of satellite navigation systems (such as BD, GPS, GLONASS, etc.), the number of available satellites has increased significantly. For the multimode receiver, as the satellite signals from a plurality of different systems can be received simultaneously, the indexes such as the positioning accuracy, the integrity and the like of the multimode receiver are effectively improved, and the navigation positioning performance is further improved.
In the positioning and resolving process of the multimode receiver, a Geometric Dilution of Precision (GDOP) has important significance for aspects such as satellite selection, positioning Precision evaluation, system morbidity diagnosis and the like. In general, the smaller the GDOP value, the higher the positioning accuracy. Therefore, in the multi-mode receiver positioning calculation process, the calculation of the GDOP minimum value has very important significance.
In the positioning calculation process of the multimode receiver, the time deviation between subsystems can be processed from the two angles of a system layer and a user layer respectively. In the two processing modes, the geometric observation matrixes are also obviously different, so that the GDOP minimum value calculation method is also obviously different. Furthermore, in practical applications (especially for ground users), the constraint condition that the altitude angle of the visible satellite is greater than zero degree should be satisfied; therefore, the conventional method for calculating the theoretical minimum (or mathematical minimum) of the GDOP of the multimode receiver is not suitable for calculating the minimum of the GDOP under the constraint condition.
Disclosure of Invention
In order to solve the technical problem, the invention provides a method for calculating the minimum value of the geometric precision factor of the multimode receiver system and the user under the constraint condition, the constraint condition of the satellite altitude angle is introduced into the calculation process of the minimum value of the GDOP, and the minimum value of the GDOP of the multimode receiver under the constraint condition can be effectively solved.
One of the technical schemes adopted by the invention is as follows: a method for calculating the minimum value of geometric accuracy factors of a multimode receiver system layer under a constraint condition takes a satellite altitude angle as the constraint condition, and specifically comprises the following steps:
a1, constructing a system layer geometric observation matrix H under constraint conditions S ；
A2, calculating a matrix
Figure BDA0003196643300000011
And processing it by blocks, and using block matrix inversion method to make it
Figure BDA0003196643300000012
Performing inversion to obtain
Figure BDA0003196643300000013
Expressed as:
Figure BDA0003196643300000014
a3, constructing a system layer geometric precision factor calculation model expressed as:
Figure BDA0003196643300000021
wherein tr (·) represents the representation matrix tracing, (·) T Representing a matrix transposition;
a4, respectively calculating
Figure BDA0003196643300000022
And
Figure BDA0003196643300000023
minimum value of (d);
a5 according to step A4
Figure BDA0003196643300000024
And
Figure BDA0003196643300000025
and a system layer geometric accuracy factor calculation model in the step A3 to obtain a system layer geometric accuracy factor minimum calculation model, which is expressed as:
Figure BDA0003196643300000026
wherein u, v denote satellite altitude.
System layer geometric observation matrix H in step A1 S The expression is as follows:
Figure BDA0003196643300000027
wherein h is i Denotes the directional cosine vector, h, between the ith satellite and the multimode receiver i ＝[h xi ,h yi ,h zi ]。
Figure BDA0003196643300000028
Wherein the content of the first and second substances,
Figure BDA0003196643300000029
Figure BDA00031966433000000210
the second technical scheme adopted by the invention is as follows: a method for calculating the minimum value of geometric accuracy factors of a user layer of a multimode receiver under a constraint condition takes a satellite altitude angle as the constraint condition, and specifically comprises the following steps:
b1, constructing a user layer geometric observation matrix H under constraint conditions U ；
B2, calculating matrix
Figure BDA0003196643300000031
And the block processing is carried out on the data, and a block matrix inversion method is adopted to carry out the block processing on the data
Figure BDA0003196643300000032
Inversion is carried out to obtain
Figure BDA0003196643300000033
Expressed as:
Figure BDA0003196643300000034
and B3, constructing a user layer geometric precision factor calculation model expressed as:
Figure BDA0003196643300000035
wherein tr (·) represents a representation matrix tracing, (·) T Representing a matrix transposition;
b4, respectively calculating
Figure BDA0003196643300000036
And
Figure BDA0003196643300000037
minimum value of (d);
b5, according to the stepB4 (all previous system layers are A4, why this is not B4)
Figure BDA0003196643300000038
And
Figure BDA0003196643300000039
and B3, obtaining a user layer geometric precision factor minimum value calculation model expressed as:
Figure BDA00031966433000000310
wherein u and v represent satellite altitude.
User layer geometric observation matrix H in step B1 U The expression is as follows:
Figure BDA00031966433000000311
wherein h is i Denotes the directional cosine vector, h, between the ith satellite and the multimode receiver i ＝[h xi ,h yi ,h zi ]。
Figure BDA00031966433000000312
Figure BDA0003196643300000041
The invention has the beneficial effects that: the method comprises the steps of respectively constructing geometric observation matrixes of a system layer and a user layer under constraint conditions, combining matrix blocking and matrix inversion after the matrix blocking to obtain the non-diagonal elements which have no influence on calculation of the GDOP minimum value, and calculating the GDOP minimum value of the system layer and the user layer under the constraint conditions through tracing of the diagonal element matrix.
Drawings
FIG. 1 is a flow chart of the GDOP minimum for the computing system layer of the present invention;
FIG. 2 is a flow chart of the present invention for calculating the GDOP minimum for the user layer.
Detailed Description
In order to facilitate the understanding of the technical contents of the present invention by those skilled in the art, the present invention will be further explained with reference to the accompanying drawings.
Taking a BD/GPS receiver as an example, in the positioning calculation process, 5 unknown parameters (including 3-dimensional position information and 2 time parameters) need to be calculated, so at least 5 satellites are required to perform positioning calculation. The invention mainly considers a GDOP minimum value calculation method under the constraint condition of 5 satellites. In the BD/GPS receiver, when 5 satellites are observed, the present invention mainly discusses the case of 3 BD (or GPS) satellites and 2 GPS (or BD) satellites.
Fig. 1 shows a method for calculating a system-level GDOP minimum under constraint conditions, which includes the following calculation processes:
without loss of generality, when 3 BD satellites and 2 GPS satellites are observed, the system layer geometric observation matrix H S The following were used:
Figure BDA0003196643300000042
wherein: h is i ＝[h xi ,h yi ,h zi ]The directional cosine vector between the ith satellite and the multimode receiver is represented and can be calculated according to the initial position of the multimode receiver and the position of the ith satellite. Order to
Figure BDA0003196643300000043
And r i ＝(x i ,y i ,z i ) Respectively represent the initial position coordinates of the multimode receiver and the position coordinates of the ith satellite, then
Figure BDA0003196643300000051
Furthermore, h i Is a unit vector, i.e. | | h i ||＝1。
In practical applications, for a multimode receiver (especially for terrestrial users), a constraint condition that the altitude of the visible satellite is greater than zero degrees should be satisfied. I.e. the directional cosine vector h between the ith satellite and the multimode reception i Third element h of zi Greater than zero.
System layer geometric dilution of precision (GDOP) in a multi-mode satellite navigation system S ) The expression of (a) is as follows:
Figure BDA0003196643300000052
wherein tr (·) represents the representation matrix tracing, (·) T Representing a matrix transposition.
In the formula (2), matrix
Figure BDA0003196643300000053
Can be expressed as
Figure BDA0003196643300000054
To pair
Figure BDA0003196643300000055
Block processing is carried out to obtain
Figure BDA0003196643300000056
Wherein A is S ∈R 2×2 、Ω S ∈R 2×3 、D S ∈R 3×3 The expression is as follows:
Figure BDA0003196643300000061
and (3) inverting the formula (4) according to a block matrix inversion formula to obtain:
Figure BDA0003196643300000062
in equation (6), the pair of off-diagonal elements calculates GDOP S The minimum value has no effect. When formula (6) is substituted into formula (2), GDOP S Can be converted into:
Figure BDA0003196643300000063
according to the formula (7): by separately calculating
Figure BDA0003196643300000064
And
Figure BDA0003196643300000065
can calculate the system layer GDOP under the constraint condition S A minimum value. Wherein, for
Figure BDA0003196643300000066
Minimum values for:
Figure BDA0003196643300000067
matrix A S And phi S Are all symmetric non-negative definite matrices, and A S ≥φ S Then, then
Figure BDA0003196643300000068
If and only if Ω S No =0 equals, i.e.
Figure BDA0003196643300000071
And calculating
Figure BDA0003196643300000072
The minimum value is similar when Ω S When the value is not less than 0, the reaction time is not less than 0,
Figure BDA0003196643300000073
can be simplified into
Figure BDA0003196643300000074
I.e. when Ω S When the value is not less than 0, the reaction time is not less than 0,
Figure BDA0003196643300000075
while taking the minimum value.
Assuming that u and ν represent the altitude angles of the 1 st and 2 nd BD satellites, respectively, and the other 2 GPS satellites, a family of general solutions of equation (10) can be constructed, namely:
Figure BDA0003196643300000076
in combination of formulas (9) and (10), the following results are obtained:
Figure BDA0003196643300000077
substituting equation (12) into equation (7), the minimum value of the geometric precision factor of the system layer under the constraint condition can be expressed as
Figure BDA0003196643300000078
If and only if Ω S No =0 equals.
Fig. 2 shows a method for calculating a user-layer GDOP minimum under a constraint condition, which includes the following calculation processes:
and system layer geometric observation matrix H S Different, constrained user layer geometric observation matrix H U Can be expressed as:
Figure BDA0003196643300000081
comparing equation (14) with equation (1), it can be seen that in the multimode satellite navigation system, the geometric observation matrix structure is significantly different between the system layer and the user layer, which is mainly due to the difference between the above two methods for processing the time information. The observation matrix structure will further influence the geometric accuracy factor minimum calculation result.
Accordingly, constrained user-layer geometric dilution of precision (GDOP) U ) The expression of (a) is as follows:
Figure BDA0003196643300000082
for is to
Figure BDA0003196643300000083
Block processing is carried out to obtain
Figure BDA0003196643300000084
Wherein the content of the first and second substances,
Figure BDA0003196643300000085
similar to the structure of equation (4), only the subscripts differ; r represents a real number; a. The U ∈R 2×2 、Ω U ∈R 2×3 、D U ∈R 3×3 ，A U 、Ω U 、D U Is a pair of
Figure BDA0003196643300000089
H U The submatrix after being partitioned is similar to the structure of formula (5), and only subscripts are different, in the invention, subscript U is used for representing User layer (User), and subscript S is used for representing System layer (System).
And (3) inverting the formula (16) according to a block matrix inversion formula to obtain:
Figure BDA0003196643300000086
similar to the minimum value calculation process of the geometric precision factor of the system layer under the constraint condition, and simultaneously combines the property of a non-negative matrix when the matrix omega is in omega U When =0, the user layer geometric precision factor minimum can be expressed as
Figure BDA0003196643300000087
When omega is higher than U When =0, namely:
Figure BDA0003196643300000088
when the formula (19) is compared with the formula (12)
Figure BDA0003196643300000091
Time, omega U =0, i.e. the user layer geometric dilution of precision takes a minimum. By substituting equation (20) for equation (14), the user layer geometric observation matrix under the constraint condition can be simplified as follows:
Figure BDA0003196643300000092
accordingly, the number of the first and second electrodes,
Figure BDA0003196643300000093
substituting equation (22) into equation (18), and further sorting, the minimum value of the user layer geometric precision factor under the constraint condition can be expressed as:
Figure BDA0003196643300000094
it will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (3)

1. A method for calculating the minimum value of geometric accuracy factors of a user layer of a multimode receiver under a constraint condition is characterized in that the satellite altitude angle is used as the constraint condition, and the method specifically comprises the following steps:
b1, constructing a user layer geometric observation matrix H under constraint conditions U ；
B2, calculating matrix
Figure FDA0004067951450000011
And the block processing is carried out on the data, and a block matrix inversion method is adopted to carry out the block processing on the data
Figure FDA0004067951450000012
Inversion is carried out to obtain
Figure FDA0004067951450000013
Expressed as:
Figure FDA0004067951450000014
and B3, constructing a user layer geometric precision factor calculation model expressed as:
Figure FDA0004067951450000015
wherein tr (·) represents the matrix tracing, (·) T Representing a matrix transpose;
b4, respectively calculating
Figure FDA0004067951450000016
And
Figure FDA0004067951450000017
minimum value of (d);
b5 according to step B4
Figure FDA0004067951450000018
And
Figure FDA0004067951450000019
and B3, obtaining a user layer geometric accuracy factor minimum value calculation model expressed as:
Figure FDA00040679514500000110
wherein u and v represent satellite altitude.
2. The method according to claim 1, wherein the user layer geometric figure of merit minimum calculation method in step B1 is a geometric user layer observation matrix H U The expression is as follows:
Figure FDA00040679514500000111
wherein h is i Denotes the directional cosine vector, h, between the ith satellite and the multimode receiver i ＝[h xi ,h yi ,h zi ]。
3. The method according to claim 2, wherein the step B2 is performed in order to calculate the minimum value of the geometric accuracy factor of the user plane of the multimode receiver under the constraint condition
Figure FDA00040679514500000112
The expression is as follows:
Figure FDA0004067951450000021
wherein the content of the first and second substances,
Figure FDA0004067951450000022
Figure FDA0004067951450000023
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