WO2008102098A1

WO2008102098A1 - Improved non-gps positioning systems

Info

Publication number: WO2008102098A1
Application number: PCT/GB2008/000331
Authority: WO
Inventors: Kin Kwong Leung; Alessandro Nicola Magnani
Original assignee: Imperial Innovations Limited
Priority date: 2007-02-23
Filing date: 2008-02-01
Publication date: 2008-08-28
Also published as: GB0703616D0

Abstract

A method for determining the relative position of each of a plurality of devices, each device having a three-dimensional local coordinate system; the method comprising the steps of: aligning one of the axes of the local coordinate system of each device with a reference direction; and determining the elevation and azimuth angles, and distance, from each device to another such device. Preferably the reference direction is collinear with the direction of gravity. Preferably the method further comprises a step of aligning the local coordinate systems of the devices, particularly preferably by propagating the local coordinate system of a first device to a second device, and so on throughout all the devices. Preferably each device also comprises a wireless sensor, and may thus collect and generate sensing data such as temperature data, pressure data, force data, stress data, strain data, humidity data, vibration data, presence data, pH data, radioactivity data, gas or liquid level data, or gas or liquid flow rate data. As a consequence of the devices' positioning capability, the method may further comprise each device transmitting location data together with the sensing data. The method may be implemented in areas where GPS positioning methods are not applicable or available, such as within underground tunnels, along pipes, inside buildings, or in war zones. Also provided is a system operable to determine the relative position of each of a plurality of devices, and a device for use in such a system.

Description

IMPROVED NON-GPS POSITIONING SYSTEMS

This invention relates to non-GPS positioning systems. It is particularly suitable, but by no means limited, for use in conjunction with wireless sensors - for example to provide both location data and sensing data from within an underground tunnel.

Background to the Invention

There is a desire to be able to determine the position of locations within a three-dimensional environment. Aboveground and in relatively open spaces,

GPS (global positioning system) devices may be used. However, due to the requirement of GPS devices to be in line-of-sight communication with satellites in order to receive positioning signals, GPS devices are not suitable for use underground, indoors, or in other locations where the devices cannot receive the signals from the satellites.

One field in which positioning is important is that of wireless sensor networks. Wireless sensor networks have been a very active area of research since the late 1990s. Despite such intensive efforts, many technical challenges remain for large-scale deployment of wireless sensors in practical environments (see e.g. references [1-3]). Nevertheless, with advances of low-cost technologies, wireless sensors are expected to be widely deployed in the near future for a large variety of applications ranging from environmental and building monitoring, healthcare, agriculture, national security, to military operations and home usage, to name a few.

In many cases, sensing data is not useful unless the location where the data is collected is also known to the end users. For this reason, localization and positioning of sensor nodes have attracted much research attention and many algorithms have been proposed in the literature (e.g. references [4-6 and 13]). Despite the previous efforts on the subject, the proposed algorithms are often not applicable in certain environments. Furthermore, there is always a need to reduce their complexity and cost and to improve the accuracy of these algorithms.

A GPS-free localization algorithm for two-dimensional service areas has been proposed by Capkun et al. [9]. However, this is only suitable for two- dimensional service areas. A direct extension of Capkun's two-dimensional method [9] into three-dimensions is not straightforward. This is because the added dimension provides too much "freedom" in fixing the coordinate systems for various nodes.

Examples of applications of underground wireless sensors include monitoring conditions in underground railway tunnels and water supply or sewerage networks. As discussed above, positioning methods based on GPS are not applicable in underground environments because they are out of reach of GPS signals. Moreover, tunnels and water pipes are not located at a constant horizontal level, so the existing algorithms proposed (e.g. by Capkun et al.) for two-dimensional deployment areas are inadequate.

There is therefore a desire for a non-GPS positioning system that may be used in a three-dimensional environment (e.g. along the inside of an underground tunnel), and which may be used in conjunction with wireless sensors in order to be able to provide location data in conjunction with sensing data. For practical purposes, it is also desired that the positioning system should be distributed, self-organised and scalable. Summary of the Invention

According to a first aspect of the present invention there is provided a method as defined in Claim 1 of the appended claims. Thus there is provided a method for determining the relative position of each of a plurality of devices, each device having a three-dimensional local coordinate system; the method comprising the steps of: aligning one of the axes of the local coordinate system of each device with a reference direction; and determining the elevation and azimuth angles, and distance, from each device to another such device. By determining the elevation and azimuth angles and distance measurements, the relative position of the devices can be determined without using GPS. By virtue of the devices having a three-dimensional local coordinate system, they may advantageously be used in underground tunnels and water pipes etc. in which the devices are not all at the same vertical position. By aligning one of the axes of the local coordinate system of each device with a reference direction, this advantageously constrains one of the degrees of freedom of each device, and thereby enables the relative positions of the devices to be determined in three dimensions.

Preferable, optional, features are defined in the dependent claims.

Thus, preferably the reference direction is collinear with the direction of gravity. This provides the advantage of being a very easy direction to determine, for example by using a plumb line, a pendulum or a spirit level vial.

Preferably the step of determining the elevation and azimuth angles, and distance, from each device to another such device is performed using a wireless transmitter and receiver present at each device. This advantageously enables the system to be readily reconfigurable and scalable. Preferably the method further comprises a step of aligning the local coordinate systems of the devices. This is particularly preferably done by propagating the local coordinate system of a first device to a second device, and so on throughout all the devices. This advantageously enables the positioning system to be distributed and self-organised. However, in an alternative embodiment that is presently less preferred, the local coordinate systems of the devices may be aligned by obtaining elevation and azimuth angle measurements from one device to another and processing the said measurements centrally (e.g. at a central computer workstation).

If it is desired to know the absolute positions of the devices, then one such device may be a reference device at a known absolute position. Preferably the reference device is located substantially centrally with respect to the other such devices, in order to minimise the compounding of measurement errors as they are propagated from device to device.

Preferably each device also comprises a wireless sensor, and may thus generate sensing data such as temperature data, pressure data, force data, stress data, strain data, humidity data, vibration data, presence data, pH data, radioactivity data, gas or liquid level data, or gas or liquid flow rate data. Other parameters that may be measured will be apparent to those skilled in the art, and the present disclosure is intended to encompass any measurable parameters. As a consequence of the devices' positioning capability, advantageously the method may further comprise each device transmitting location data together with the sensing data.

According to a second aspect of the present invention there is provided a system as defined in Claim 28 of the appended claims. According to a third aspect of the present invention there is provided a device as defined in Claim 55 of the appended claims.

With all the aspects of the invention, preferable, optional, features are defined in the dependent claims.

Brief Description of the Drawings

Embodiments of the invention will now be described, by way of example only, and with reference to the drawings in which: Figure 1 illustrates a schematic side view of a series of wireless sensors distributed in three dimensions;

Figure 2 illustrates an example of a wireless sensor structure;

Figure 3 illustrates one possible arrangement for aligning one of the axes of a sensor with the direction of gravity; Figure 4 illustrates another possible arrangement for aligning one of the axes of a sensor with the direction of gravity;

Figure 5 illustrates two wireless nodes, each having its z-axis pointing in the same direction (e.g. vertically upwards);

Figure 6 illustrates two wireless nodes having z-axes pointing in opposite directions;

Figure 7 illustrates two wireless nodes having z-axes both pointing in the same direction (e.g. vertically upwards), and the adjustment of the coordinate system of the second node to correspond with that of the first node;

Figure 8 illustrates two wireless nodes having z-axes pointing in opposite directions, and the adjustment of the coordinate system of the second node to correspond with that of the first node;

Figure 9 illustrates two wireless nodes, with the z-axis of the first node pointing vertically upwards, and the z-axis of the second node being aligned horizontally; Figure 10 illustrates the computation of positions of three nodes, the local coordinate systems of the nodes having first been adjusted to correspond with one another;

Figure 11 illustrates a simulation of the positions of wireless sensors deployed along an underground railway tunnel;

Figure 12 illustrates estimated positions of the sensors shown in Figure 11; and Figure 13 illustrates simulation results for different communication radii and different error standard deviations in the range measurements.

In the figures, like elements are indicated by like reference numerals throughout.

Detailed Description of Preferred Embodiments

The present embodiments represent the best ways known to the applicants of putting the invention into practice. However, they are not the only ways in which this can be achieved.

1. A new three-dimensional non-GPS positioning system and algorithm

The embodiments of the present invention provide a non-GPS positioning system and a positioning algorithm. The new positioning algorithm is an anchor-free scheme, and may therefore be used to determine the relative positions of constituent devices (also referred to herein as "nodes") without requiring any absolute reference positions. The algorithm has a very high degree of flexibility and scalability because no knowledge about the current network information is needed, and new nodes can be added without a need to change the algorithm for existing nodes. Localization is therefore possible in environments that are out of reach of GPS signals. The present scheme provides a distributed, self-organized, infrastructure-free positioning system and positioning algorithm that enables easy and flexible sensor deployment in underground environments, or elsewhere where GPS devices are unsuitable.

By way of an initial overview, the new positioning algorithm makes use of techniques based on the Time Difference of Arrival (TDOA) and the Angle of

Arrival (AOA) [11, 13, 15] to measure the range (distance) and angles between sensors. Each sensor uses the measurements obtained locally to build a network coordinate system. Then, by two-way communications with neighbouring nodes, each sensor can adjust its coordinates by appropriate axis rotations and shifting to finally obtain a consistent, global coordinate system.

The new algorithm may be employed in three-dimensional environments, by virtue of using the following two techniques:

• A combined TDOA and AOA technique to accurately estimate the range and angles between sensors

• The use of a specified direction (e.g. the direction of earth gravity) as one of the axes in the 3D coordinate systems.

The second bullet point, namely the use of a specified direction such as that of gravity, enables easy sensor deployment. This is because, regardless of the nature of the operating environment, installation engineers can always use simple tools (e.g. a plumb line, a pendulum or a spirit level vial) to identify the direction of earth gravity. To meet the requirements for monitoring of civil- engineering infrastructures [14], sensors are expected to be deployed manually. As long as sensors are installed with an orientation such that the gravity direction becomes one of the axes in their 3D coordinates, sensors can be placed anywhere appropriate for the applications, instead of at particular calculated locations. 2. A brief review of related work

A localization method consists of two components: distance and angle measurements, and a localization process. This section presents a brief review of related work for both components.

2.1 Range (distance) estimation

Following the U.S. FCC regulations for locating E911 callers, positioning services in mobile systems have attracted much attention recently. RF-based ranging, as exemplified by the SpotON [7] system, is based on the premise that by measuring received signal strength, a receiver can determine its distance from a transmitter. Range estimate errors of more than 10% have been reported in the literature, despite using a fairly involved calibration step that estimates the path loss parameters and adjusts for variations in transceiver characteristics. Such an accurate calibration can be carried out only with a complete knowledge of the environment, which is not available in practice. Other methods based on received signal strength, such as the RADAR [4] system, are not useful either because substantial effort is involved to calibrate and establish the centralized database of multi-path signatures.

On the other hand, infrared techniques can provide very accurate positioning. However, they cannot be applied to non-line-of-sight environments.

The Time Difference of Arrival (TDOA) method uses the hyperbolic transmitted function concept. With more than two receivers, we can compute more hyperbolic functions, which ideally intersect in one unique point. The TDOA measurement is computed as follows: the sender transmits a signal s{τ) to a receiver /, which is delayed by a time period T₁. A minimum of four receivers (in a 3D environment) is needed to locate the sender through the estimation of the time delay T₁ - T₁ corresponding to the path differences between the sender and receivers i andy.

In addition, the Angle of Arrival (AOA) technique enables us to identify the location of the radio source by use of an antenna array, as the incoming signal does not reach all the antennas at the same time. This phase shift enables us to obtain the angles of the incoming signal.

The combination of the TDOA and AOA techniques, also called TDOA/AOA Hybrid [15], requires only two connections (receivers) with a sensor node to estimate its location. The combined technique also provides far more accuracy than the individual AOA or the TDOA methods by themselves. For both advantages, we adopt this combined technique in this work.

2.2 Localization systems

Virtually all localization methods proposed in the literature make use of some anchor nodes for localization. Anchor nodes know their exact locations through separate means such as GPS [6], or by manual configuration or some other positioning mechanism. Thus, these known localization algorithms require another scheme to bootstrap the anchor node positions, and cannot be applied without the other positioning scheme. In practice, a large number of anchor nodes may be needed.

Triangulation becomes possible when a sensor is connected to three or four other sensors via wireless links in the 2D and 3D environments, respectively. Triangulation is the process of finding coordinates and distances to a point by calculating the length of a triangle formed by that point and two other points with known positions. Many algorithms have been proposed to perform the triangulation. For example, the Assumption Based Coordinates (ABC) Algorithm [5] determines the location of unknown sensors one at a time in order that they establish communication, making assumptions where necessary, and compensating for errors through corrections and redundant calculations as more information becomes available. The ABC is an incremental algorithm, which results in error propagation.

An anchor-free method by Capkun et al. [9] is a distributed, infrastructure-free positioning algorithm that does not rely on the GPS. The algorithm uses the distances between nodes to build a relative coordinate system in which the node positions are computed in two dimensions. In the second part of the algorithm, the relative coordinate systems are corrected in order to have the same directions for their axes. The method however applies only to 2D environments and it cannot be readily extended to 3D environments. Furthermore, the algorithm in [9], which does not apply the AOA technique, requires densely deployed sensors to be able to construct the relative coordinate systems accurately.

3. The new ad-hoc sensor system

Figure 1 illustrates a schematic side view of a system 10 comprising a series of wireless non-GPS positioning devices 12, 14, 16, 18, 20 distributed in an ad- hoc manner in three dimensions. As will be explained in detail below, the system 10 is operable to determine the relative positions of the devices 12, 14, 16, 18, 20. If the absolute position of any one of the devices is known, then the absolute positions of all the other devices may be readily determined using their relative positions. It will be appreciated that the absolute positions of the devices may be required in some applications, whereas in other applications their relative positions may be sufficient. By virtue of the devices 12, 14, 16, 18, 20 being non-GPS, they may be deployed in an environment in which GPS signals cannot be received or used, such as in an underground tunnel or mine, along a pipe, inside a building, or in a war zone in which GPS signals are being (or could be) jammed.

In the system 10, each device 12, 14, 16, 18, 20 preferably comprises a wireless sensor. Thus, as well as being operable to determine its position relative to the other devices, each device is also operable to measure one or more parameters in its vicinity. Examples of such parameters include temperature, pressure, force, stress, strain, humidity, vibration, presence, pH, radioactivity, gas or liquid levels, or gas or liquid flow rates. It will be appreciated that other physical parameters may be measured. By virtue of the positioning capability of each device, each device may transmit its position data together with its sensing data. The data generated by each device 12, 14, 16, 18, 20 may be transmitted wirelessly, from one device to another, and thence to a data processing or storage device 22, or onto a network.

Each device 12, 14, 16, 18, 20 has its own local (internal) coordinate system defined by x, y and z axes. As illustrated in Figure 1, there is no need for the local coordinate systems of the devices to be oriented in correspondence with one another. This is an important benefit of the present system and will be discussed in detail below.

4. The new ad-hoc sensor structure

Since the present system is anchor-free, all the devices (also referred to herein as "sensors" or "nodes") 12, 14, 16, 18, 20 can have the same features and capabilities, thus reducing the equipment cost for deployment. Figure 2 illustrates the structure of a typical sensor 30. Each sensor consists of two main components: a communication device 32 with a planar antenna array 34, and a sensing unit 36 for the intended application such as sensing temperature, water pressure, humidity, presence detection (e.g. the detection of the presence of a person), vibration, and so on. It will be appreciated that the sensor 30 will also include a processor, a memory, and a power supply (or a connection to an external power supply).

The planar antenna array 34 is used to support the AOA technique for the angle estimations, which makes it possible to extend into 3D environments Capkun's method for 2D environments. Furthermore, using the AOA technique enables our new algorithm to work properly in a more scattered and less dense network because only a single radio connection between two sensor nodes is needed to determine the angles between them. In contrast, for all existing methods, a sensor's position could not be identified without having at least three other sensors connected to it.

To meet the needs of the underground environments, expanding existing positioning techniques for 2D environments into 3D is challenging, and a tradeoff must be made between using expensive devices for ranging and angular estimations, and limiting the directional orientation of the sensors during installation. Each sensor node has its own local 3D coordinate system with x, y and z axes. Regardless of the operating environments, installation engineers can identify the direction (axis) of earth gravity by simple tools. By installing each sensor in a way that one of its axes is fully aligned with the gravity direction, extending the 2D method of Capkun et al. [9] to 3D environments becomes possible by appropriate rotations and translations of the coordinate system of each sensor in a distributed manner. The details of how rotations and translations may be carried out are presented below.

Figures 3 and 4 illustrate possible ways in which one of the axes of the local coordinate system of a device 30 may be aligned with the direction of gravity. In Figure 3, the communication device 32 incorporates a pair of orthogonally- oriented spirit level vials 38, 39, each vial 38, 39 being orthogonal to the z-axis of the device's local coordinate system. By aligning the device 32 such that the spirit bubble is in the centre of each vial 38, 39, the device's z-axis may thus be aligned with the direction of earth's gravity. As will be discussed below, it does not matter whether the z-axis of the device's local coordinate system is aligned upwards or downwards with the direction of gravity.

Figure 4 illustrates an alternative configuration whereby the communication device 32 incorporates a single circular (dome-shaped) spirit level vial 40 oriented orthogonal to the z-axis of the device's local coordinate system. By aligning the device 32 such that the spirit bubble is in the centre of the vial 40, the device's z-axis may thus be aligned with the direction of gravity.

In some circumstances it may not be feasible to orient the z-axis of the device with the direction of gravity, and in such cases it is possible to orient one of the other axes of the device's local coordinate system with the direction of gravity.

To enable this to be achieved, the device may incorporate additional spirit level vials (e.g. of the type shown in Figure 3 or Figure 4) on other external surfaces of the device, and appropriately oriented, as those skilled in the art will appreciate.

Other techniques are possible for aligning one of the axes of the local coordinate system of each device with the direction of gravity. For example, instead of each device incorporating one or more spirit level vials, an engineer may use a separate (external) spirit level to orient the device during installation. Alternatively, a plumb line or pendulum may be used, which would naturally orient itself with the direction of gravity. Reference mark(s) may be provided on the casing of the device, and the installation engineer may be required to align the casing such that the reference mark(s) is/are aligned with the plumb line or pendulum, thus ensuring that one of the axes of the device's local coordinate system is aligned with the direction of gravity.

Instead of the direction of gravity, one of the axes of the local coordinate system of each device may be aligned with some other reference direction, such as a horizontal or vertical direction external from the device. To enable this to be implemented, the device may incorporate means for aligning the device with the external direction, such as a built-in set square or other angular form. In those cases in which the installation engineers do not wish to align the devices with the direction of gravity, but instead choose for example the ground or a horizontal part of a building as their 'absolute' horizontal line, it is possible that the devices will all have their coordinate systems tilted from the true horizontal. However, given the high probability that all the devices will be tilted by the same angle, this ought not prevent the system from working perfectly well.

For simplicity, in the embodiments described below, the direction of gravity will be used as the reference direction.

5. The new localization algorithm

The localization algorithm is preferably executed on each sensor 30 in three phases:

• Define its local 3D coordinate system (with one of the axes aligned with the gravity direction) • Correct the local coordinate systems with respect to the reference coordinate system

• Define the global coordinate system for positioning. The scattered sensors use their antenna technology 34 to sense the neighbouring sensors and to construct their local coordinate systems. The localization process requires a reference. We consider that the whole localization process is done with respect to the reference coordinate system of a particular sensor, to be referred to as sensor 1 (which may be easily accessible for maintenance and/or directly connected to a gateway node to a network (e.g. the Internet)). The absolute position of sensor 1 may be known if it is desired to obtain the absolute positions of the other nodes. However, the absolute position of sensor 1 need not be known if only the relative positions of the other nodes are required.

As discussed above, sensor 1 is installed such that its z-axis is precisely aligned with the direction of earth gravity (which points downward towards the earth centre) or in the opposite direction pointing upward. Once every sensor has detected all sensors that are within its range of communication, every coordinate system may be adjusted in order to have the same directions as the reference coordinate system. The adjustment is a step-by-step process that starts from node 1. The adjustment process is done between the coordinate system on a neighbouring node and the reference coordinate system. Once the neighbour's coordinate system is calibrated with the reference coordinate system, the former can now serve as a new reference for adjustment of other nodes. The process continues until the reference system has propagated throughout the entire system and each node has adjusted its coordinates according to the reference coordinates.

On the basis that each sensor node has its z-axis aligned with the gravity direction (in either an upward or downward sense), the plane defined by its x-y axis is parallel to the x-y plane of the reference coordinate system. The elevation angles are defined as the elevation from the x-y plane. If we define ψ_λ as the elevation angle of sensor j in the coordinate system of sensor i, and ψ _j as the elevation angle of sensor i in the coordinate system of sensor j, we can see from Figure 5 that both elevation angles ψ_t and ψ _} have an equal absolute magnitude.

If the z-axis of both sensors i and y is pointing in the upward direction, then the elevation angles have opposite signs (i.e. one positive, the other negative), as shown in Figure 5. However, if the z-axis of one sensor points upwards, and the z-axis of the other sensor points downwards, then the elevation angles have the same sign, as shown in Figure 6. Since both elevation angles between the node pair i and j have equal absolute magnitude, our localization process for 3D environments is now reduced to that for 2D problems. Indeed, as the z-axis for the two coordinate systems are aligned in either direction, it is just a matter of rotation of the coordinate system about the z-axis using the azimuth angles. To correct the coordinate system of a second sensor node, we need to adjust its x-y plane with a rotation about the z-axis, similar to the adjustments in the 2D method by Capkun et al.

In a first situation as shown in Figure 7, in which the z-axes both point in the same direction (e.g. vertically upwards), the correction angle for node j is φ_} -φ_t +π . In a second situation as shown in Figure 8, in which the z-axes point in opposite directions, the correction angle for node j is φ_} + φ_t , and the mirroring is done with respect to the y-axis. All the rotations are in the positive direction of each device's local coordinate system.

In certain deployment environments, it may be difficult or impossible to align the z-axis of a sensor node (which may represent the direction normal to the planar antenna 34) with the earth gravity. Instead, it may be more convenient to align the x-axis, say, with the earth gravity. In such a case, in which a reference node (node ϊ) has its z-axis aligned with the earth gravity, and a second sensor node (node J) has its x-axis aligned with the earth gravity, the x- y plane of the second node (node J) is perpendicular to the x-y plane of the reference node (node i), as shown in Figure 9. This case can be easily detected because the elevation angles ψ_x and^_y have different absolute magnitudes.

Once this case is detected, a rotation of 90° of the coordinate system of node j about the y-axis is needed. The result of this rotation can give us a z-axis pointing in a downward or upward direction. In either case, the next adjustments to be taken are exactly those in the situation illustrated in Figures 7 and 8.

At the end of the correction process, all the coordinate systems at all the sensor nodes have their axes aligned and pointing in the same directions.

In practice, when comparing the measured elevation angles ψ_i and ψ_j from a pair of sensors to determine whether the elevation angles are of equal absolute magnitude (e.g. a situation as shown in Figure 5 or Figure 6), or whether the elevation angles are of unequal absolute magnitude (e.g. the situation shown in Figure 9), measurement errors should be taken into account. For example, if a first sensor detects a second sensor with an elevation angle of 52°, while the second sensor detects the first sensor with an elevation angle of 50°, we can nevertheless say that they have measured the same absolute magnitude of elevation angle, within the limits of measurement errors. The extent of the measurement errors will depend on the types of AOA antennas that are used (i.e. either more accurate and more expensive, or less expensive and less accurate). Now, consider node k which is two hops from node 1 via node j. Node j defines and adjusts its coordinate system based on the reference system of node 1. In turn, node k calibrates its coordinate system relative to that of node j. After adjustments, the coordinate systems of the nodes are identical. The position of the node k in the coordinate system of node 1 is obtained by summing two vectors, as illustrated in Figure 10. Thus, if the position of nodey in the coordinate system of node 1 is given by a vector l_y , and the position of node k in the coordinate system of node j is given by a vector j_k , then the position of node k in the coordinate system of node 1, l_k , is given by 1_; + j_k .

This procedure may be applied to adjust and obtain consistent coordinate systems for all nodes with multiple hops away from node 1, and to determine the positions of all the nodes relative to node 1.

Measurements of elevation and azimuth angles and distances between sensor nodes by use of antenna techniques have errors, and are therefore regarded as estimates. Estimation errors propagate from the nodes surrounding node 1 towards other nodes at the edge of the network. In order to reduce the propagation of estimation errors (which is a compounding effect), it is advantageous to place the reference sensor in approximately the middle of the sensor network (e.g. in the middle of the tunnel).

Propagation of estimation errors may also be reduced by using sensor nodes that are able to measure elevation and azimuth angles and distances with greater accuracy. Such devices of greater accuracy may in particular be employed in the middle of the sensor network, since the compounding effect of measurement errors is more significant there. Less accurate devices may be employed towards the edges of the network, where the compounding of errors is less significant. In the following section, we study how estimation errors can affect the effectiveness of the new localization method for sensors installed in a tunnel.

6. Performance of the new positioning algorithm We used Matlab to simulate and verify the accuracy of the proposed positioning algorithm. Our simulation model, as shown in Figure 11 , considers an underground railway tunnel 300 metres long, in which three types of sensors are deployed at the top, side-walls and the bottom of the tunnel, respectively. Pressure sensors are deployed along the top of the tunnel, temperature sensors are deployed along the side-walls, and presence sensors (to detect the presence of a train car/carriage) are deployed along the bottom.

Node 1 (the reference system) is located at the coordinates of (2,0,0) in the figure. Sensors of the same type are separated by 20 metres in a straight line along the tunnel. However, sensor communication range is assumed to be an adjustable parameter in the simulation. Specifically, we consider sensors can communicate with a neighbouring node of any type located within 20, 30 and 40 metres. That is, a node cannot reach directly to other nodes located beyond the given range parameter. The cross section of the tunnel is represented by a semi-ellipse with 8 metres width at the bottom and 6 metres from the ground to the highest point in the tunnel ceiling.

We first assume that the range estimate errors (the distance between a pair of nodes) have a Gaussian distribution with zero mean and a fixed standard deviation normalized to the actual distance between two nodes. We evaluate the proposed algorithm with the normalized standard deviation being 0.1, 1, 2.5, 5, 7.5 and 10%, and three different communication ranges, 20 m, 30 m and 40 m. Using the proposed algorithm with a 2.5% normalized standard deviation in the range estimations, the estimated positions of all the sensors in the tunnel is presented in Figure 12. Due to the range estimation errors, the estimated positions do not lie on a straight line. To quantify the quality of the proposed positioning method, we consider the relative mean estimate error ε as follows:

cr where n is the total number of sensor nodes, (x,,y,,z, ) and (x,,y,,z, ) are the exact and estimated position of node i by the proposed algorithm, and cr is the communication range.

Our results, shown in Figure 13, reveal that the longer the communication range, the lower is the relative mean error ε (i.e. the y-axis in Figure 13), because a longer range means a smaller number of hops from the reference node to the other nodes in the system, and consequently less propagation of estimation errors .

We also repeated our simulation with uniform, random estimation errors. That is, for a given relative error percentage (say X%) and a communication range of Y metres, the estimation error is uniformly distributed between -XY/100 and XY/100. Our results show that the mean estimate error for the uniform error model is similar to that for the Gaussian distributed errors with the same standard deviation.

Since it is reasonable to expect that TDOA technique can provide a range estimate of 5% error standard deviation, our results in Figure 13 suggest that the relative average position estimate error is in the range of a few percent, which is satisfactory for many applications. 7. Conclusion

This work has been motivated by the need for a new localization algorithm for applications and flexible sensor deployment in underground environments such as train tunnels and water networks. We have proposed and studied a new localization method, which makes use of the direction of earth gravity for sensor installation. It consists of: (a) using the TDOA and AOA techniques for estimating the ranges and angles between sensors; and (b) a distributed scheme to adjust the three-dimensional coordinate system for each sensor based on local measurements.

A Matlab simulation model has been constructed to validate the proposed algorithm and to assess its error performance. Our results indicate that for an example of underground tunnel, the new algorithm yields satisfactory positioning with a relative error of few percent when the standard deviation for the range estimation error is less than 5%. This accuracy would be satisfactory for many applications.

Since no central control is required for the new algorithm, it is appropriate for large-scale sensor networks. Further, new sensor nodes can be added to a network incrementally and they simply adjust their coordinate systems based on measurements exchanged with their neighbours in a distributed manner. Thus, such a distributed, self-organized three-dimensional location technique using available wireless technology is suitable for practical use in harsh environments such as underground tunnels and water networks.

8. Summary

The embodiments of the present invention provide a distributed, self-organized, scalable, infrastructure-free positioning algorithm and system that enable easy and flexible sensor deployment in harsh environments such as underground tunnels and water networks. Furthermore, our computer simulation reveals that the new scheme achieves a satisfactory, relative average position error of less than 5% when the errors for distance estimations between sensors have a standard deviation of no more than 5%.

Our localization process enables a significant reduction in both labour cost and time to install sensors and to have the sensor network ready to work. Compared with existing wireless localization processes, the new process is completely scalable as it is anchor-free and there is no need to have a minimum percentage of anchor nodes in the network for positioning purposes.

The present positioning algorithm has the following advantages:

1) Technical advantages • Scalable, as it works when new sensors are added to the network without affecting its existing operation;

• GPS-free, thus applicable to challenging environments such as underground tunnels and water networks;

• Self-organized, distributed process for localization.

2) Economic advantages

• Easy to install sensors where they are needed in harsh environments;

• Reduction of time to set up the network ready for operations;

• No need to use expensive central stations or base stations for positioning purposes.

Civil engineering, construction, and underground railway sectors are envisaged to be among the first exploiters of this new technology, as it would enable them to cut cable costs and labour costs when establishing sensor networks in tunnels. This technology is also applicable for underground pipes used to provide utilities such as water or gas, since sensors may be put along the pipes to monitor the pH, chlorine or salinity level, without requiring cables running along the pipes to collect the data from the sensors. Highly advantageously, the measurement data from each sensor may be sent from the sensor together with the location of the sensor, thus making the measurement data more meaningful and useful.

References

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Claims

1. A method for determining the relative position of each of a plurality of devices, each device having a three-dimensional local coordinate system; the method comprising the steps of: aligning one of the axes of the local coordinate system of each device with a reference direction; and determining the elevation and azimuth angles, and distance, from each device to another such device.

2. A method as claimed in Claim 1, wherein the other such device is a neighbouring device.

3. A method as claimed in Claim 1 or Claim 2, wherein the reference direction is collinear with the direction of gravity.

4. A method as claimed in Claim 3, wherein the reference direction is the direction of gravity, or in the opposite direction to the direction of gravity.

5. A method as claimed in any preceding claim, wherein the step of determining the elevation and azimuth angles, and distance, from each device to another such device is performed using a wireless transmitter and receiver present at each device.

6. A method as claimed in Claim 5, wherein the elevation and azimuth angles are determined using an angle of arrival technique.

7. A method as claimed in Claim 5 or Claim 6, wherein the distance is determined using a time difference of arrival technique.

8. A method as claimed in any of Claims 5 to 7, wherein the transmitters and receivers communicate along lines of sight.

9. A method as claimed in any of Claims 5 to 8, wherein the transmitters and receivers communicate at radio frequency.

10. A method as claimed in any preceding claim, further comprising a step of aligning the local coordinate systems of the devices.

11. A method as claimed in Claim 10, wherein the step of aligning the local coordinate systems of the devices comprises propagating the local coordinate system of a first device to a second device.

12. A method as claimed in Claim 11, wherein the step of propagating the local coordinate system of the first device to the second device comprises: measuring the elevation angle of the second device from the first device, in the local coordinate system of the first device; measuring the elevation angle of the first device from the second device, in the local coordinate system of the second device; and comparing the sign and the magnitude of the measured elevation angles.

13. A method as claimed in Claim 12 wherein, if the measured elevation angles are of equal magnitude, the method further comprises determining that the first and second devices have the same local coordinate axis oriented vertically.

14. A method as claimed in Claim 13 wherein, if the measured elevation angles are of opposite sign, the method further comprises determining that the vertically-oriented local coordinate axes of the first and second devices are both oriented in the same direction.

15. A method as claimed in Claim 13 wherein, if the measured elevation angles are of the same sign, the method further comprises determining that the vertically-oriented local coordinate axes of the first and second devices are oriented in opposite directions.

16. A method as claimed in Claim 12 wherein, if the measured elevation angles are of unequal magnitude, the method further comprises determining that the first and second devices have different local coordinate axes oriented vertically.

17. A method as claimed in Claim 15 or Claim 16, further comprising a step of reorienting the local coordinate system of the second device such that the first and second devices have the same local coordinate axis oriented vertically.

18. A method as claimed in any of Claims 12 to 17, further comprising the steps of: measuring the azimuth angle of the second device from the first device, in the local coordinate system of the first device; measuring the azimuth angle of the first device from the second device, in the local coordinate system of the second device; and reorienting the local coordinate system of the second device based on the measured azimuth angles.

19. A method as claimed in Claim 18, wherein the step of reorienting the local coordinate system of the second device comprises rotating the local coordinate system of the second device.

20. A method as claimed in Claim 18 or Claim 19, wherein the step of reorienting the local coordinate system of the second device comprises applying a mirror transformation on the local coordinate system of the second device.

21. A method as claimed in Claim 10, wherein the step of aligning the local coordinate systems of the devices comprises obtaining elevation and azimuth angle measurements from one device to another and processing the said measurements centrally.

22. A method as claimed in any preceding claim, wherein one such device is a reference device at a known absolute position.

23. A method as claimed in Claim 22, wherein the reference device is located substantially centrally with respect to the other such devices.

24. A method as claimed in any preceding claim, further comprising each device generating sensing data.

25. A method as claimed in Claim 24, wherein the sensing data is transmitted from one device to another and thence to a data processing or storage device or onto a network.

26. A method as claimed in Claim 24 or Claim 25, wherein the sensing data is transmitted together with location data.

21. A method as claimed in any preceding claim, implemented in a location selected from a group comprising: within an underground tunnel; along a pipe; inside a building; in a war zone.

28. A system comprising a plurality of devices, the system being operable to determine the relative position of each of the devices; wherein each device has a three-dimensional local coordinate system, one of the axes of the local coordinate system being aligned with a reference direction; and wherein each device comprises means for determining the elevation and azimuth angles, and distance, from the device to another such device.

29. A system as claimed in Claim 28, wherein the other such device is a neighbouring device.

30. A system as claimed in Claim 28 or Claim 29, wherein each device further comprises means for aligning one of the axes of its local coordinate system with the said reference direction.

31. A system as claimed in any of Claims 28 to 30, wherein the reference direction is collinear with the direction of gravity.

32. A system as claimed in Claim 31, wherein the reference direction is the direction of gravity, or in the opposite direction to the direction of gravity.

33. A system as claimed in any of Claims 28 to 32, wherein the means for determining the elevation and azimuth angles, and distance, comprises a wireless transmitter and receiver present at each device.

34. A system as claimed in Claim 33, wherein the elevation and azimuth angles are determined using an angle of arrival technique.

35. A system as claimed in Claim 33 or Claim 34, wherein the distance is determined using a time difference of arrival technique.

36. A system as claimed in any of Claims 33 to 35, wherein the transmitters and receivers communicate along lines of sight.

37. A system as claimed in any of Claims 33 to 36, wherein the transmitters and receivers communicate at radio frequency.

38. A system as claimed in any of Claims 28 to 37, operable to align the local coordinate systems of the devices.

39. A system as claimed in Claim 38, operable to align the local coordinate systems of the devices by propagating the local coordinate system of a first device to a second device.

40. A system as claimed in Claim 39, wherein the first and second devices are operable to: measure the elevation angle of the second device from the first device, in the local coordinate system of the first device; measure the elevation angle of the first device from the second device, in the local coordinate system of the second device; and compare the sign and the magnitude of the measured elevation angles.

41. A system as claimed in Claim 40, wherein, if the measured elevation angles are of equal magnitude, the system is configured to determine that the first and second devices have the same local coordinate axis oriented vertically.

42. A system as claimed in Claim 41 wherein, if the measured elevation angles are of opposite sign, the system is further configured to determine that the vertically-oriented local coordinate axes of the first and second devices are both oriented in the same direction.

43. A system as claimed in Claim 41 wherein, if the measured elevation angles are of the same sign, the system is further configured to determine that the vertically-oriented local coordinate axes of the first and second devices are oriented in opposite directions.

44. A system as claimed in Claim 40 wherein, if the measured elevation angles are of unequal magnitude, the system is further configured to determine that the first and second devices have different local coordinate axes oriented vertically.

45. A system as claimed in Claim 43 or Claim 44, further configured to reorient the local coordinate system of the second device such that the first and second devices have the same local coordinate axis oriented

/ vertically. /

46. A system as claimed in any of Claims 40 to 45, wherein the first and second devices are further operable to: measure the azimuth angle of the second device from the first device, in the local coordinate system of the first device; measure the azimuth angle of the first device from the second device, in the local coordinate system of the second device; and reorient the local coordinate system of the second device based on the measured azimuth angles.

47. A system as claimed in Claim 38, operable to align the local coordinate systems of the devices by obtaining elevation and azimuth angle measurements from one device to another and processing the said measurements centrally.

48. A system as claimed in any of Claims 28 to 47, wherein one such device is a reference device at a known absolute position.

49. A system as claimed in Claim 48, wherein the reference device is located substantially centrally with respect to the other such devices.

50. A system as claimed in any of Claims 28 to 49, wherein each device further comprises a sensor operable to generate sensing data.

51. A system as claimed in Claim 50, wherein the sensor of each device comprises a wireless sensor.

52. A system as claimed in Claim 50 or Claim 51, wherein each device is configured to transmit sensing data from one device to another and thence to a data processing or storage device or onto a network.

53. A system as claimed in any of Claims 50 to 52, wherein each device is configured to transmit sensing data together with location data.

54. A system as claimed in any of Claims 28 to 53, installed in a location selected from a group comprising: within an underground tunnel; along a pipe; inside a building; in a war zone.

55. A device for use in a system as claimed in any of Claims 28 to 54, said device having a three-dimensional local coordinate system, said device comprising: means for aligning one of the axes of its local coordinate system with a reference direction; and means for determining the elevation and azimuth angles, and distance, from the device to another such device.

56. A device as claimed in Claim 55, wherein the reference direction is collinear with the direction of gravity.

57. A device as claimed in Claim 56, wherein the said means for aligning comprises a plumb line, a pendulum or a spirit level vial.

58. A device as claimed in any of Claims 55 to 57, wherein the means for determining the elevation and azimuth angles, and distance, comprises a wireless transmitter and receiver.

59. A device as claimed in Claim 58, operable to determine the elevation and azimuth angles using an angle of arrival technique.

60. A device as claimed in Claim 58 or Claim 59, operable to determine the distance using a time difference of arrival technique.

61. A device as claimed in any of Claims 58 to 60, wherein the transmitter and receiver are configured to communicate along lines of sight.

62. A device as claimed in any of Claims 58 to 61, wherein the transmitter and receiver are configured to communicate at radio frequency.

63. A device as claimed in any of Claims 55 to 62, further comprising processing means configured to align the local coordinate system of the device with that of other such devices.

64. A device as claimed in any of Claims 55 to 63, further comprising a sensor operable to generate sensing data.

65. A device as claimed in Claim 64, wherein the sensor comprises a wireless sensor.

66. A device as claimed in Claim 64 or Claim 65, configured to transmit sensing data together with location data.

67. A device as claimed in any of Claims 64 to 66, wherein the sensor is arranged to measure a property selected from a group comprising: temperature; pressure; force; stress; strain; humidity; vibration; presence; pH; radioactivity; gas or liquid levels or flow rates.

68. A method substantially as herein described with reference to and as illustrated in any combination of the accompanying drawings.

69. A system substantially as herein described with reference to and as illustrated in any combination of the accompanying drawings.

70. A device substantially as herein described with reference to and as illustrated in any combination of the accompanying drawings.