GB2564146A

GB2564146A - Determining a state of a tracked object

Info

Publication number: GB2564146A
Application number: GB1710792.1A
Authority: GB
Inventors: Mauricio Munoz; Popham Thomas; Bashar Ahmad; Langdon Patrick
Original assignee: Cambridge Enterprise Ltd; Jaguar Land Rover Ltd
Current assignee: Cambridge Enterprise Ltd; Jaguar Land Rover Ltd
Priority date: 2017-07-05
Filing date: 2017-07-05
Publication date: 2019-01-09
Anticipated expiration: 2037-07-05
Also published as: GB201710792D0; GB2564146A8; GB2564146B

Abstract

A method of determining a state of a tracked object with respect to an entity, comprising determining one or more received signal characteristics at one of each of a plurality of receiver means distributed around the entity, the signal being transmitted by the tracked object. The method comprises determining a state of the tracked object in dependence on the one or more received signal characteristics at each receiver means and a partitioned region proximal the entity, the partition being according to a logarithmic and/or curvilinear partitioning scheme. Also disclosed is an analogous arrangement where the signal is received by the tracked object from plural transmitters distributed around the entity. Preferably the received signal characteristics are received signal strength. The tracked object is preferably a mobile device and the entity is preferably a vehicle.

Description

The present disclosure relates to determining a state of a tracked object and particularly, but not exclusively, to methods and apparatus for determining the state of a tracked object. Aspects of the invention relate particularly, although not exclusively, to determining a state of a tracked object with respect to a vehicle. Aspects of the invention relate to method, to a controller, to a system, to a vehicle and computer software.

BACKGROUND

It is often useful to determine a state of a tracked object. For example, one or more actions associated with an entity may be initiated dependent upon the state of the tracked object. The entity may correspond to, for example, a building or vehicle and the tracked object may correspond to an electronic device associated with a person, such as a mobile device i.e. mobile telephone, tablet etc. Dependent upon the state of the object, the one or more actions may be initiated. The one or more actions may prepare the entity for arrival of the tracked object. For example, where the entity is a vehicle, one or more systems of the vehicle may be energised, such as to heat one or more components of the vehicle.

It is an object of embodiments of the invention to at least mitigate one or more of the problems of the prior art.

SUMMARY OF THE INVENTION

Aspects and embodiments of the invention provide a method, a controller, a system, a vehicle and computer software as claimed in the appended claims.

According to an aspect of the invention, there is provided a method of determining a state of a tracked object with respect to an entity, wherein the state of the tracked object is determined in dependence on the one or more received signal characteristics at each of a plurality of receiver means or for each of a plurality of transmitter means, and one or more predetermined distributions associated with the one or more signal characteristics.

Advantageously the state of the tracked object may be remotely determined. The state of the tracked object may be a location of the tracked object.

According to another aspect of the invention, there is provided a method of determining a state of a tracked object with respect to an entity, wherein the state of the tracked object is determined in dependence on the one or more received signal characteristics at each of a plurality of receiver means or for each of a plurality of transmitter means, and one or more skewed distributions associated with the one or more signal characteristics. Advantageously the state of the tracked object may be remotely determined using the one or more skewed distributions.

The one or more skewed distributions may be asymmetric distributions. Advantageously the asymmetric nature of the distribution may allow the state of the tracked object to be more accurately determined.

According to a further aspect of the invention, there is provided a method of determining a state of a tracked object with respect to an entity, the method comprising determining one or more received signal characteristics at one of each of a plurality of receiver means distributed around the entity, wherein the signal is transmitted by the tracked object, or the tracked object for each of a plurality of signals each transmitted by a transmitter means at a respective location around the entity, wherein the method comprises determining a state of the tracked object in dependence on the one or more received signal characteristics at each receiver means or for each transmitter means, respectively, and one or more skewed distributions associated with the one or more signal characteristics. Advantageously the state of the tracked object may be remotely determined using the one or more skewed distributions. The state of the tracked object may be a location of the tracked object.

The received signal characteristics may be received signal strength, RSS. Advantageously RSS may be easily measured. The received signal characteristics may be time of flight, ToF. Advantageously ToF may provide more accurate determinate of the state of the tracked object.

In some embodiments, the plurality of receiver means or the plurality of transmitter means may be Ultra-Wide Band, UWB. Advantageously use of UWB may allow the ToF of signals to be determined.

The state of the object optionally comprises one or more spatial-temporal characteristics of the tracked object. Advantageously characteristics of the object which change over time may be determined.

The state of the tracked object may be a location of the tracked object. The one or more spatial-temporal characteristic of the tracked object comprises a location of the tracked object with respect to the entity.

Optionally the one or more spatial-temporal characteristic of the tracked object comprise one or more of a velocity, acceleration, heading angle and/or distance to the entity.

The one or more spatial-temporal characteristics of the tracked object may be determined with respect to one of a logarithmic or a curvilinear partitioning of at least a portion of a region proximal to the entity. Use of a portioned region may advantageously allow a posterior distribution to be determined conveniently. The partitioning may provide allow the state of the object to be determined deterministically. Furthermore, determining the state of the tracked object from a posterior with a deterministic grid, when the grid is adapted to partitions of interest, may be efficiently achieved. A method may include selecting a grid point or cell with a maximum weight.

The one or more spatial-temporal characteristics of the tracked object may be determined with respect to a logarithmic curvilinear partitioning, LCP, of at least a portion of a region proximal to the entity. The LCP provides partitioning to the region which allows the one or more signal characteristics to be determined with respect to the portioning.

The state of the tracked object may be determined in dependence on a stochastic model. The stochastic model may be a Hidden Markov model, HMM. Advantageously the HMM allows a continuous state space to be utilised. The state of the tracked object may be determined in dependence on a Jump Markov Model, JMM. Advantageously, the JMM allows discrete state space to be utilised.

The one or more spatial-temporal characteristics of the tracked object are optionally determined in dependence on a Jump Markov motion model indicative of a probability of transitioning between partitions of a region. Advantageously the JMM provides an indication of the probability of moving to other partitions of the region.

The location of the mobile device may be determined with respect to the LCP of the region. Advantageously the location may be determined as a respective partition of the LCP.

Optionally the location of the mobile device is determined as a probability of the mobile device being located in one or more partitions of the LCP. Advantageously the probability of the mobile device being located in the one or more partitions is determined.

The state of the tracked object may be determined in dependence upon one or more prior estimates of the state of the tracked object. Advantageously the prior estimates may allow more accurate determination of the state of the tracked object.

The one or more skewed distributions may be indicative of noise associated with the one or more signal characteristics. Advantageously the skewed distributions may more accurately model the noise associated with the signal.

The state of the tracked object is optionally determined by Bayesian inference method. Advantageously the Bayesian inference method utilises available evidence to determine the state of the tracked object.

The Bayesian inference method comprises determining a posterior probability associated with each partition of the LCP. Advantageously the posterior probability is determined based on the one or more signal characteristics.

The tracked object may be a mobile device. Advantageously a user of the vehicle may carry a mobile device. Optionally the mobile device comprises a display means. The display means may advantageously provide feedback to the user. Optionally the entity is a vehicle. It may be desired for the vehicle to determine the state of the tracked object. Optionally the mobile device comprises, or consists of, an electronic key for the vehicle. Advantageously a user returning to the vehicle may be carrying the electronic device I key.

According to yet another aspect of the invention, there is provided a controller for determining a state of a tracked object with respect to an entity, the controller comprising input means for receiving data indicative of one or more received signal characteristics at each of a plurality of receiver means distributed around the vehicle, wherein the signal is transmitted by the tracked object, or one or more received signal characteristics at the tracked object for each of a plurality of signals, wherein each signal is transmitted by a transmitter means at a respective location around the entity, and processing means arranged to determine a state of the tracked object in dependence on the one or more received signal characteristics at each receiver means or for each transmitter means, respectively, and one or more skewed distributions associated with the one or more signal characteristics.

A controller as described above, wherein:

the input means are one or more electrical inputs for receiving an electrical signal; and the processing means is one or more electronic processors.

The processing means may comprise electronic circuitry. The controller may comprise an output means for outputting a signal indicative of the determined state. The output means may be an electrical output.

Optionally the data indicative of the one or more received signal characteristics is indicative of one or both of a received signal strength, RSS and time-of-flight, ToF.

The state of the object may comprise one or more spatial-temporal characteristics of the tracked object. The one or more spatial-temporal characteristics of the tracked object may be determined with respect to a logarithmic curvilinear partitioning, LCP, of a region proximal to the entity.

The one or more skewed distributions are optionally indicative of noise associated with the one or more signal characteristics. The state of the tracked object may be determined by a Bayesian inference method.

According to a still further aspect of the invention, there is provided a system, comprising a controller according to an aspect of the invention, and one or more receiver means each arranged to output an electrical signal indicative of a received signal, wherein the controller is arranged to receive data indicative of the electrical signal output by each receiver means.

The system as described above, wherein the receiver means comprises one or more receiver devices. Each receiver device may be associated with an antenna.

According to another aspect of the invention, there is provided method of determining a location of a mobile device with respect to an entity, the method comprising determining one or more received signal characteristics at one of each of a plurality of receiver means distributed around the vehicle, wherein the signal is transmitted by the mobile device, or the mobile device for each of a plurality of signals each transmitted by a transmitter means at a respective location around the vehicle, the method comprising determining the location of the mobile device in dependence on the one or more received signal characteristics at each receiver means or for each transmitter means, respectively, and one or more skewed distributions associated with the one or more signal characteristics. Advantageously the location of the mobile device may be determined with respect to the vehicle.

According to yet another aspect of the invention, there is provided a vehicle arranged to perform a method as described above or comprising a controller as described above or a system as described above.

According to an aspect of the invention, there is provided computer software which, when executed by a computer, is arranged to perform a method as described above. The computer software may be stored on a computer readable medium. The computer readable medium may be non-transitory. The computer software may be tangibly stored on the computer readable medium.

According to an aspect of the invention, there is provided a method of determining a state of a tracked object with respect to an entity, the method comprising determining one or more received signal characteristics at one of each of a plurality of receiver means distributed around the entity, wherein the signal is transmitted by the tracked object, or the tracked object for each of a plurality of signals each transmitted by a transmitter means at a respective location around the entity, the method comprising determining a state of the tracked object in dependence on a partitioned region proximal to the entity and on the one or more received signal characteristics at each receiver means or for each transmitter means, respectively. Advantageously the partitioning of the region allows the one or more received signal characteristics to be binned. Advantageously the partitioning of the region allows application of statistical techniques to determine the state of the tracked object.

Partitioning the region around the entity may enable more accurate and robust estimation of a posterior of a state of the tracked object. The partitioning may facilitate applying simple, yet representative, models, such as motion models, of the tracked object and may enable a principled treatment of sensory measurements, which are typically asynchronous and contaminated with various sources of noise and/or occlusions, i.e. ambiguous.

Optionally the partitioned region is at least partly partitioned according to one or a combination of a logarithmic and a curvilinear first partitioning scheme. Advantageously the first partitioning scheme effectively partitions the region.

According to a further aspect of the invention, there is provided method of determining a state of a tracked object with respect to an entity, the method comprising determining one or more received signal characteristics at one of each of a plurality of receiver means distributed around the entity, wherein the signal is transmitted by the tracked object, or the tracked object for each of a plurality of signals each transmitted by a transmitter means at a respective location around the entity, the method comprising determining a state of the tracked object in dependence on a partitioned region proximal to the entity and on the one or more received signal characteristics at each receiver means or for each transmitter means, respectively, wherein the partitioned region is at least partly partitioned according to one or a combination of a logarithmic and a curvilinear first partitioning scheme. Advantageously the first partitioning scheme effectively partitions the region.

A first portion of the region proximal to the entity may be partitioned according to the first partitioning scheme and a second portion of the region proximal to the entity may be partitioned according to a second partitioning scheme. Advantageously the second partitioning scheme may provide more accurate determination of the state of the tracked object in the region partitioned according to the second partitioning scheme. The second partitioning scheme may be applied to a region proximal to the entity.

The second partitioning scheme optionally partitions the second into polygonal cells. The polygonal cells may be square or rectangular. Advantageously square or rectangular cells may allow coverage of the region of the second partitioning scheme.

The polygonal cells may comprise one or more linear sides. Advantageously the linear sides may allow tessellation of the cells.

The first partitioning scheme is a logarithmic curvilinear partitioning, LCP.

The state of the tracked object is determined by a Bayesian inference method. Advantageously the Bayesian inference method utilises available evidence to determine the state of the tracked object. The partitioned region optionally provides a support for the Bayesian inference method.

The state of the tracked object is determined in dependence on a stochastic model. The stochastic model may be a Hidden Markov model, HMM. Advantageously the HMM allows a continuous state space to be utilised. The state of the tracked object may be determined in dependence on a Jump Markov Model, JMM. Advantageously, the JMM allows discrete state space to be utilised. Advantageously the JMM allows for an analytical solution.

Optionally the JMM is indicative of a probability of the tracked object moving between cells of the partitioned region.

The partitioned region is optionally partitioned into a plurality of cells each associated with an identifier. Advantageously the identifier allows a transition matrix to be determined.

The JMM may be represented as a transition matrix and the identifier of each cell is used to determine a probability associated with a transition between first and second cells. Advantageously the matrix allows for a solution to be more conveniently determined.

The Bayesian inference method optionally comprises determining a posterior probability associated with each partition of the LCP.

According to a still further aspect of the invention, there is provided controller for determining a state of a tracked object with respect to an entity, the controller comprising input means for receiving data indicative of one or more received signal characteristics at each of a plurality of receiver means distributed around the vehicle, wherein the signal is transmitted by the tracked object, or one or more received signal characteristics at the tracked object for each of a plurality of signals, wherein each signal is transmitted by a transmitter means at a respective location around the entity, and processing means arranged to determine a state of the tracked object in dependence on a partitioned region proximal to the entity and on the one or more received signal characteristics at each receiver means or for each transmitter means, respectively, wherein the partitioned region is at least partly partitioned according to one or a combination of a logarithmic and a curvilinear first partitioning scheme.

A controller as described above, wherein:

A first portion of the region proximal to the entity is optionally partitioned according to the first partitioning scheme and a second portion of the region proximal to the entity is optionally partitioned according to a second partitioning scheme.

The second partitioning scheme may partition the second into polygonal cells. The polygonal cells may comprise one or more linear sides. Optionally the first partitioning scheme is a logarithmic curvilinear partitioning, LCP.

The processing means may be arranged to determine the state of the tracked object using a Bayesian inference method. Optionally the partitioned region provides a support for the Bayesian inference method.

The processor is optionally arranged to determine the state of the tracked object in dependence on a Jump Markov Model, JMM. The JMM may be indicative of a probability of the tracked object moving between cells of the partitioned region.

The partitioned region is optionally partitioned into a plurality of cells each associated with an identifier. The JMM may be stored in a memory accessible to the processing means as a transition matrix and the identifier of each cell is used to determine a probability associated with a transition between first and second cells.

According to an aspect of the invention, there is provided a system, comprising a controller according to an aspect of the invention, and one or more receiver means each arranged to output an electrical signal indicative of a received signal, wherein the controller is arranged to receive data indicative of the electrical signal output by each receiver means.

According to another aspect of the invention, there is provided a method of determining a location of a mobile device with respect to a vehicle, the method comprising determining one or more received signal characteristics at one of, each of a plurality of receiver means distributed around the vehicle, wherein the signal is transmitted by the mobile device, or the mobile device for each of a plurality of signals each transmitted by a transmitter means at a respective location around the vehicle, the method comprising determining a state of the mobile device in dependence on a partitioned region proximal to the vehicle and on the one or more received signal characteristics at each receiver means or for each transmitter means, respectively, wherein the partitioned region is at least partly partitioned according to one or a combination of a logarithmic and a curvilinear first partitioning scheme. Advantageously the location of the mobile device may be determined with respect to the vehicle.

According to a still further aspect of the invention, there is provided a vehicle arranged to perform a method as described above or comprising a controller as described above or a system as described above.

Within the scope of this application it is expressly intended that the various aspects, embodiments, examples and alternatives set out in the preceding paragraphs, in the claims and/or in the following description and drawings, and in particular the individual features thereof, may be taken independently or in any combination. That is, all embodiments and/or features of any embodiment can be combined in any way and/or combination, unless such features are incompatible. The applicant reserves the right to change any originally filed claim or file any new claim accordingly, including the right to amend any originally filed claim to depend from and/or incorporate any feature of any other claim although not originally claimed in that manner.

BRIEF DESCRIPTION OF THE DRAWINGS

One or more embodiments of the invention will now be described by way of example only, with reference to the accompanying drawings, in which:

Figure 1 shows a method according to an embodiment of the invention;

Figure 2 shows an illustration of a system according to an embodiment of the invention;

Figure 3 shows architectures according to embodiments of the invention;

Figure 4 illustrates a skewed distribution according to an embodiment of the invention;

Figure 5 illustrates partitioning of a region according to an embodiment of the invention;

Figure 6 illustrates a jump Markov model and associated matrix according to an embodiment of the invention;

Figure 7 illustrates interpolated received signal strength for a plurality of receivers according to an embodiment of the invention;

Figure 8 illustrates aggregated signal strength for a plurality of receivers according to an embodiment of the invention;

Figure 9 illustrates a tracked object posterior estimation probability for position according to an embodiment of the invention;

Figure 10 is a further illustration of a tracked object posterior estimation probability for position according to an embodiment of the invention;

Figures 11 and 12 show received signal strength at various distance from an entity along with their distributions per distance (i.e. likelihood) for line of sight and non-line of sight; and

Figure 13 illustrates a probability of detection of a wireless signal according to an embodiment of the invention

DETAILED DESCRIPTION

Figure 1 illustrates a method 100 of determining a position of a tracked object 210 with respect to an entity 220 according to an embodiment of the invention. Figure 2 illustrates a system 200 according to an embodiment of the invention. The system 200 comprises a tracked object 210 and an entity 220, as will be explained. Figure 3 illustrates example architectures of the system 200 according to embodiments of the invention.

Embodiments of the invention will be explained, particularly, with reference to determining a state of a tracked object 210 with respect to an entity 220, which in the described example is a vehicle 220, as is illustrated in Figure 2. It will, however, be appreciated that embodiments are not limited in this respect. The entity 220 with respect to which the state of the tracked object 210 is determined may be, for example, a building or other entity. The vehicle 220 may be a land-going vehicle. In other embodiments, the vehicle may be a watercraft or aircraft.

Furthermore, embodiments of the invention will be explained, particularly, with reference to determining a state of a tracked object 210 which is a mobile device 210, as illustrated in

Figure 2. The mobile device 210 may be one which comprises a display means, such as a display screen for outputting information to a user thereon. The mobile device 210 may be a mobile telephone, such as a smartphone, a tablet computer or other mobile computing device. In some embodiments the mobile device 210 is an electronic key for the vehicle 220 which operatively allows access to the vehicle for a possessor of the key. The key may comprise a transmitter means which operatively transmits identification information to the vehicle, such as a code, to provide access to the vehicle 220. In some embodiments the mobile device 210 comprises measurement means for determining one or more characteristics of the mobile device 210. The measurement means may comprise an orientation determining means, such as a gyroscope, for determining an orientation of the mobile device 210. The measurement means may comprise an acceleration determining means, such as an accelerometer, for determining accelerations of the mobile device 210. The measurement means may comprise a magnetic determining means, such as a magnetometer, for determining a magnetic field at the mobile device 210. Measurement data indicative of the measurements may be transmitted to the entity 220 in some embodiments.

As illustrated in Figure 3, the tracked object 210, such as the mobile device 210, comprises at least one communication means 310 which may be one of transmitter means 310, receiver means 310, or transceiver means 310 for transmitting, receiving or transmitting and receiving wireless signals, respectively. In some embodiments, the tracked object, such as the mobile device 210 may comprise a plurality of communication means which are distributed about the tracked object. The distribution of communications means around the tracked object may allow an orientation of the tracked object to be determined.

In one embodiment, which will be particularly described, the tracked object 210 comprises the receiver means 310 for wirelessly receiving a signal. It will be appreciated that the receiver means 310 may also be the transceiver means 310. The signal is received at the vehicle 220 as will be explained. However in other embodiments, the tracked object 210 may comprise the transmitter 310 or transceiver for wirelessly receiving signals. The wireless signal transmitted from the entity 220 may be indicative of one or more characteristics of each received signal at the entity 220, as will be explained. The communication means may be Ultra-Wide Band (UWB) although other embodiments may be envisaged.

In some embodiments, the tracked object 210 comprises signal determining means for determined one or more characteristics of each received signal, as will be explained. In other embodiments, the signal determining means is arranged at the vehicle 220. The one or more characteristics may be received signal strength (RSS) of each signal. The one or more characteristics may be a Time of Flight (ToF) of the signal between a transmitter, such as located at the vehicle 220, and the receiving means 310. Other signal characteristics may be envisaged. In embodiments where the one or more signal characteristics are determined at the mobile device 210, an indication of the determined one or more characteristics may be transmitted from the mobile device 210. In some embodiments, data indicative of the one or more characteristics of the tracked object or mobile device 210 may be used additionally.

For the purposes of further explanation, an embodiment will be described where the tracked object 210, referred to for clarity as the mobile device 210, comprises the receiver means 310, with it being appreciated that embodiments of the invention are not limited in this respect. Furthermore, the entity 220 will be described as being a vehicle 220. It will be appreciated from the above that embodiments of the invention are not limited in this respect.

Referring to Figure 2, the vehicle 220 comprises a plurality of communication means 231,

232, 233, 234, 235, 236. The plurality of communication means 231, 232, 233, 234, 235, 236 are distributed around the vehicle 220. In the described example, the plurality of communication means 231, 232, 233, 234, 235, 236 are transmitter means 231, 232, 233,

234, 235, 236 for each transmitting a wireless signal, i.e. radio signal, for receipt by the receiver means 310 of the mobile device 210. The plurality of transmitter means may be transmitter means 231, 232, 233, 234, 235, 236 or transceiver means 231, 232, 233, 234,

235, 236.

The embodiment illustrated in Figure 2 comprises six transmitter means 231, 232, 233, 234, 235, 236 although it will be appreciated that other numbers may be envisaged. As noted above, in some embodiments, the vehicle 220 comprises a plurality of receiver and transmitter means 231, 232, 233, 234, 235, 236 which may be transceiver means 231, 232,

233, 234, 235, 236. In some embodiments, one or both of the transceiver means at the vehicle 220 or the tracked object 210 repeats or reflects i.e. receives and then transmits a corresponding signal which is transmitted by the other of the vehicle 220 or the tracked object 210, This may be useful in embodiments where the one or more signal characteristics comprise ToF. Further

In some embodiments, the plurality of transmitter means 231, 232, 233, 234, 235, 236 are arranged in respective locations around the vehicle 220. The plurality of transmitter means 231, 232, 233, 234, 235, 236 may be arranged around a periphery of the vehicle 220, such as around front, back and sides of the vehicle 220. One or more transmitter means may be otherwise located about the vehicle such as on top of, such as generally centrally about the vehicle 220 and inside the vehicle 220. Other locations may be envisaged.

In the embodiment illustrated in Figure 2, first transmitter means (S1) 231 is arranged at a front of the vehicle 220. Second and third transmitter means (S2, S3) are arranged at a respective first side of the vehicle (right-hand side in Figure 2). Fourth transmitter means (S4) 234 is arranged at a rear of the vehicle 220. Fifth and sixth transmitter means (S5, S6) 235, 236 are arranged at a respective second side (left-hand side) of the vehicle 220. At least some of the plurality of transmitter means 231, 232, 233, 234, 235, 236 may be arranged around flanks of the vehicle 220. The plurality of transmitter means 231,232, 233, 234, 235, 236 may be arranged at an intermediate vertical position or height of the vehicle’s body, such as at a mid-vertical location of the body. In some embodiments, those transmitter means 232, 233, 234, 235 located at sides of the vehicle may be associated with door-handles or other access controls of the vehicle 220. It will be appreciated that other locations, either around the vehicle 220 or vertically about the vehicle 220 may be envisaged. In use, for a receiver 310 positioned at a location around the vehicle 220, at least some of the signals transmitted by the plurality of transmitter means 231, 232, 233,

234, 235, 236 are received as Line of Sight (LoS) signals, whilst others of the signals transmitted by some of the plurality of transmitter means 231, 232, 233, 234, 235, 236 are received as Non-Line of Sight (NLoS) signals i.e. some self-occlusion of the signal by the vehicle 220 may occur. Occlusion may also occur because of other objects, such as other vehicles parked relative to the vehicle 220 for example.

Each of plurality of transmitter means 231, 232, 233, 234, 235, 236 may comprise an antenna for transmitting a wireless signal in dependence on an electrical signal provided thereto from transmitter circuitry. Similarly, the mobile device 210 comprises an antenna for receiving the wireless signal and outputting an electrical signal corresponding thereto to receiver circuitry.

In some embodiments, the receiver means 310 and transmitter means 231, 232, 233, 234,

235, 236 may be Bluetooth (RTM) devices, such as Bluetooth Low Energy (BLE). It will be appreciated that embodiments of the invention are not limited to use of Bluetooth or BLE. In some embodiments, as used to produce experimental data discussed below, the transmitter means 231, 232, 233, 234, 235, 236 may be Apple iBeacons (RTM) which comprise a transceiver based on BLE. In other embodiments the receiver means 310 and transmitter means 231,232, 233, 234, 235, 236 may conform to another wireless protocol, such as WiFi i.e. IEEE 802.11 or a variant thereof. Embodiments are not limited to these protocols.

Figure 3 illustrates an architecture of the system 200. The system comprises the mobile device 210 and the vehicle 220. In some embodiments, such as shown in Figure 3(c), the system 200 further comprises a remote computing means 340 as will be explained. As noted above, in the described embodiment the mobile device 210 comprises the receiver means 310. The vehicle 220 comprises the plurality of transmitter means 231, 232, 233, 234, 235, 236 (not shown in Figure 3) which each output a wireless signal, corresponding to the electrical signal. The receiver means outputs an electrical signal corresponding to a received wireless signal to a received signal strength means (RSSM) 320. The RSSM 320 is arranged to operatively determine a received signal strength (RSS) for each i.e. associated with each of the plurality of transmitter means 231, 232, 233, 234, 235, 236. That is, the RSSM 320 operatively determines a value indicative of the RSS at the receiver means from each of the plurality of transmitter means 231, 232, 233, 234, 235, 236 corresponding to the signal wirelessly received at the receiver means 310 of the mobile device 210. The RSSM 320 is arranged to output a signal, or value, corresponding to the RSS for each of the plurality of transmitter means 231, 232, 233, 234, 235, 236. It will be appreciated that the RSSM 320 may be replaced by another signal characteristic determining means, such as a ToF determining means.

In the embodiment illustrated in Figure 3(a) the vehicle 220 comprises a State Determination Means (SDM) 330. The SDM 330 is arranged to operatively determine a state of the mobile device 210 in dependence on the plurality of RSS. The RSS may be provided from each of a plurality of receiver means 231, 232, 233, 234, 235, 236 or for each of a plurality of transmitter means 231, 232, 233, 234, 235, 236 about the vehicle 220. Where the vehicle comprises a plurality of transmitter means RSS values may be communicated from the mobile device 210 to the vehicle 220 to the SDM 330. In some embodiments, the SDM 330 is arranged to determine a location of the mobile device 210. The SDM 330 operatively outputs a signal, or one or more values, indicative of the state of the mobile device 210. The state of the tracked object may comprise one or more spatial-temporal characteristics of the tracked object i.e. characteristics of the tracked object which may change over time. The one or more spatial-temporal characteristic of the tracked object may comprise a location of the tracked object with respect to the entity. The one or more spatial-temporal characteristic of the tracked object comprises one or more of a velocity, acceleration, heading angle and/or distance to the entity.

In one embodiment, the SDM 330 may output one or more values indicative of the location of the mobile device 210. The location may be with respect to a current location of the vehicle 220. In one embodiments, the location may be output by the SDM330 may be coordinate values indicative of the position of the mobile device 210 with respect to the vehicle 220.

In some embodiments the vehicle 220 comprises a State Response Means or Module (SRM) 350 which is arranged to initiate a response of one or more systems of the vehicle 220 in dependence on the state of the mobile device 210.

In some embodiments, the RSSM 320, SDM 330 and SRM 350 may be modules which operatively execute on one or more processing means such as one or more electronic processors which operatively execute computer-readable instructions which are stored in a computer-readable medium such as one or more memory devices (not shown). Thus the RSSM 320, and also in some embodiments, the SDM 330 and/or SRM 350 form a controller for the vehicle 220. In some embodiments, at least some of the RSSM 320, SDM 330 and SRM 350 may be formed by electronic circuitry. The processing means may comprise one or more input means for receiving a signal indicative of the one or more signal characteristics. The input means may be, for example, an electrical input to the processing means. The processing means may comprise one or more output means for outputting a signal indicative of the state of the tracked object. The output means may be, for example, an electrical output of the processing means. The input means and output means may, in some embodiments, be a connection to a communication bus of the vehicle, such as to a CANBus or Ethernet network, although other communication busses may be envisaged.

In some embodiment, such as illustrated in Figure 3(b) the SDM 330 may be located at the mobile device 210. The SDM 330 may be provided with the RSS values for the plurality of transmitter means 231,232, 233, 234, 235, 236 from the receiver means 310. One or more values indicative of the state of the mobile device 210, such as the location of the mobile device 210, may be communicated from the SDM 330 to the SRM 350 at the vehicle 220.

In some embodiments, the remote computing means 340 is arranged to receive a signal such as RSS data indicative of the RSS for each of the plurality of transmitter or receiver means 231,232, 233, 234, 235, 236. The RSS data may be wirelessly communicated from one of the mobile device 210 or the vehicle 220 to the remote computing means 340. The remote computing means 340, such as a server computer, operatively executes the SDM 330. The SDM 330 determines the state of the tracked object 210, such as the location of the mobile device 210 in dependence on the received RSS data. State data indicative of the determined state, such as location, may be wirelessly communicated from the remote computing means 340 to the vehicle 220. The SRM 350 may then operate in dependence on the received state data.

Referring to Figure 1, the method 100 comprises a step 110 of receiving one or more wireless signals. In step 110, for the described example, the receiver means 310 of the mobile device 210 is arranged to wirelessly receive a signal. The signal received by the mobile device 210 is transmitted by at least some of the plurality of transmitter means 231, 232, 233, 234, 235, 236 of the vehicle 220.

In step 120, one or more one or more received signal characteristics are determined. As noted above, the one or more characteristics may be received signal strength (RSS) of the signal or may be a Time of Flight (ToF) of the signal between a respective on of the transmitter means 231, 232, 233, 234, 235, 236 and the receiver means 310. An embodiment where RSS is determined will be described in detail with it being appreciated that this is not limiting.

Step 130, which in the illustrated embodiment of Figure 1 comprises determining a state of the tracked object 210. The state of the tracked object is determined in dependence on the one or more received signal characteristics determined in step 120. As illustrated in Figure 1, in some embodiments step 130 may comprise a plurality of sub-steps as will be explained.

Received signal strength has previously been modelled using a log-distance model, such as the Okumura-Hata model. In such a model, measurement noise, w_k is often assumed to have a symmetric distribution, such as a Gaussian distribution. However the present inventors have realised that due to occlusions and Non-Line of Sight (NLoS) measurements, the symmetric or Gaussian assumption does not necessarily hold. Instead, a skewed distribution model is used in some embodiments of the invention. Capturing the impact of measurements of the signal characteristics using a skewed distribution may lead to significantly more accurate determination of the state of the tracked object 210, such as the mobile device 210. For example, more accurate determination of location or proximity estimates, as will be explained. NLoS measurements may arise from the fact that at least some of the plurality of receiver means 231, 232, 233, 234, 235, 236 are obscured or occluded from the transmitter means 310 by the vehicle 220. Furthermore, it will be appreciated that other entities may occlude, at least partly, the signals at the plurality of receiver means 231, 232, 233, 234, 235, 236, such as other proximal vehicles. However in other embodiments of the invention a symmetric, such as Gaussian, distribution may be used.

Since the maximum RSS cannot exceed the transmit signal strength, the present inventors have realised that the RSS noise can only belong to a limited range of positive values. Whereas, due to occlusions, RF signal can be substantially attenuated and, thereby, the likelihood of RSS measurements in dBm, i.e. z in Equation 1 below, taking large negative values may be captured by skewed models. This implies that a skewed distribution, rather than a symmetric one, is expected to better model RSS. In some embodiments, the skewed distribution may be more heavy-tailed to negative values. For other signal characteristics, such as ToF, skewness of ToF measurements is toward larger ToF values. In ToF signal delay cannot be below a minimum value for a signal to propagate over a distance, but may be toward arbitrarily large values of ToF due to signal reflection.

An example of a distribution for RSS measurement error in dBm derived from experimental data is illustrated in Figure 4 fitted with various distributions. As can be appreciated, one distribution which may fit the experimental data well is a skew-t distribution. The skew-t distribution has both skew and is heavy tailed i.e. exhibits kurtosis. However other distributions may be used which are only skewed and are not heavy tailed. A skew parameter may be used in association with the distribution to define the skew. In some embodiments, a direction of the skew may be associated with the distribution representing a LOS signal or a NLOS signal. For some distributions a heavy-tail parameter may be used to define the heavy tailed nature of the distribution, as explained below. A heavy tailed distribution may include very large values, such as very large positive as well as negative values, with many outliers. In some embodiments the skew may adopt a different sign in some distributions. For example, a sign of the skew may be determined according to whether the distribution represent a LOS or NLOS signal. In particular, for a LOS signal, some signal measurements may actually be NLOS due to occlusions not accounted for. While for the NLOS signal, the signal is received with relatively little attenuation due to, for example, errors in modeling, lossless reflections as well as fluctuations in transmitter power. Further, the mobile device may be held at an orientation relative to the holder which creates a LOS for the mobile device 210, while the user carrying the mobile device 210 is located in an NLOS partition.

A univariate skew ^-distribution may be parameterised by a location parameter μ e IR, spread parameter σ e IR⁺, shape parameter δ e IR and degrees of freedom v e IR⁺. A Probability Density Function (PDF) may be described by:

ST (z; μ, σ², δ,ν) = 2 t(z; μ, δ² + σ², υ)Τ(ζ; 0,1, ν + 1), (1) such that ϋ(ζ; μ,σ²,ν) is the PDF of Student’s /-distribution, and z is defined by:

v + 1 ν (δ² + σ²) + (z — μ)²

2)

Whereas, the Cumulative Distribution Function (CDF) of Student’s /-distribution with degrees of freedom v and scale 1 is denoted by T(z; 0,1, v).

For a skew-t distribution, increasing δ increases the skewness of the distribution, whereas decreasing v increases the distribution heavy-tailedness.

A useful representation of the skew /-distribution is a hierarchical representation.

ζ\η,λ ~ Ν(μ + δη, λ^-1 ,σ²), (3α) αμ-Λί+ζΟ,λ-¹), (3b) (V V\ ^(2'2)'

Where μ and λ are scalar random variables and N₊(m,s²} denotes the truncated normal distribution with closed positive orthant as support, location parameter m, and scaleparameter

s. Furthermore, G(a, B) is a gamma distribution with shape parameter a and rate parameter B.

Although a skewed t-distribution has been discussed specifically, it will be appreciated that other skewed distributions such as skew normal, Rayleigh, gamma and mixture distribution, e.g. Gaussian mixtures, can be utilised and embodiments of the present invention are not limited in this respect. Whilst each of these distributions are skewed distributions, it will be noted that not all distributions are heavy tailed. For example, skew-normal and inverted shifted gamma distributions are not heavy-tailed. Furthermore, in some embodiments a symmetric distribution may be used, such as Gaussian.

In some embodiments of the invention a region around the entity or vehicle 220 is partitioned into sub-regions or cells 510, 520. In Figure 5 two cells are indicated with reference numerals for clarity. The partitioning is used with the one or more received signal characteristics, such as RSS or ToF, to determine the state of the tracked object, such as the mobile device 210. The partitioning is used to provide a support for an inference method for determining the state of the tracked object, as discussed in more detail below. The partitioning of at least a portion of the region may be one or both of curvilinear and logarithmic in some embodiments of the invention. In some embodiments, a hybrid partitioning is used. In the hybrid partitioning first and second partitioning schemes are used. The first and second partitioning schemes may be different partitioning schemes, as will be explained.

The partitioning is achieved in some embodiments with a curvilinear grid with the entity 220, such as the vehicle 220, at a centre of the curvilinear grid. By curvilinear it is meant that concentric divisions between cells are curvilinear. That is, the partitions curve around the entity, such as the vehicle 220. Some curvilinear partitions between cells are arranged to be parallel around the vehicle 220. In some embodiments, an area-per partition increases logarithmically with increasing radial distance from the entity or vehicle 220. That is, in a direction extending radially outward from the vehicle an area of each partition increases logarithmically. The logarithm may be a base-10 logarithm, although other base logarithms may be used. In some embodiments, the partitioning may be logarithmic curvilinear partitioning (LCP) 500as shown in Figure 5. An illustration of such LCP 500 is provided in Figure 5. A distance of each radial grid is provided on a left-hand side of Figure 5. It will be appreciated that other partitioning distances may be used.

In some embodiments of the invention a likelihood is determined of the mobile device 210 being positioned in one or more of the sub-regions 510, 520. The partitioning may form a support which is discretised (or discrete) which allows a Bayesian inference model to be solved analytically in some embodiments, as will be explained.

In some embodiments, a hybrid portioning scheme may be used which combines two portioning schemes for the region around the entity. A first portioning scheme may be used in one portion of the region whilst a second portioning scheme may be used in a second portion of the region. For example, for some applications, the LCP portioning shown in

Figure 5 may be used for a first portion of the region which may be a region distal to the entity 220. A second portion of the region proximal to the entity or vehicle 220 may be partitioned according to another scheme. The other scheme may utilise partitions having a smaller area than those of the LCP. The other scheme may utilise rectangular, square and/or non-logarithmic partitions. Advantageously the use of partitions having a smaller area may allow more accurate determination of a location of the tracked object proximal to the vehicle. A division between the first and second partitioning schemes may be provided at a radius from the entity, such as 1m, although other distances may be used.

As can be seen in Figure 5, each partitioned area or cell 510, 520 is provided with an identifier, which in the illustrated embodiment is a numerical identifier which increases in value in a circular and outwardly increasing manner. Other numbering or identification schemes may be used. Such a numbering scheme may allow a transition matrix to be easily formed, as will be explained.

Figure 6 illustrates a heat map for each of the plurality of transmitter means 231, 232, 233, 234, 235, 236. The data illustrated in Figure 7 is learnt from experimental measurements. The heat map is indicative of RSS in dBm against distance. The heat maps in Figure 7 are partitioned using the LCP 500 shown in Figure 5.

As can be appreciated, a probability of detection (or rate of detection) for each of the plurality of transmitter means 231,232, 233, 234, 235, 236 is higher in the LoS direction i.e. away from the vehicle 220 in comparison to the NLoS direction i.e. toward the vehicle 220 with respect to the location of the respective receiver means 310. Thus it can be appreciated that for each of the plurality of transmitter means 231,232, 233, 234, 235, 236 a skewed distribution may be used to represent detection probability.

Whilst the detection probability for each of the plurality of transmitter means 231, 232, 233,

234, 235, 236 may differ or may be non-uniform, an aggregated or combined detection probability may be formed based upon the likelihoods for all sensors.

Figure 7 illustrates RSS measurement likelihood combined for all of the plurality of transmitter means 231,232, 233, 234, 235, 236. A left hand side of Figure 7 is determined directly from measured RSS, whilst a right hand side of Figure 7 illustrates the measurement likelihood where smoothing is applied which ‘fills in’ parts of the heat map where signals were not received for at least some of the plurality of transmitter means 231, 232, 233, 234,

235, 236.

A method of calculating likelihood probabilities from RSS heat maps, such as shown in Figures 6 and 7, is described below in connection with Figures 11 and 12.

Based on at least some of the foregoing, the method 100 illustrated in Figure 1 can be further explained. In some embodiments of the invention, the state of the tracked object is determined by a Bayesian inference method. In particular, the location of the tracked object, or mobile device 210, may be determined by the Bayesian inference method. The Bayesian inference method may determine a posterior of the state of the tracked object 210 given observations of the tracked object. As noted above, the state of the tracked object 210 may be the location of the tracked object with respect to the LCP 500 shown in Figure 5 where the observations are RSS measurements at the vehicle 220.

The RSS may be determined as the signal characteristic in step 120 at each of a plurality of time steps t. The time step t may be 3 seconds, although it will be realised that other time steps may be chosen. At each time step, the posterior is updated by the method 100. In the explanation below, k denotes a current measurement number i.e. at time t, where k is incremented with each time step.

In the method 100, y_k is recorded RSS measurement for the plurality of receiver means 231, 232, 233, 234, 235, 236 determined in step 120. That is y_k may be a multidimensional vector, 1xn where n is the number of receiver means 231, 232, 233, 234, 235 such as 6 in the example of Figure 2 i.e. y_k is a 1x6 vector in some embodiments. The recorded RSS measurements are at a point in time i.e. at t. x_k represents a latent system state (e.g. a position of the mobile device 210 in two dimensions i.e. (x, y).

Step 140 of the method 100 comprises determining a posterior probability. The posterior probability is a probability of the system state x_k given the previous RSS measurements y_rkas explained below.

A likelihood p(y_k\x_k) (i.e. of obtaining the vector of RSS measurements given the location of the mobile device 210) may be represented by a skewed distribution in embodiments of the invention, which along with a continuous state transition distribution constitutes a possible solution for the problem of estimating the state of the tracked object 210 e.g. the position of the mobile device 210 which may be in two dimensions (2D) or three dimensions (3D). This class of solutions use a continuous support for the unknown state variables such as x_k. The inference in this case can be accomplished using a Bayesian method as well as an optimization approach (e.g. numerical maximum likelihood estimators) where a cost function is minimized. An alternative approach, which is discussed below, is to utilise a discrete support for the unknown system state (i.e. the position of the mobile device 210), for example via discretising the region around the entity, for example using the LCP 500.

In some embodiments of the invention, a Bayesian filter is used for inference, which may be known as a point-mass filter.

In some embodiments of the invention, a Jump Markov Model (JMM) is used a dynamic model. The JMM models a probability or likelihood of moving transitioning between nodes. Each of the partitioned areas or cells 510, 520 shown in Figure 5 may be assumed to correspond to a node of the JMM. Example probabilities associated with the JMM are illustrated in Figure 8 associated with transition arrows. A current node 610 is indicated at a centre in Figure 8, where the current node 610 is a current location of the mobile device 210. The current node 610 corresponds to one of the cells 510, 520 illustrated in Figure 5 in which the mobile device 210 may currently reside e.g. at a time t. Some adjacent nodes are indicated in Figure 8 with reference numeral 620. Movement between nodes in a next time step t+1 is indicated by arrows in Figure 8, one of which is indicated with reference numeral 630 for clarity. A probability of moving between nodes between t and t+1 is indicated as being associated with the respective arrow. It will be noted at Figure 8 also indicates a probability of not moving to another node i.e. to remain at the current 610, indicated as a looped arrow 635. As indicated in Figure 8, the current node 610 has eight neighbouring nodes in some embodiments of the invention. It will be appreciated that the probability values shown in Figure 8 are merely provided as an example and that other values may be assumed.

A right hand side of Figure 8 graphically illustrates a transition matrix of values corresponding to the JMM 600 using the cell numbering scheme illustrated in Figure 5. The transition matrix encodes a transition probability between cells 510, 520. Axes correspond to cell numbers as used in Figure 5. A scale present in Figure 8 indicates a probability of the transition between cells. As can be appreciated, a probability 640 of remaining in a current cell between t and t+1 is greatest. A probability 650 of moving to an adjacent cell is also illustrated.

A conditional density p(x_k\x_k_f) represents a probability of obtaining a current system state x_k given a previous system state x_k_i. The conditional density encodes the probability values of the transition matrix as depicted in Figure 6. Using the conditional densities p(x_k\xk-i) and p(y_fc|%_fc) which is a likelihood 170, along with a last (prior) estimate p(x_fe-i|yi_:fe-i) 150 the posterior p(x_fc|yi_:fc) can be computed via a marginalization as in Equation 1:

p(^fc|yi:fc-i) = J p(^fcRfc-i)p(^fc-ilyi_:fc-i)ri%_fc-i

Equation 1 followed by the application of the Bayes rule, as in Equation 2:

, . _λ p(yfcRfc)p(^|yi_:fc-i)

Equation 2

When the support of x_k is discrete (or discretised), such as by using the LCP 500, and the transition density p(x_k\x_k_^ 160 is a jump Markov model (JMM), as discussed above, the integral in Equation 1 can be solved analytically.

Here, the unknown state variable x_k e ...,x^(r9} and the transition probability between two members of the support x^w and x^ (i.e. movement of the mobile device 210 from cell x^w to cell x® of the LCP 500) is denoted by π_ί; and matrix Π = [π^].

Similarly, when the measurement belongs to a finite support set y_k e {y⁽¹⁾,y⁽²⁾,...,y^(m)} the likelihood p(y_k\x_k) can be computed for each point of the support, such as each cell of the LCP 500, of x_k and the finite range of measurements. That is, we define the matrix L = [Ltj] e IJ4^nxmas in Equation 3:

L_i;· = Pr(y_k =y⁽J')\x_k = %(0)

Equation 3

Now, let Prtx/c-i = x®|yi_:fc-i) = The posterior given the observation y_k = yW can be computed as in Equation 4 where w_k is vector having a size corresponding to a number of cells of the partition, each vector element corresponding a weight of the respective cell: ^wfc|fc-l = flWfc-llfc-1

,.,(0 „ j ,.,(0 ^Wk\k ^{K L}ij^wk\k-1

Equation 4 where v/ is the rth element of the vector w.|. and

Pr(x_k =x®|yi_:fc) =

Equation 5 When there are multiple independent measurements, the likelihood matrices corresponding to available measurements are multiplied element-wise.

Figure 9 illustrates operation of an embodiment of the invention. Figure 9 shows an LCP with the vehicle 220 located at its centre in relation to a path taken by a person carrying the mobile device 210. Figure 9 is formed by six sub-Figures (a)-(f) each representing a successively later point in time (at three second intervals) as the mobile device 210 approaches the vehicle 220, where a current location of the mobile device 210 is indicated. A shading intensity of each cell indicates a likelihood of the mobile device 210 being located in the respective cell, as determined by step 140 of the method 100. An RSS for each of the plurality of transmitter means 231, 232, 233, 234, 235, 236 is indicated around the LCP. Where a receiver means did not receive the signal, an indication Φ is provided.

As can be appreciated from Figure 9(a) when the mobile device 210 is a distance from the vehicle 220, a large number of cells are associated with a posterior probability for position of the mobile device 210 being located within those cells. Furthermore, there is no strong ‘peak’ in the posterior probability indicative of the position of the mobile device 210. However, as the mobile device 210 approaches the vehicle 220, posterior probability values associated with some cells increase and, furthermore, a number of cells being associated with a significant value in the posterior reduces.

Figure 10 illustrates operation of an embodiment of the invention in the same way as Figure 9. However Figure 10 is for a ‘longer-track’ or longer path of the mobile device 210 to the vehicle 220.

In optional step 180, in some embodiments of the method 100, a decision is made in dependence on the posterior determined in step 140.

Step 180 may comprise determining a location of the mobile device 210 with respect to the vehicle 220 in dependence on the posterior. The location of the mobile device 210 may be referred to as a likely location or an estimated location. In some embodiments, determining the location of the mobile device 210 may comprise determining a cell having a greatest posterior probability value or largest weight w. In some embodiments, step 180 may comprise determining a Maximum a Posteriori (MAP) estimate. The MAP estimate may be based on one or more decision criterion. The criteria may comprise a threshold criterion (i.e. if a posterior probability for a given cell exceeds a certain threshold value, e.g. 0.3). In some embodiments, the criterion may be required to be satisfied for a predetermined duration of time e.g. 1 second, 5 second etc. It will be appreciated that other threshold values and durations may be used.

In some embodiments, step 180 comprises determining whether to initiate one or more actions. The determination may be made in dependence upon the posterior determined in step 140 or the location of the mobile device 210 as determined in step 180. For example, in the case of a vehicle 220, step 180 may comprise determining whether to initiate heating of one or more portions of the vehicle, such as an occupant cabin of the vehicle 220. Alternatively or additionally step 180 may comprise determining whether to adapt one or more systems of the vehicle 220, such as to activate one or more systems of the vehicle 220. For example, a lighting system or a heating system of the vehicle 220. The determination as to whether to initiate the one or more actions may be made on priori learned information. For example, the learned information may be associated with a position of one or more seats in the vehicle, although other information may be used. It will be appreciated that other actions may be taken or systems initiated, particularly in embodiments whether the entity is not a vehicle, such as, for example, a building.

In some embodiments, feedback may be provided to one or both of the mobile device 210 and vehicle 220. The feedback may be indicative of the decision in step 180. For example, if it not possible to determine the state of the mobile device 210 sufficiently, then feedback may be provided indicative thereof. The feedback may request a user input to confirm the state of the mobile device 210.

In step 190 it is determined whether a time delay or time step has elapsed i.e. t=t+1. Step 190 provides a delay between iterations of the method 100 which, as noted above may be 3 seconds, or may be another value. The time delay may be selected in dependence on an expected rate of change of the spatial-temporal characteristics of the tracked object.

A method of calculating likelihood probabilities from RSS heat-maps as shown in Figures 6 and 7 is now described. A likelihood probability distribution can be determined in various ways, three of which are presented here with it being understood that these are not limiting. Figure 11 shows RSS measurements for a LOS transmitter-receiver against distance from a centre of a vehicle on which one of the transmitter and receiver are arranged. Figure 12 shows RSS measurements for a NLOS transmitter-receiver against distance from a centre of a vehicle on which one of the transmitter and receiver are arranged. Partitioning ranges around the vehicle are illustrated in both figures. Figures 11 and 12 are shown with distance plotted as loglO(distance).

Figures 11 and 12 illustrate RSS against range with possible likelihood distributions, wherein each range corresponds to a given circle on the LCP 500. Thus it can be appreciated how distributions in each case change with distance from the vehicle 220.

In a first method, a distribution of RSS measurements for a given location in the LoS case and the NLoS case are different. In this method measurements of RSS are collected and are divided into LOS and NLOS classes using ground truth data. The ground truth data is true position data of the tracked object and recorded LoS and NLoS RSS measurement data which provides reference data. Consequently, the data in each class from all transmitters/receivers are divided into partitions corresponding to the LCP 500 based on the ground truth positions. The data from partitions with the same range (distance) to the car and same LoS/NLoS class are aggregated in bigger partitions and a distribution is fitted to them as in Figure 11. These distributions are found via minimizing a cost function depending on the data and a parametric family of distributions capable of modelling skewness in the data. The second method is similar to the first method described above, but the measurement data is not classified into LoS/NLoS classes.

In the third method, instead of fitting a parametric family of distributions a nonparametric approach such as Gaussian processes or kernel density estimate is used to obtain a smooth functional from for the likelihood and when necessary the likelihood function is normalized to obtain a likelihood distribution function.

Similar methods can be applied to ToF likelihood functions. However, ToF, particularly for UWB transmitter/receivers is likely to be much more accurate and the partitions may therefore be smaller.

A probability of detecting a transmission (detection rate of transmissions) is utilised with the Bayesian inference process described above. The probability of detecting a transmission or signal may differ for each receiver or transmitter means 231, 232, 233, 234, 235, 236 distributed around the entity or vehicle 220. Figure 11 illustrates probability values for each of the plurality of transmitter means 231, 232, 233, 234, 235, 236. As can be seen from

Figure 11, the probability for each receiver or transmitter means 231, 232, 233, 234, 235, 236 distributed around the vehicle 220 is reduced in a NLoS direction. Furthermore it can be seen that the probability distribution for each receiver or transmitter means 231, 232, 233, 234, 235, 236 differs. However a combined probability distribution, similar to Figure 7, may be determined for all of the plurality of transmitter means 231,232, 233, 234, 235, 236 which is then orientated according to a position of the transmitter means 231, 232, 233, 234, 235, 236 with respect to the vehicle 220. Advantageously using such probabilities may improve the accuracy of estimating the sought state posterior.

As noted above, the mobile device may comprise, in some embodiments, one or more measurement means for determining one or more characteristics of the mobile device 210.

The measurement data indicative of the measurements may be combined, in some embodiments, with the one or more signal characteristics (i.e. RSS or ToF) to determine the state of the tracked object 210. For example, to improve the determination of the location of the mobile device 210. In particular, the measurement data may be used to determine the posterior of the state (e.g. position) of the tracked object within the Bayesian inference process. For example, the mobile device 210 may determine or detect a number of steps made by a person carrying the mobile device. The determined step count or odometry may be used to provide information on if/how-much has the person has moved. This can be from: a) sensors in the tracked object (e.g. mobile device 210) such as one or more inertia measurement units (accelerometer, gyroscope and magnetometer) and/or b) sensors in the surrounding infrastructure, e.g. cameras in a car park, or even beacons, etc.

It will be appreciated that embodiments of the present invention can be realised in the form of hardware, software or a combination of hardware and software. Any such software may be stored in the form of volatile or non-volatile storage such as, for example, a storage device like a ROM, whether erasable or rewritable or not, or in the form of memory such as, for example, RAM, memory chips, device or integrated circuits or on an optically or magnetically readable medium such as, for example, a CD, DVD, magnetic disk or magnetic tape. It will be appreciated that the storage devices and storage media are embodiments of machine-readable storage that are suitable for storing a program or programs that, when executed, implement embodiments of the present invention. Accordingly, embodiments provide a program comprising code for implementing a system or method as claimed in any preceding claim and a machine readable storage storing such a program. Still further, embodiments of the present invention may be conveyed electronically via any medium such as a communication signal carried over a wired or wireless connection and embodiments suitably encompass the same.

All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and/or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features 5 and/or steps are mutually exclusive.

Each feature disclosed in this specification (including any accompanying claims, abstract and drawings), may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise. Thus, unless expressly stated otherwise, 10 each feature disclosed is one example only of a generic series of equivalent or similar features.

The invention is not restricted to the details of any foregoing embodiments. The invention extends to any novel one, or any novel combination, of the features disclosed in this 15 specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed. The claims should not be construed to cover merely the foregoing embodiments, but also any embodiments which fall within the scope of the claims.

Claims

1. A method of determining a state of a tracked object with respect to an entity, the method comprising:

determining one or more received signal characteristics at one of:

each of a plurality of receiver means distributed around the entity, wherein the signal is transmitted by the tracked object; or the tracked object for each of a plurality of signals each transmitted by a transmitter means at a respective location around the entity;

the method comprising:

determining a state of the tracked object in dependence on a partitioned region proximal to the entity and on the one or more received signal characteristics at each receiver means or for each transmitter means, respectively, wherein the partitioned region is at least partly partitioned according to one or a combination of a logarithmic and a curvilinear first partitioning scheme.

2. The method of claim 1, wherein a first portion of the region proximal to the entity is partitioned according to the first partitioning scheme and a second portion of the region proximal to the entity is partitioned according to a second partitioning scheme.

3. The method of claim 2, wherein the second partitioning scheme partitions the second portion of the region proximal to the entity into polygonal cells.

4. The method of claim 3, wherein the polygonal cells comprise one or more linear sides.

5. The method of any preceding claim, wherein the first partitioning scheme is a logarithmic curvilinear partitioning, LCP.

6. The method of any preceding claim, wherein the state of the tracked object is determined by a Bayesian inference method.

7. The method of claim 6, wherein the partitioned region provides a support for the Bayesian inference method.

8. The method of any preceding claim, wherein the state of the tracked object is determined in dependence on a Jump Markov Model, JMM.

9. The method of claim 8, wherein the JMM is indicative of a probability of the tracked object moving between cells of the partitioned region.

10. The method of any preceding claim, wherein the partitioned region is partitioned into a plurality of cells each associated with an identifier.

11. The method of claim 10 when dependent on claim 9, wherein the JMM is represented as a transition matrix and the identifier of each cell is used to determine a probability associated with a transition between first and second cells.

12. The method of claim 6 or 7 when dependent on claim 5, wherein the Bayesian inference method comprises determining a posterior probability associated with each partition of the LCP.

13. A controller for determining a state of a tracked object with respect to an entity, the controller comprising:

input means for receiving data indicative of one or more received signal characteristics at each of a plurality of receiver means distributed around the entity, wherein the signal is transmitted by the tracked object; or one or more received signal characteristics at the tracked object for each of a plurality of signals, wherein each signal is transmitted by a transmitter means at a respective location around the entity; and processing means arranged to determine a state of the tracked object in dependence on a partitioned region proximal to the entity and on the one or more received signal characteristics at each receiver means or for each transmitter means, respectively, wherein the partitioned region is at least partly partitioned according to one or a combination of a logarithmic and a curvilinear first partitioning scheme.

14. The controller of claim 13, wherein a first portion of the region proximal to the entity is partitioned according to the first partitioning scheme and a second portion of the region proximal to the entity is partitioned according to a second partitioning scheme.

15. The controller of claim 14, wherein the second partitioning scheme partitions the second portion of the region proximal to the entity into polygonal cells.

16. The controller of claim 15, wherein the polygonal cells comprise one or more linear sides.

17. The controller of any of claims 13 to 16, wherein the first partitioning scheme is a logarithmic curvilinear partitioning, LCP.

18. The controller of any of claims 13 to 17, wherein the processing means is arranged to determine the state of the tracked object using a Bayesian inference method.

19. The controller of claim 18, wherein the partitioned region provides a support for the Bayesian inference method.

20. The controller of any of claims 13 to 19, wherein the processing means is arranged to determine the state of the tracked object in dependence on a Jump Markov Model, JMM.

21. The controller of claim 20, wherein the JMM is indicative of a probability of the tracked object moving between cells of the partitioned region.

22. The controller of any of claims 13 to 21, wherein the partitioned region is partitioned into a plurality of cells each associated with an identifier.

23. The controller of claim 22 when dependent on claim 20, wherein the JMM is stored in a memory accessible to the processing means as a transition matrix and the identifier of each cell is used to determine a probability associated with a transition between first and second cells.

24. A system, comprising:

a controller according to any of claims 13 to 23; and one or more receiver means each arranged to output an electrical signal indicative of a received signal;

wherein the controller is arranged to receive data indicative of the electrical signal output by each receiver means.

25. A method of determining a location of a mobile device with respect to a vehicle, the method comprising:

determining one or more received signal characteristics at one of:

each of a plurality of receiver means distributed around the vehicle, wherein the signal is transmitted by the mobile device; or the mobile device for each of a plurality of signals each transmitted by a transmitter means at a respective location around the vehicle;

the method comprising:

determining a state of the mobile device in dependence on a partitioned region proximal to the vehicle and on the one or more received signal characteristics at each receiver means or for each transmitter means, respectively, wherein the partitioned region is at least partly partitioned according to one or a combination of a logarithmic and a curvilinear first partitioning scheme.

26. A vehicle arranged to perform a method according to any of claims 1 to 12 or 25, comprising a controller according to any of claims 13 to 23 or a system according to claim 24.

27. Computer software which, when executed by a computer, is arranged to perform a method according to any of claims 1 to 12 or 25.

28. The computer software of claim 27 stored on a computer readable medium.