GB2519306A

GB2519306A - Timing, range and location determining method and apparatus

Info

Publication number: GB2519306A
Application number: GB1318263.9A
Authority: GB
Inventors: Khalid Nur; Washington Yotto Ochieng; Cong Li
Original assignee: Imperial Innovations Ltd
Current assignee: Ip2ipo Innovations Ltd
Priority date: 2013-10-15
Filing date: 2013-10-15
Publication date: 2015-04-22
Also published as: WO2015056002A2; GB201318263D0; WO2015056002A3

Abstract

An arrangement is provided for estimating the timing of a direct-path signal component in a signal comprising multi-path distortion. The arrangement is particularly suited for the provision of more accurate range and location measurements. The arrangement comprises a wireless communication interface for receiving a signal transmitted from a first device, such as a mobile device. The signal comprises a direct-path component and a plurality of indirect-path components wherein each component comprises a delayed version of the transmitted signal. A data store stores a model of the received signal, and a controller is coupled to the wireless communication interface and to the data store. The controller is configured to truncate the received signal to select a portion, b, of the signal associated with a selected time interval. The controller further obtains a set of functions based on the model of the received signal, wherein each function comprises the model shifted by a different respective delay, and each delay is less than the selected time interval. The controller then fits the portion of the received signal using the set of functions to determine the time of arrival of the direct-path component.

Description

-Timing, Range and Location Determining Method and Apparatus The present disclosure relates to methods and apparatus for determining the timing of a direct path componcnt of a signal in the presence of multi-path distortion, examples of the disclosure therefore find application in determining the distance between devices, and more particularly for determining the location of mobile devices in a network in the presence of multi-path signal distortion. Aspects of the disclosure relate to the application of sparse estimation techniques to the detection of direct path signals in dense multi-path environments.

Ranging refers to the process of computing the distance (range) between two objects, and may comprise measuring the distance between an object and a known reference location. If an object is constrained to move only in one dimension, the location of the object can be determined by a single range measurement.

To determine the position of an object in a two dimensional space it is possible to obtain measurements of the distance between the object and multiple reference locations. The location in a two dimensional space can be uniquely identified by the measurement of the range to three or more known reference locations. This process is referred to as trilateration, or multilateration. Tt is also possible to determine the position of an object in a two dimensional space based on a range measurement and some other information such as directional information.

Time of flight, TOF, range measurements can be provided by measuring the time a signal takes to propagate from a reference location and multiplying it by the signal propagation speed.

The accuracy of time of flight based location measurements depend upon the ability to uniquely identify the time of flight of a signal. Given that the propagation speed of a radio signal in free space is about 300000000 mW', a timing accuracy on the order of 10 nano-seconds or less is generally considered necessary to achieve meter level accuracy in a range measurement.

Tn urban environments sources of signal distortion are common, and signal to noise ratio of ranging signals may be low. In particular, signal multi-path effects may degrade the accuracy of ranging measurements, and this may be a particular problem in indoor environments where conventional location determining systems, such as GPS, are less useful.

Aspects of the disclosure provide methods and apparatus for estimating the timing of a direct-path signal component in a signal comprising multi-path distortion, and these may enable the provision of more accurate range and location measurements.

Signal transmission in indoor and urban environments can give rise to dense multi-path signals.

Some aspects of the disclosure exploit features of existing wireless communications protocols, such as those used in wireless local area networks, to control the sampling rate of nodes in a network. This may enable oversampling so that so-called "sparse" estimation techniques can be applied to what might otherwise be considered "dense" problems.

For example, wireless communications protocols may use defined signal patterns, such as those 1 5 associated with a frame preamble, and/or those associated with request and response sequences (such as a request-to-send clear-to-send sequence), to initiate communication. Embodiments of the disclosure control sampling rates of nodes of a wireless network based on such signal patterns to assist in the efficiency and accuracy of range finding. This may enable the application of sparse estimation techniques to problems they have conventionally been thought of as being ill suited to.

Network nodes at krown locations may be used to provide reference locations for a location determining system. By estimating the distance between a number, for example at least three, reference locations and a mobile device, the location of the mobile device can be estimated. More generally, where a number of network nodes have access to a common time reference, the time difference of the arrivals, TDOA, of a single signal sent from a mobile device to each of the network nodes can be used to determine the location of the mobile device.

Where network nodes are coupled to communicate by a communication interface having a known delay (e.g. known distance with lineottsight wireless communication, or wired communication), but do not have access to a common time reference, a differential time difference of arrival approach, DTDOA, may be used to determine the location of a mobile device.

Examples of methods and apparatus for estimating the time delay of the direct-path signal from the mobile device are described in more detail below.

Described herein is an apparatus for determining the time of arrival of a direct path component of a multi-path signal. The apparatus comprises a wireless communication interface for receiving a signal transmitted from a first device, for example a mobile device. The signal comprises a direct-path component and a plurality of indirect-path components, each component being a delayed version of the transmitted signal.

A controller of the apparatus is configured to truncate the received signal to select a portion, b, of the signal associated with a selected time interval, and to obtain a set of basis ffinctions based on the model of the received signal. Each of these basis functions comprises the model shifted by a different respective delay and each delay is less than the selected time interval.

1 5 The controller fits the portion of the received signal using the set of basis functions to determine the time of arrival of the direct-path component.

The communication interface may be configured to obtain signal samples at a first sampling rate suitable for communicating with a first device according to a wireless communication protocol, and operable to obtain signal samples at a second sampling rate that is higher than the first sampling rate. hi these examples, the controller, is configured to determine, based on signal samples obtained at the first sampling rate, whether a first device is communicating with the apparatus using the wireless conrnmnication protocol. The controller is also configured to control the wireless communication interface to obtain samples at the second sampling rate in the event that it is determined that a first device is communicating with the apparatus.

The controller can then use this signal, sampled at the higher sampling rate, to determine the time of arrival of a direct path component, for example by truncating and fitting the signal as described above.

The model used to fit the signal comprises a response function of the wireless communication interface, and/or a model of a signal associated with a data sequence (such as a short frame prcamblc) of a wirclcss communication protocol.

As will be apprcciatcd, typically, multi-path signals in indoor cnvironmcnts arc typically dcnsc sials with many components. Embodiments of the disclosure however may employ sparse estimation. in such examples the controller is configured to: determine a regularisation parameter, X, fit the basis ffinctions to thc sclcctcd portion, b, of thc rcccivcd signal bascd on reducing the value of a merit function, and modify the fit based on the regularisation parameter, X. Examples of the disclosure will now be described, by way of example only, with reference to the 1 0 accompanying drawings, in which: Figure 1A and Figure lB show flow charts illustrating a method of estimating the timing of a direct-path signal; Figure 2 shows an example of a network configured to determine the location of a mobile device bascd on a mcthod such as that Ulustratcd in Figure 3; 1 5 Figure 3 shows a schematic diagram of a network node; Figure 4 illustrates a network frame comprising a frame preamble; and Figure 5 illustrates the selection of a time interval from a received multi-path signal based on correlation of thc received multi-path signal with a rnodd of the transmitted signal.

In the drawings like reference numerals are used to indicate like elements.

Figure 1 illustrates a computer implemented method 100 of determining the time of arrival of a dircct path signal from a mobile device in a network. The method tOO comprises recciving 2, at a network node, a signal transmitted from the mobile device. This signal includes multi-path distortion and so comprises a direct path component, and a plurality of indirect-path components.

Each of these components comprises a delayed version of a signal transmitted by the mobile device. The direct path component is delayed by the line-of-sight propagation delay of the signal, and the indirect-path components are generaHy more delayed.

The received signal is truncated 4 in time to provide a representation, b, of the received signal during a sclcctcd tirnc intcrval. This time intcrval is sclcctcd to include the time delay associatcd with the direct path component (e.g. the line-of-sight propagation delay of the signal received from the mobile node).

A model of the signal received from the mobile device can be obtained 6, for example based on knowledge of the response function Rç of the transmitter, the response ffinction of the receiver Bp3, and the actual signal transmitted, Tx. As will be appreciated in the context of the prcsent disclosure, given knowledge of a wireless network protocol used for communication between the network nodes and the mobile device, the actual transmitted signal, Tx, can be known a priori.

Thus, a model of the multipath-free and noise-free observed signal at the receiver can be written: = r t i l1rs El) U Examples of the response functions Rx, BRX of a communications device include the impulse response of the device filter for example a time domain representation of the transfer function of the device. An impulse response may comprise the signal output from a receiver device in response to a received unit impulse, or the signal transmitted from a device based on a unit impulse. Exact knowledge of these functions may not be required -embodiments of the present disclosure have been found to be robust to variations in the form of the response functions B and so in some embodiments these contributions can be approximated with any technically sensible response function, for example response functions based on filters whose pass band includes frequencies of the transmitted signal. For example such filters may comprise a bandwidth selected based on one or more communications protocols used by the device andlor the physical layer specifications of those protocols. Examples of filter transfer functions upon which response functions can be based include Gaussian functions, Boxcar functions, Polynomial functions, Half-sinusoids, Hamming windows, and linear combinations thereof Data sequences used in any given protocol may also be known a priori, such as frame or packet headers used in packet switched communications. A physical signal pattern may be associated with a known data sequence. Accordingly, a data sequence such as a frame preamble, transmitted as part of a wireless protocol can be associated with a known physical signal, e.g. a radio signal without the need to demodulate or decode that signal. Examples of such data sequences include frame prcamblcs and dcar-to-scnd signals, but other protocol sequences may also be used.

In this context, the obtained 6 model of the received signal can be based on a known physical signal associated with a wireless communication protocol, and an approximation to the response function of a wireless communication interface associated with that protocol.

This model of the received signal is then used to provide a set of basis functions. Each basis function comprises the model shifted by a different selected delay. For example, one basis function may comprise the model signal with zero delay with respect to the start of the truncated signal, and other basis functions may comprise the model delayed by a number of samples with respect to the start of the truncated signal. In some examples, e.g. where the basis functions completely span the selected time interval, the basis functions may include one basis function for each possible delay within the selected time interval, e.g. each integer number of samples.

The portion of the received signal, b, is fitted 10 using the basis functions to determine 12 the time of arrival of the direct-path component. Based on the time of arrival of the direct path component, the distance between the mobile device and the network node can be determined 12.

One way to determine the time of arrival of the direct path component can be based on the model Ax+v=b (1), where, * A comprises a matrix of the basis functions, * ii is a vector describing an estimate of the fit of those basis functions to the portion of the received signal, b, and * v is the noise in the received signal.

There are many different ways to estimate the fit, x, of the basis functions, A, to the portion, b, of the received signal in this model. In some examples, the fit is weighted to reduce the number of non-zero contributions from the basis functions.

One way of estimating the fit, x, comprises applying the iterative relation: = argminAx_b2 +WLxF, (2) where: * argminAx -bflndicates an argument, x, selected to reduce (e.g. to minimise) the merit function Ax -br * Wk 1 is a matrix of zeros with a leading diagonal defined by the estimate of the fit, xk provided by the previous iteration, and * 2. is a regularisation parameter.

A possible solution, x, to the optimisation defined in Equation 2 can be determined according to: = Wk+IAk I(Ak+IAk+I + Al) b (3) Where: 1 0 1 is an identity matrix, and Ak=AW1.

As will be appreciated by the skilled addressee in the context of the present disclosure, this may he interpreted as a Tikhonov regularisation problem. Tn this context, the regularisation parameter, 1 5 2., may be selected based on the desired performance. For example relatively smaller values of 2.

apply heavier weighting to the fit to the received signal, b, whilst relatively larger values of 2.

favour sparse solutions.

The regularisation parameter, 2., may be determined according to any one of a number of methods.

For example the rcgularisation parameter may simply be estimated, e.g. by trial and crror, or it may be based on an a priori knowledge such as an estimate of noise level in the signal. In some wireless network devices, such estimates of the noise level are provided by the hardware. The regularisation parameter, 2. may also be estimated based on a prediction of the number of multi-path components. Tn other examples the regularisation parameter, 2., may be determined for each iteration of Equation 2 based on a singular value decomposition. b other examples, the regularisation parameter, 2., may be selected based on a trade-off between minimizing WL 42 and minimizing VAx -bM2. This may be achieved by determining the values of these two quantifies at a number of values of the regularisation parameter, 2., and selecting the value ot 2., which reduces both quantities. For example, if WI 4 is plotted against Ax -bM2 for a number of values of the regularisation parameter, X, an estimate of 2. can be obtained from the plot. For example, an L-shaped curve may be obtained, and an estimate of?. can be obtained based on the value of ? at the corner of the L-shape. The values of the regularisation parameter, 2, used in this procedure may be restricted to a selected range, for example based on an estimate, or based on a priori Irnowledge such as knowledge of the level of noise in received signals. Other methods of estimating this regularisation parameter may also be used, such as those discussed in more detail below.

1 0 In addition to range finding based on a single node (e.g.to determine the location in one dimension), time of arrival measurements from more than one node can be combined, for example using time differcncc of arrival, TDOA, or differential time difference of arrival, DTDOA approaches.

One example of an apparatus suitable for performing such methods is illustrated in Figure 2 Figure 2 shows a network 200 comprising a plurality of nodes 202, 204, 206, and a location determiner 208. As illustrated, the network of Figure 2 comprises a mobile device 212, and a wireless access point 214. The nodes 202, 204, 206 are operable to communicate with the location determiner 208 via the wireless access point 214. The nodes 202, 204, 206 are also operable to communicate with one another, and with the mobile device 212. Communication between the nodes 202, 204, 206 and the location determiner may be performed by a wired connection, and/or by wireless communication. This communication may be performed according to a wireless network protocol such as an IEEESO2.1 1 protocol.

The method illustrated in Figure 1A may further comprise a network node 202, 204, 206 obtaining samples at a first sampling rate to detect the presence of a mobile device 212, and then switching to a second higher sampling rate when a mobile device 212 is detected in order to resolve the timing of a direct path signal component, for example according to the method 100 of Figure 1A. One example of such a method 110 is illustrated in Figure lB.

As illustrated in Figure lB. a network node 202, 204, 206, obtains 20 samples at a first sampling rate for detecting 22 the presence of a mobile device. Tn the event that a selected trigger signal (such as short frame preamble or a clear-to-send signal) is not detected 22, samples continue to be obtained 20 at the first sampling rate. In the event that the selected trigger signal is detected 22, the node 202, 204, 206 obtains 24 an identifier of the mobile device based on the selected signal, for example by deriving an identifier such as a media access control, MAC, identifier from the signal. This can enable communication with multiple mobile devices 212 to be performed so that multiple devices can be tracked and uniquely identified. Further samples are then obtained 26 at a second sampling rate that is higher than the first sampling rate.

A signal transmitted 28 by the mobile device can then be received by at least one of the network nodes 202, 204, 206, or the access point 214. The other network nodes 202, 204, 206, 214 receive the transmitted signal and apply a method such as one of those described with reference to Figure IA, to determine the liming of the direct path component of the signal transmitted from the mobile device.

The Access Point 214 or at least one of the network nodes may then transmit 30 a response to the signal transmitted from the mobile device. If transmitted, the response is received 100 by the network nodes 202, 204, 206, which each determine a time of arrival of the response signal.

Each node 202, 204, 206 that received both the initial signal from the mobile device, and the response can then transmit, to the location determiner 208, the time of arrival of the direct path component of the signal from the mobile device, and the time of arrival of the component of the response. In some examples however only the difference between the two times of arrival need be sent.

The location determiner 208 then determines 32 the location of the mobile device 212 based on the differences between the time of arrival at each network node 202, 204, 206 of the direct path component of the signal from the mobile device, and the time of arrival of the response at each node. This may be performed according to a differential time difference of arrival technique. The location may be a relative location, relative to the locations of the nodes, or an absolute location based on the time differences and data indicating the location of one more of the nodes. -10-

The transmission of a response signal from the nodes to the mobile device is optional, only the time of arrival of the direct path component of the signal from the mobile device is needed. For example, the time difference between arrival of the direct path signal at a first network node and a second network node can be used to determine that the location of the mobile device lies along a defined hyperbola, e.g. a hyperbola with a constant range difference to the first and second network nodes, which are located at the hyperbola foci. If the time of arrival of the direct path signal at a third network node is also known, the time difference between arrival of the direct path signal at the first network node and the third network node can be used in combination with the 1 0 time difference between arrival of the direct path signal at a first network node and a second network node to uniquely determine the location of the mobile device, in some examples the network nodes may operate using a common time reference, for example they may use a synchronised common clock.

The data store 210 may store the locations of the nodes 202, 204, 206, however this too is optional. In sonic embodiments the reference nodes may provide information describing their location to the location determiner 208. This information may be sent to the location determiner 208 with the time difference measurements.

The increase in sampling rate applied at the nodes in response to detecting the presence of the mobile device 212 is optional, however it may be advantageous as it can enable the use of sparse estimation techniques, for example based on a weighting to reduce the number of non-zero components in an estimated fit of a model to a signal. These techniques may be used to determine the direct path delay without placing unnecessary processing and memory burden on the network nodes 202, 204, 206.

Naturally, it is not necessary to switch sampling rates, the nodes 202, 204, 206 may simply sample at a single rate, e.g. the higher rate, at all times. The first, lower, sampling rate may be selected based on the wireless protocol, and may comprise a sampling rate selected based on the communication bandwidth of the protocol. Examples of low sampling frequencies include the sampling frequency of the communications protocol, for example at least 4x10' samples per second, or a multiple thereoL and the second, higher, sampling rate may be selected based on the desired precision of the ranging measurements and the propagation speed of the signal transmitted from the mobile device. Examples of higher sampling rates include rates of at least 10, or at least i09 samples per second.

The location determiner 208 shown in Figure 2 may be provided in any one of the nodes, and the functionality of the location determiner 208 may be distributed between the nodes, or it may be provided in the wireless access point 214, or in a processor coupled to communicate with the nodes, for example the mobile device 212 may comprise the location determiner. Only one node 1 0 in the network need comprise a location determiner 208, and the other nodes may simply receive signals at the selected sampling rates. The determination of the direct path component timings may be performed at the nodes, or elsewhere in the network.

Without wishing to be bound by theory, it is believed that Equation I above can be modified to include a perturbation parameter, Pr, to take account of multi-path components excluded from the truncated signal, b, and from the model provided by the matrix of basis functions, A. Accordingly, Equation I, above, may be rewritten: AX+V+P=b (4) To take account of this, the methods and apparatus described above with reference to Figure 3 and Figure 2 may be configured to estimate the regularisation parameter based on residuals obtained from fitting the basis ffinctions, A, to the received signal, e.g. the residuals from an un-regularised fit, such as a least squares fit.

For example, the basis functions may be fitted to the truncated signal (selected portion, b) by a matrix inversion, e.g. by inverting a matrix of the basis functions onto the selected portion, b, of the received signal.

Such a fitting procedure may be compactly expressed in matrix notafion, thus: -12-XLS(A A)-' A'.b (5) The regularisation parameter, X, may then be estimated according to the relation: 1 Mb-(AxLS)M2 (6) where, N is the number of samples in the selected portion of the received signal b.

Naturally, although matrix notation is used here for the purposes of convenience, it will be appreciated by the skilled addressee in the context of the present disclosure that fitting methods 1 0 other than matrix inversion may be used to estimate this remainder, and in some examples non-least squares methods such as maximum likelihood estimators can be used to determine this remainder. This method may be applied by the controllers of any apparatus described herein.

Figure 3 shows a schematic illustration of a network node which may be used in the methods 100, 110 and apparatus 200 described above with reference to Figure 1A, Figure lB. and Figure 2.

The network node of Figure 3 comprises a wireless communication interface 302, and a controller 304 coupled to the wireless communication interface 302. The network node also comprises a data storc 306 coupled to the controller 304.

The network node 300 is operable to communicate, according to a wireless network protocol, via the wireless communication interface 302 with a plurality of other network nodes, such as network nodes 202, 204, 206 illustrated in Figure 2.

The controller 304 is coupled to the data store 306 and is operable to obtain data from the data store. The data store 306 stores a signal model associated with a known data sequence of the wireless network protocol. The signal model may also be based on at least one response function associated with the wireless communications of the protocol. For example the model may comprise a signal associatcd with the known data sequence modified (e.g. convolved with) such a response function. -13-

The controller 304 is also coupled to the wireless communication interface 302 to receive signals and is operable to truncate a received signal to select a portion, b, of the received signal that includes the direct path component. Of course, where the location of the mobile device 212, and thc time that the signal is sent from the mobile device 212, are both unknown, the estimated time of arrival of this direct path component cannot be known a priori. Accordingly, the controller is configured to determine a cross-correlation function between the model of the transmitted signal and a signal received over the communication interface.

An illustration of one such correlation ffinction is shown in Figure 5. The inventor has found that the peak of the cross correlation function is generally associated with a delay that exceeds the arrival time of the direct path component. Following this finding, the controller 304 is configured to select the time interval to which the received signal is to be truncated by identifying the timing of a peak in the cross-correlation, and selecting a time interval that ends with that peak, e.g. by discarding signals arriving with a delay greater than the delay of the correlation peak. The length of the time interval (e.g. the amount by which its start precedes the peak in the cross correlation function) is selected according to a root mean square, r.m.s, channel delay spread, which can be determined based on the physical propagation environment in which a network node is located.

The controller is also operable to obtain a set of basis functions based on the model of the received signal. The controller 304 may also be operable to transmit wireless requests over the wireless communication interface to cause other devices in the network (e.g. nodes 202, 204, 206 and mobile device 212 shown in Figure 2) to transmit a wireless response signal back to the network node 300.

In operation, the network node 300 is configured to receive a wireless signal transmitted from a mobile device. The signal may comprise a direct-path component, and a plurality of indirect-path components. The controller 304 then obtains a model of the signal from the data store 306, and truncates the received signal to select a portion, b, of the signal that includes the direct path signal component as explained above.

The controller 304 then obtains a set of basis ffinctions, A, based on the model. Each basis function comprises the model shifted by a different respective selected delay. The delays can be -14-selected to span the time interval, (e.g. incrementally). For example, each selected delay is less than or equal to the length of the time interval.

The controfler 304 then fits the truncated portion, b, of the reecived signal using the set of basis functions, A to determine the time of arrival of the direct-path component at the network node 300. To perform this fit, the controller obtains a regularisation parameter, X, and fits the basis functions, A, to the selected portion, b, of the received signal by reducing the value of a merit function, and modifying the fit based on the regularisation parameter, X. This fitting process may be iterative.

The controller 304 may then providc the determined time delay to a controller of another device in the network (e.g. to the location determiner 208 illustrated in Figure 2), or it may receive determined time delays from controllers of other nodes (202, 204, 206) in the network so that it itself can perform location determining functions. Tn either case, the controller which receives the 1 5 determined time delays can determine the location of the mobile device based on these time delays. As will be appreciated, the controller 304 of the network node 300 may be configured to determine the time delay of arrival according to any of the methods described above with reference to Figure 3 and/or Figure 2.

Although it is possible to determine a selected time interval over which to truncate the received signal (for example based on the cross-correlation of the received signal with a signal model) in sonic examples the estimated direct-path delay may be known, or can be determined when the network is set up. For example the maximum possible line of sight distance from a node to a mobile device in the network may be fixed by the physical environment in which the node is installed.

Tn some possibilities the time that the signal is sent from the mobile device 212 may be known, for example the signal may be sent in response to a trigger of some kind which may be sent from a node of the network, or in some cases the mobile device may be configured to send signals at predetermined intervals, e.g. periodically. Accordingly, although the controller can be configured to determine a cross-correlation function between the model of the transmitted signal and a signal received over the communication interface, this is not essential. For example, the methods -15-described above may be applied periodically to a time window of a received signal.

in some possibilities, the presence of the mobile device may be detected based on the wireless communication intcrface receiving a trigger signal such as a short frame preamble or a Wi-Fi (RTM) clear-to send signal.

in some possibilities, the controller may be configured to determine the regularisation parameter, X, but the regularisation parameter can also be obtained from the data store 306 (e.g. based on an estimate) but in some examples the controller 304 is configured to determine the regularisation 1 0 parameter, 2, based on the residuals obtained from an un-regularised fit of the basis functions to the selected portion, b, of the signal e.g. according to any of the methods described with reference to Equation 4, Equation 5, or Equation 6.

Tn some embodiments the selected signal comprises a signal transmitted in a frame of a wireless 1 5 network protocol, for example the selected signal may comprise a model of one of a short frame preamble and a clear-to-send signal. in some possibilities the protocol comprises a wireless local area network protocol. The wireless local area network protocol may comprise Wi-Fi (RTM), for example an IEEESO2. II protocol.

in some examples of the disclosure a mobile device may be configured to communicate with a plurality of network nodes, and to apply the methods described above with reference to Figure IA, Figure I B, Figure 2 and Figure 3 to determine its own location. For example, the mobile device can be configured to send a request to at least one network node, and to determine the time delay to arrival of a direct path response signal from the at least one network node based on a stored model of the response signal. As will also be appreciated, information describing the location of the at least one network node can be sent to (and/or stored in) the mobile device to enable the mobile device to determine its own location.

Any feature of any one of the examples disclosed herein may be combined with any selected features of any of the other examples described herein. For example, features of methods may be implemented in suitably configured hardware, and the configuration of the specific hardware described herein may be employed in methods implemented using other hardware. In some examples the functionality of the controllers described herein may be provided by a general -16-purpose processor, which may be configured to perform a method according to any one of those described herein. Tn some examples the controller may comprise digital logic, such as field programmable gate arrays, FPGA, application specific integrated circuits, ASIC, a digital signal processor, DSP, or by any other appropriate hardware. hi addition, all of the methods described herein may be embodied as computer program products operable to program computer apparatus such as network nodes to perform these methods. These computer program products may be carried on non-transitory computer readable storage media. -17-