EP4713709A1

EP4713709A1 - Localisation method and apparatus implementing the method

Info

Publication number: EP4713709A1
Application number: EP24726628.1A
Authority: EP
Inventors: David GONZALEZ GONZALEZ; Osvaldo Gonsa; Niclas Günter Jürgen FÜHRLING; Giuseppe Thadeu FREITAS DE ABREU
Original assignee: Aumovio Germany GmbH
Current assignee: Aumovio Germany GmbH
Priority date: 2023-05-17
Filing date: 2024-05-16
Publication date: 2026-03-25
Also published as: WO2024236122A1; CN121175587A

Abstract

A method of locating objects emitting wireless signals, in an environment having at least two receivers adapted to RSS values of the object's wireless signals is presented. The at least two receivers have known positions in the environment and are communicatively connected to a common computing unit. The method comprises, at the common computing unit, determining an optimised RSS value- based coordinate mapping function for the environment under consideration of shadowing noise, using the known positions of the receivers and of training objects. The RSS values for the objects and from each of the two or more receivers are aggregated, and the aggregated RSS values are arranged into a received signal power vector containing, for each individual object, the sums of the RSS values determined at all receivers. For each object, vectors containing the RSS values received by the two or more receivers are mapped onto x and y coordinates of the environment using the optimised mapping function.

Description

202302178 -1- LOCALISATION METHOD AND APPARATUS IMPLEMENTING THE METHOD FIELD OF THE INVENTION The present invention relates to the field of object localisation using wireless signals emitted by the objects, in particular wireless communication signals. NOTATIONS Throughout this specification, bold symbols represent vectors or matrices, respectively. Scalar values are denoted herein by lowercase letters in italics, as in x. Superscripts T and H, respectively denote the transpose and complex conjugate transpose of a vector or matrix. BACKGROUND Wireless localisation technology, both indoors and outdoors, has gained great attention and development in the last few decades, inter alia in connection with autonomous vehicles, where knowing a vehicle’s location is essential for safe and efficient operation. Localisation information can further be used for tracking vehicles and predicting their paths, which may be useful for collision prevention or detection. Other uses of wireless localisation include near-field radio frequency identification (RFID) positioning and Internet-of-Things (IoT) sensor networks in smart factories and homes. Traditional localisation techniques have typically relied on global navigation satellite systems (GNSS) for the satellite-based geolocation and time information, but such methods exhibit poor power-efficiency, precision, latency, and robustness in dense urban scenarios, especially for the expected requirements of beyond fifth- generation (B5G) communication applications. Therefore, alternative positioning systems have been investigated to utilise wireless signals from a more proximate environment, such as wireless sensors, devices, and access points, capable of capturing signal metrics such as time of arrival (ToA), angle of arrival (AoA), or received signal strength (RSS) values. Such localisation scenarios generally resolve to a multidimensional, multivariate 202302178 -2- optimisation problem based on the received signal metrics from the sensors, where the position information of the targets is the solution. In order to alleviate such challenging optimisation problem, recently proposed methods leverage machine learning (ML) techniques. For example, in "Autonomous 3d UAV localisation using Taylor series linearised TDoA-based approach with machine learning algorithms," 202213th International Conference on Information and Communication Technology Convergence (ICTC), 2022, pp.783-785, V. Tilwari and S. Pack, suggest using a supervised ML method to evaluate Taylor series-linearised time difference of arrival (TDOA) measurements to localise autonomous unmanned aerial vehicles. In "A deep learning based AoA estimation method in NLOS environments," 2021 IEEE Globecom Workshops (GC Wkshps), 2021, pp.1-6, Y. M. T. Wang and Y. Shen use a deep residual network for evaluating AoA measurements for a single sensor non-line-of-sight (NLOS) indoor environment. A method to incorporate heterogeneous sensor information was proposed by N. T. A. M. I. Al Hajri and R. M. Shubair, in "Indoor localisation for IoT using adaptive feature selection: A cascaded machine learning approach," IEEE Antennas and Wireless Propagation Letters vol.18, no.11, pp.2306-2310, Nov. 2019. There, a K-nearest-neighbour (KNN) algorithm is used to adaptively select and combine the various signal radio frequency (RF) features for indoor localisation. An increasingly popular technique is to only operate with RSS values at the sensors, with the advantageous trait that the encoded information of the wireless signal itself is not relevant, such that it can be used for other applications such as communication or channel estimation. For example, in "RSS-based multiple sources localisation with unknown log-normal shadow fading,” arXiv:2110.10435v1, 2021, Y. Chu, W. Guo, K. You, L. Zhao, T. Peng, and W. Wang suggest detecting RSS values at distributed sensors and use this information to localise the signal- emitting targets on a discrete grid. The positions of the targets are initially estimated via a sparse dictionary updating and a K-means clustering, and are iteratively refined by a dynamic update of the dictionary. 202302178 -3- While the prior art methods provide viable solutions for specific environments and scenarios, they provide sub-optimal accuracy in the presence of noise and are mostly suitable for limited indoor environments only. SUMMARY OF THE INVENTION It is, therefore, desirable to provide a localisation method that exhibits improved robustness and accuracy in noisy environments, and an apparatus implementing the method. This need is addressed by the method of claim 1, the receiver of claim 5, the common compute unit of claim 7 and the computer program product of claim 8. A corresponding computer-readable storage medium is presented in claim 9. Embodiments and developments of the method and apparatus, respectively, are provided in the respective dependent claims. The invention will be described in the following assuming a multi-user (MU) distributed massive multiple-input multiple-output (DM-MIMO) scenario, consisting of K single-antenna transmit devices, also referred to herein as objects or targets, which are served by M single-antenna remote radio heads (RRHs), also referred to herein as receivers or sensors, the latter being connected to a computing unit (CU) via error-free fronthaul links with infinite rate, as schematically depicted in figure 1. The radio signals emitted from the objects are received at the multiple receivers at different signal strengths, depending on their respective distances. Throughout the following specification the terms RSS and RSSI may be used interchangeably for the received signal strength. The two-dimensional (2D) positions of the ^-th receiver and the ^-th objects, with ^ ∈ ^ ≜ {1, ⋯ , ^} and ^ ∈ ^ ≜ {1, ⋯ , ^}, are respectively described by the 2D coordinate vectors 202302178 -4- where ^_^ ^{^^}, ^_^ ^{^^} and ^^^ ^ , ^^^ ^ are respectively the ^- and ^-coordinates of the ^-th receiver and ^-th object. Following the above, the Euclidean distance between the ^-th receiver and the ^-th object is given by Considering a single line-of-sight (LOS) path, the received signal vector at the ^-th receiver over T consecutive transmission instances is given by where ^_^ ∈ ℂ is the received symbol at the ^-th receiver, ℎ_^^ ∈ ℂ is the flat-fading uplink channel gain between the ^-th receiver and the ^-th object, assumed to remain constant during T consecutive transmissions, ^ ∈ ℂ^{^×^} respectively the transmit power and the arbitrary transmit symbol vector from the ^-th object, is the additive white Gaussian noise (AWGN) received at the ^-th receiver. In this specification it is assumed that the transmit powers of all objects are uniform, such that ^_^ = ^, ∀^ ∈ ^. The flat-fading uplink channel gain coefficient ℎ_^^ in equation (3) is further modelled by where ^_^^ ∼ ^ ^(0,1) is the small-scale fading factor, and ^_^^ is the large-scale fading factor given by with ^_^ ∈ ℝ representing the reference path loss coefficient, i.e., the path loss at a reference distance, and ^ ∈ ℝ representing the path loss exponent determined by environmental assumptions. ^ ∈ ℝ and ^_^^ ∼ are respectively 202302178 -5- distance as defined in equation (2) and the channel gain due to random shadowing of the path between the ^-th receiver and the ^-th object. In light of the above, the RSSI value of the received signal at a receiver is obtained by where ^_^^ ∈ ℝ is the RSS value of the ^-th transmitter received at the ^-th receiver, described by which can be estimated – either semi-blindly by leveraging short orthogonal pilot sequences together with independent payload data, or blindly by exploiting the sparsity resulting from intermittent user activity, such that only a relatively small random subset of transmitters share the channel at each transmission instance – based on the relation where W ≜ respectively, denote a matrix collecting the transmit signals and the powers from all K transmitters at the m-th receiver. The powers pmK can be equivalently expressed in decibel (dB) scale as where ^^^ ^ ≜ 10log_^^ (^ ⋅ ^_^), ^ ^^ ^_^ ≜ 10log_^^ (^_^^) and ^^{^^} is the radio sensitivity. 202302178 -6- Consequently, the RSSI values from all M RRHs are aggregated at the CU, and stacked into a vector (in dB) as In the following subsection the coordinate model upon which the location is based will be discussed, considering two arbitrary functions ^_^(⋅) and ^_^(⋅) that map the received signal power vector of any ^-th object to its ^- and ^-coordinates, respectively, i.e., Implying that if the functions ^_^(⋅) and ^_^(⋅) are known at the CU, the positions of any object can be obtained, provided the aggregated RSSI values. Remark: As the expressions are identical for the ^-coordinate and the ^-coordinate functions and derivations, the subscripts (⋅)_^ and (⋅)_^ are omitted for conciseness from this point onward, and the following expressions are assumed to apply identically for both ^- and ^-coordinates unless stated otherwise. Occasionally, the letter c may be used, indicating either interchangeably. In the method proposed herein, GPR is utilised to model the coordinate mapping functions, where it is first assumed that the target function is drawn from a user- defined GP prior, i.e., ^(⋅) ∼ ^ ^(0, ^) (12) where ^ ^(0, ^) denotes the GP prior with zero mean and covariance matrix ^ ∈ whose element at the ^-th row and ^-th column is given by the covariance function ^^^_^, ^_^^, dependent on the RSSI between the ^-th and ^-th object. To accurately model the relationship of the RSSI values and the coordinates, a covariance function must be designed to carefully capture the differences in power between any two objects in the region of interest (ROI). The proposed method 202302178 -7- follows the covariance function proposed by K. N. R. S. V. Prasad, E. Hossain, and V. K. Bhargava, in "Machine learning methods for RSS-based user positioning in distributed massive MIMO,” IEEE Transactions on Wireless Communications, vol. 17, no.12, pp.8402-8417, 2018, which is designed to capture both stationary and non-stationary transmitter object pairs, as where ^_^ ∈ ℝ^{^×^} and ^_^ ∈ ℝ^{^×^} are respectively the RSSI vectors of the ^-th and ^-th object, ^_^ ^{^} _^ ∈ ℝ is the variance of the measurement error, ^_^^ is the indicator variable taking on the value 1 if ^ = ^ and 0 if ^ q, and the parameters ^, ^, ^ are the weight parameters to be learned, with ^ ≜ diag ∈ ℝ ∀ ^ ∈ ^ are the weights corresponding to each RSS vector in exponential term of the covariance function defined in equation (13). In light of the discussion above relating to the coordinate model, it can be seen that in hand of the RSS vectors yielding to the covariance matrix, the actual coordinate value can be obtained by evaluating the mean of the GP ^(⋅) in equation (12). This requires the information of the ^ + 2 unknown weight parameters ^, ^_^, ⋯ , ^_^ , ^ of the covariance function, whose ML-based optimisation is described in this section. For convenience, define the vector collecting the ^ + 2 unknown weight parameters, as Also define the sets of coordinates c ∈ ℝ^{K×^} corresponding to K training locations, and the associated set of training RSSI vectors p ^{^×^} ^ ∈ ℝ , with k= 1, …, K. Accordingly, also define the training covariance matrix Ψ ∈ ℝ^K×K associated with the K training locations and corresponding RSSI values, and the cross-covariance matrix ^ ∈ ℝ^K×K between the K training and the ^ target object locations, 202302178 -8- constructed from the corresponding sets of RSSI values, respectively. Then, the joint distribution of the coordinate vectors of the training and target object locations, according to a conventional GP approach, is given by, where the k-th row and ^ th column of the cross-covariance matrix ^ ∈ ℝ^{K×^} between the training RSS and the actual RSS data is given by Φ (pk, pk), as obtained from equation (13). In possession of the joint distribution in equation (16), the conditional distribution of c is given by where the conditional mean vector ^ ∈ ℝ^{^×^} and covariance matrix ^ ∈ ℝ^{^×^} is obtained via Thus, the marginal distribution of the individual object coordinate can be obtained as where ^_^ and ^_^ are respectively the marginal mean and variance of the estimate of the coordinate of the ^-th object, given by where [⋅]_^ and [·]k,i, respectively, denote the ^ th element of a vector and the matrix element at the k-th row and i-th column. 202302178 -9- Since ^_^ is Gaussian distributed, the marginalized mean ^_^ is directly the maximum-a-posteriori estimate of ^_^, and hence the final predicted coordinate of the ^-th target. It can be inferred from the procedure described above that the performance of the GPR-based RSSI localisation algorithm is highly dependent on the accuracy of the covariance matrix model given in equation (13), which in turn is fundamentally determined by the parameter vector ^. Consequently, a core step of the inventive method is to optimally determine ^, given a certain amount of training data. In "Machine learning methods for RSS-based user positioning in distributed massive MIMO,” this is achieved via a maximum likelihood fitting of the distribution of the training coordinates c, given the corresponding set of K RSSI vectors pk, assumed to be free of errors. Such an assumption is not only virtually impossible to meet in practice, as assuming error-free RSSI implies the need for pilot signals of either extremely high power or in extremely large numbers, which is already idealistic in the case of a single transmitter-sensor pair, let alone in the multitarget- multisensor setting under consideration, but also a cause of poor performance in real-life applications, since the inevitable presence of errors in RSSI values collected is not mitigated by design. The multi-object localisation problem presented above will require a suitable solution for obtaining a viable implementation under non-ideal, i.e., real-world, circumstances. In accordance with the present invention a noise-robust ML-based solution to the multi-object localisation problem using exclusively RSSI values of wireless signals emitted by the objects is presented, which effectively translates to an optimisation problem over the ^ pairs of real-valued 2D coordinates, given the aggregated RSS values at the ^ RRHs and the known positions of the ^ RRHs, which is solved via SGD. 202302178 -10- In accordance with the invention the problem of robustness against noise will be addressed by determining the parameter vector ^ using noisy training data, lending both feasibility and robustness to the overall location method. Using noisy training data affected by random shadowing noise reflects the real-world scenario, in which the actual signals are likewise affected by random shadowing noise, and thus distinguishes the present method from the known location methods, which assume a perfect match between the training data and the base model. In other words, similarly to measured target RSSI values utilized in the actual localisation operation of the method, the training RSSI vectors used to obtain the optimal parameter vector ^ are modelled as with zmk ~ ^(0, ^_^ ^{^} ^_^ ). It should be noted that equation (21) describes a single-path model without the loss of generality to the multi-path model. This is equivalent to treating the coordinates c of the training points not as deterministic, but rather as random variables with a distribution that, under the GPR model can be assumed to be approximated by where the elements of the covariance matrix Ψ∈ℝ^K×K are determined via equation (13), that is Given the distribution in equation (22), the optimal weight parameters ^ can then be determined as the solution of the maximum likelihood problem ^^∗ = argmin −log ^ 202302178 -11- where the objective ^(^; p1, …, pK) is implicitly defined, which for the purpose of training is a function of the parameter vector ^, as highlighted by the notation, and which in view of the Gaussian approximation in equation (22), can be modelled as where | ⋅ | denotes the determinant of the argument matrix. It is evident from equations (13), (23), and (25), that ^(^; p₁, …, pK) is not convex on the optimisation variable ^. In fact, the determinant and inversion operations onto ^, and the nonlinear dependence of the latter on the parameters gathered in the matrix ^, render the problem highly intractable from the perspective of optimisation theory. The present invention addresses this non-convexity issue via an SGD approach discussed by S. Ruder, in “An overview of gradient descent optimisation algorithms,” 2016, arXiv:1609.04747. In the context of the present invention, first consider the partial derivative of that ^(^; p₁, …, pK) with respect to ^, which is given by 1 ∂ 1 = ^ log |^|^ + c^{^} ∂ ^ ^^{^^}^ c 2 ∂^ 2 ∂^ ^. (26) Next, the matrix derivative identities are leveraged, as discussed by K. Petersen and M. Pedersen, in “The Matrix Cookbook”, Lyngby, Denmark: Technical Univ. Denmark, 2006: 202302178 -12- to simplify the expression in equation (26) to Observing that the partial derivatives of equation (25) with respect to ^_^ and ^ are identical in form to the expression in equation (28), details of the derivations corresponding to the latter parameters are omitted herein, and only expressions for each element of the partial derivatives of provided, which are respectively given by where ^p‾ ^^ is the ^-th eleme ‾ ^ k i^ ^{^×^} ki nt of p ki ≜ p − p ∈ ℝ , and the notation [ · ]^k _, ⁱ denotes the matrix element at the k-th row and the i-th column. The gradient of the objective function in (25) can then finally be put together, yielding 202302178 -13- such that the parameter vector ^ can be optimized via gradient descent (GD), according to the update equation and ^^{(^)} are the parameter vectors at the (^ − 1)-th and ^-th SGD iterations, respectively, while ^ is the learning rate, which for convergence guarantees is bounded by the Lipschitz condition with ^ denoting the Lipschitz constant, given by ^ = max eig ⁽⁽^^{^^)^} ⋅ ^^{^^)} (32^) where max eig (⋅) denotes the operator returning the maximum eigenvalue of the argument matrix. The training procedure described above may be performed over a large data set, consisting of multiple snapshots of data collected for a large number of training locations, as exemplarily depicted by the ‘training cube’ ^ in figure 2. The training data cube ^ ∈ ℝ^{^×K×S} consists of S noisy snapshots of each and all RSSI vectors p(s) k , with k ∈ {1, …, K} and s ∈ {1, …, S}, as illustrated in figure 2. The exemplary training cube ^ corresponds to a case where the number of sensors is ^ = 5, the number of training locations is K = 7, the total number of snapshots of RSSI vectors per training location is S = 8. Since the complexity of the training method is fundamentally determined by the inversion of the covariance matrix Ψ, as evident from equation (30), the present invention further proposes applying a mini-batch SGD-based variation of the training scheme outlined above, which will be described below, aiming at lowering the complexity of its implementation. 202302178 -14- A mini-batch ^_^ ∈ ℝ^{^×K˜} ⊂ ^ consists of a number K˜ ≪ K of training RSSI vectors p(s˜) k˜ , selected randomly from ^ , with equal probability and mutually exclusively, such that k˜ ∈ {1, … , K˜} and s˜ ∈ {1, … For notational convenience, the training locations are relabelled corresponding to a given ^-th mini-batch as c˜_^ = [x˜_^, … , x˜_^˜], and the corresponding RSSI vectors as p˜_k˜, such that the mini- batch can be described An example of a mini-batch ^_^ with K˜ = 4 is also illustrated in figure 2, indicated by the grey columns, consisting of a random selection of RSSI vectors corresponding to the training locations c˜ = ^{x_^, x_^, x_^, x_^ ^}, such that snapshots taken at k˜ = {1,2,4,7} and s˜ = {2,8,5,8}, yield ^ (^) (^) ( ^ = ^p_^ , p^ , p^) ^ , p(^) ^ ^ ≜ ^p˜ ^, … , p˜ ^^. Next, consider the covariance matrix with structure similar to that of equation (22), but constructed only with respect to the training location vector c˜_^, i.e., Then, under the SGD method, the update of the parameter vector ^ for the mini- batch ^_^ is obtained by the corresponding variations of equations (30) and (32), namely 202302178 -15- A schematic block diagram of the noise-robust parameter ^ optimisation method via mini-batch SGD using the data cube mini-batch embodiment is given in Fig.3. The optimisation method is further illustrated in the flow diagram of figure 4 a). It is reminded that the method is to be run independently for each coordinate ^ and ^, such that its execution yields the optimized, i.e., trained, parameters ^_^ ^∗ and ^^∗ _^ . Inputs to the training process are the data cube ^ with S snapshots of each an all RSSI vectors p(s) k , with k ∈ {1, …, K} and s ∈ {1, …, S}, the number B of mini batches, the number ^ (^) ^_^^ of SGD iterations per mini batch, and an initial parameter vector ^, which are received in step 110. In step 120, a mini batch ^b is taken from the data cube, each mini-batch comprising a number K˜ ≪ K mutually exclusive training RSSI vectors p˜ k˜ with k˜ ∈ {1, … , The mini batch is fed to a calculation process in step 130. In step 140 the covariance matrix Ψ_^ is constructed as per equation (33), and in step 150 the gradients ∇_^ ^ (^; p1, …, pK) are computed via equation (34). In step 160 ^ is updated as per equation (35). Computing the gradients and updating the intermediate optimised values is iteratively repeated until a termination criterion is met, which is checked in step 170. If the termination criterion is not met, “no”-branch of step 170, the next iteration is carried out. Suitable termination criteria comprise, inter alia, a predetermined maximum number of iterations ^ (^) ^_^^ or a convergence of the intermediate optimised values ^ below a predetermined threshold. The convergence criterion may also comprise that such convergence is stable over a predetermined number of subsequent iterations. Once it is determined, in step 170, that the termination criterion is met, “yes”-branch of step 170, step 180 checks if the last one of the B mini batches has been fed to the calculation process. If not, “no”-branch of step 180, the process returns to step 120 and is repeated. If all mini batches have been fed to the calculation process, “yes”-branch of step 180, the training phase is completed, and the optimised values for the weight parameters ^^∗ are output in step 190. Finally, the actual localisation can be performed. A conventional approach would be to use a known RSSI-based localisation method, e.g., as described in “Machine learning methods for RSS-based user positioning in distributed massive MIMO”, which, in possession of a parameter vector ^ obtained through model training, 202302178 -16- reduces to evaluating equation (20a) for each ^-th object, given the corresponding RSSI measurements ^_^ obtained at the receivers, the noise-free training RSSI vectors pk obtained in the conventional training phase, and the associated covariance matrix The present invention benefits from having an optimised parameter vector ^^∗ obtained through the noise-robust approach described above, so that instead of noise-free training RSSI vectors noisy training RSSI vectors are available. In embodiments of the invention, an entire data-cube ^ containing multiple snapshots of noisy training RSSI vectors p(s) k is available. Multiple GP-based localisation methods can be used with the optimised parameter vector ^^∗. In the following, one exemplary method will be described. Consider the joint distribution of the coordinate vectors of the training objects and the actual objects to be located, which by leveraging conventional GP methods yields, where ^ ∈ is the cross-covariance matrix between the training RSS and the actual objects’ RSS data, whose element at the k-th row and ^ th column is given by Φ (pk, pk). In hand of the joint distribution in equation (36), the conditional distribution of c is defined as where the conditional mean vector ^ ∈ ℝ^{^×^} and covariance matrix ^ ∈ ℝ^{^×^} is obtained via Finally, the marginal distribution of the individual object coordinate can be obtained as 202302178 -17- where ^_^ and ^_^ are respectively the marginal mean and variance of the estimate of the coordinate of the ^-th object and are given by where the notation [⋅]_^ and [·]^k,i, respectively, denote the ^-th element of a vector and the matrix element at the k-th row and i-th column. Since ^_^ is Gaussian distributed, the margnialized mean ^_^ is directly the maximum-a-posteriori estimate of ^_^, and hence the final predicted coordinate. Figure 4 b) shows a flow diagram of an exemplary localisation method. The localisation comprises steps 200 through 240. Inputs to the localisation are the RSS value vectors ^_^ for each of the individual ^-th object obtained at all ^ receivers, the receiver coordinates ∀^, the coordinates ∀^ of the training nodes, and the optimised weight parameters ^^∗ _^ and ^^∗ _^ , which are received in step 200. In step 210 covariance matrices between the training RSS and the actual objects’ RSS data are computed via equation (36), and in step 220 the conditional mean and covariance are computed via equations (38a) and (38b), respectively. Next, in step 230, the marginalised mean is computed via equation (40a), which is output in step 240. The effectiveness of the proposed SGD-based robust training, using the RSSI- based GPR localisation method is evaluated via computer simulations, and compared against the method discussed in "Machine learning methods for RSS- based user positioning in distributed massive MIMO,” which utilises conjugate gradient (CG) to train a GPR localisation model with single-path RSSI. 202302178 -18- The considered scenario is a street intersection containing K = 3 objects, in a ROI of 100m×100m, serviced by M = 63 sensors placed along the roadsides. Training is conducted over a grid of K = 155 training locations distributed in a regular grid within the area, as illustrated in Figure 5. Environment parameters such as the reference path loss coefficient and exponent are set according to the 3GPP urban micro propagation model described in 3GPP, “Evolved universal terrestrial radio access (E-UTRA); further advancements for E- UTRA physical layer aspects,” 3rd Generation Partnership Project, Tech. Rep. 36.814, 2017. Radio parameters such as transmit/noise powers and radio sensitivity are set according to the LTE standard, e.g., as presented by J. Salo, M. Nur-Alam, and K. Chang, in “Practical introduction to LTE radio planning,” in Proc. Eur. Commun. Eng., Espoo, Finland, White Paper, Nov.2010. Finally SGD parameters are varied such that mini batches of smaller and larger sizes are considered. These parameters are summarized in Table I shown below, and will be consistently utilized hereafter, unless when otherwise stated. Parameter Value ^_^ = −47.5 dB Path-loss parameters 0, if ^_^^ < 10 m (3GPP UMi) ^ = ^ 2, if 10 m ≤ ^_^^ ≤ 45 m 6.7, otherwise UE transmit power ^^{^^} = 21dBm(125 mW) Noise power _^^ ^{^^^} = −107.5dBm Receiver sensitivity _^ ^{^^} _{= −106.5dBm} K^{^} ={5, 50} SGD parameters B·K^{^} = 1000 S = 200, ^ (^) ^_^^ = 100 Table I: Simulation parameters 202302178 -19- The noise power in the system is defined as −107.5dBm with a receiver sensitivity of −106.5dBm, meaning that if the RSS at a receiver is below the receiver sensitivity, the signal is assumed to have noise power. It can be seen from the cloud of points formed by the location estimates, represented by the cross symbols, that the proposed robust approach, whose estimates are all located inside the dashed ovals, is indeed superior to the known method, which has only few estimates inside the dashed ovals. The true locations of the objects are represented by the filled black dots inside the dashed ovals, while the training locations are represented by the small dots, and the locations of the receivers are shown as circles along the sides of the exemplary road intersection. A more quantitative assessment of the gains achieved by the method proposed herein in relation to the known method can be had by comparing the performances in terms of the location root mean square error (RMSE), defined as where ^[^True ^ , ^_^ ^{True ]^} denote the true coordinates of the ^-th object, while ^^^ ^ ^^_^ , ^_^ ^{^^^} ^ are the corresponding estimates obtained by the respective method. The results are given in Figure 6, and clearly show a wide gap between the GPR- based localisation with the proposed robust training methods and the known method, with the smaller mini-batch size outperforming the training with a larger mini-batch size. Here, the root mean square error (RMSE) of the object coordinates is selected as a target metric to evaluate and compare the localisation performance of the algorithms. In light of the foregoing discussion, in a first aspect of the present invention a method of locating one or more objects emitting wireless signals, in an environment having at least two receivers adapted to at least determine RSS values of the one 202302178 -20- or more object’s wireless signals is presented. The at least two receivers have known positions in the environment and are communicatively connected to a common computing unit. The method comprises, at the common computing unit, determining an optimised RSS value-based coordinate mapping function for the environment under consideration of noisy RSS training values, using the known positions of the receivers and of training objects. The training objects and their signals may be simulated. The method further comprises aggregating RSS values for each of the one or more objects and from each of the two or more receivers, and arranging the aggregated RSS values into received signal power vectors representing the RSS values of all of the one or more objects as determined in each of the receivers. The method yet further comprises mapping, for each object, vector containing the RSS values received by the two or more receivers onto x- and y- coordinates of the environment using the optimised RSS value-based coordinate mapping function. In accordance with one or more embodiments of the method, the optimised coordinate mapping function is derived by a Gaussian Process using the mean and covariance of the noisy RSS values of the training objects as input. In embodiments of the method, the optimised mapping function comprises determining a conditional distribution of the coordinates of the training transmitters and the actual transmitters, and determining a marginal distribution of the coordinates therefrom using weight parameters determined in a training phase. In accordance with one or more embodiments of the method, the parameters of the optimised coordinate mapping function are determined by iteratively feeding small batches of training data sets containing noisy training data of the training objects to a stochastic gradient descent process. In one or more embodiments the wireless signals are wireless communication signals and wherein the at last two receivers are adapted to determine identities of the one or more objects, which identities are transmitted in the respective wireless communication signals, and to transmit the identities to the common computing unit along with the respective RSS values. 202302178 -21- In accordance with second aspect of the present invention a receiver configured for use with the method presented hereinbefore is presented. The receiver comprises one or more software and/or hardware blocks configured for receiving a wireless signal from one or more objects emitting such signals, for determining at least an RSS value for the received signals, and for transmitting the signals to a common computing unit. In particular, the receiver comprises an antenna for receiving wireless signals from multiple one or more objects, one or more microprocessors, volatile and non-volatile memory, which are connected through one or more communication lines or buses. The non-volatile memory stores computer program instructions which, when executed by the one or more microprocessors, configure the one or more microprocessors to control software or hardware blocks or modules, or the combination thereof, to execute the receiving and the transmitting function mentioned above. In accordance with third aspect of the present invention a common compute unit of a wireless communication system comprising two or more receivers in accordance with the second aspect of the invention and configured for executing the method presented hereinbefore comprises one or more microprocessors, volatile and non- volatile memory, and an interface for communicatively coupling with two or more receivers, wherein the non-volatile memory stores computer program instructions which, when executed by the microprocessor, configure the common compute unit to execute the method in accordance with the first aspect of the invention. The methods described hereinbefore may be represented by computer program instructions. Accordingly, a computer program product comprises computer program instructions which, when executed by a microprocessor of a receiver, cause the microprocessor to execute methods in accordance with the first or third aspects of the present invention, and to accordingly control hardware and/or software blocks or modules of the receiver of an OTFS communication system in accordance with the first or third aspects of the invention as presented above. The computer program instructions may be retrievably stored or transmitted on a computer-readable medium or data carrier. The medium or the data carrier may by physically embodied, e.g., in the form of a hard disk, solid state disk, flash memory 202302178 -22- device or the like. However, the medium or the data carrier may also comprise a modulated electro-magnetic, electrical, or optical signal that is received by the computer by means of a corresponding receiver, and that is transferred to and stored in a memory of the computer. The method and apparatus proposed herein provide a basis for a robust object localisation based on RSS values of wireless signals emitted from the objects, in particular vehicles – autonomous or under human control – in noisy environments. The improved performance in the presence of noise is achieved, inter alia, by performing ML-based training using noisy training signals. Training the model trained using noisy training data with known positions of training users, and distributing the training data into mini batches, which are then fed to a stochastic gradient descent algorithm, leads to an optimisation of the model, which optimised model can be used with great advantage for improved localisation using RSS data from multiple transmitters. The method and apparatus proposed herein can be used in any wireless communication system environment, in particular in 6G communication systems and beyond, in indoor and outdoor environments, including industrial scenarios. BRIEF DESCRIPTION OF THE DRAWING The figures in the attached drawing are used for detailing aspects of the present invention. In the drawing Fig.1 shows a schematic representation of a system in accordance with the invention comprising a common computing unit, multiple receivers and multiple objects, Fig.2 shows a data cube used in embodiments of the invention, Fig.3 shows an exemplary block diagram of the major training steps, Fig.4 shows an exemplary flow diagram of the method steps in training and localisation, Fig.5 shows an exemplary scenario used in a simulation, Fig.6 shows a comparison of the method in accordance with the invention and prior art methods, 202302178 -23- Fig.7 shows an exemplary schematic block diagram of a receiver in accordance with the invention, Fig.8 shows an exemplary schematic block diagram of a common computing unit in accordance with the invention, In the figures, identical or similar elements may be referenced using the same reference designators. DETAILED DESCRIPTION OF EMBODIMENTS Figures 1 to 6 have been described further above and will not be discussed again. Figure 7 shows an exemplary schematic block diagram of a receiver, or RRH, 400 in accordance with the present invention. The receiver 400 comprises one or more antennas 402 and associated wireless interface circuitry 456, adapted to receive wireless signals from one or more objects, one or more microprocessors 450, volatile memory 452, non-volatile memory 454, and a communication interface 404 for communicating with a common compute unit 500. The aforementioned elements are communicatively connected via one or more signal or data connections or buses 458. The non-volatile memory 454 stores computer program instructions which, when executed by the microprocessor 450, cause the receiver 400 to receive wireless signals from one or more objects emitting such signals, to determine at least an RSS value for the received signals, and to transmit the signals to a common computing unit 500. Figure 8 shows an exemplary schematic block diagram of a common computing unit 500 in accordance with the present invention. The common computing unit 500 comprises one or more microprocessors 450, volatile memory 452, non-volatile memory 454, and a communication interface 404 for communicating with two or more receivers 400. The aforementioned elements are communicatively connected via one or more signal or data connections or buses 458. The non-volatile memory 454 stores computer program instructions which, when executed by the microprocessor 450, cause the common computing unit 500 to execute the method according to the first aspect of the invention as presented hereinbefore. 202302178 -24- LIST OF REFERENCE NUMERALS (PART OF THE DESCRIPTION) 100 method 220 compute conditional mean and 110 receive input data covariance matrices 120 determine RSS training data 230 compute marginalised mean 130 split training data into mini 240 output marginalised mean batches 140 feed mini batches to process 400 receiver/RRH 150 compute gradients 402 antenna 160 update intermediate optimised 404 interface values 450 microprocessor 170 termination criterion met? 452 volatile memory 180 termination criterion met? 454 non-volatile memory 190 output optimised weight 456 wireless interface circuitry parameters 458 signal/data connection/bus 200 receive input data 500 common computing unit/CU 210 compute covariance matrices

Claims

202302178 -25- CLAIMS 1. A method of locating one or more objects emitting wireless signals, in an environment having at least two receivers (400) adapted to at least determine RSS values of the one or more object’s wireless signals, the at least two receivers (400) having known positions in the environment and being communicatively connected to a common computing unit (500), the method comprising, at the common computing unit (500): - determining an optimised RSS value-based coordinate mapping function for the environment under consideration of noisy RSS training values, using the known positions of the receivers (400) and of training objects, - aggregating RSS values for each of the one or more objects and from each of the two or more receivers (400), - arranging the aggregated RSS values into received signal power vectors representing the RSS values of all of the one or more objects as determined in each of the receivers (400), - mapping, for each object, vectors containing the RSS values received by the two or more receivers (400) onto x-and y-coordinates of the environment using the optimised RSS value-based coordinate mapping function. 2. The method of claim 1, wherein the optimised coordinate mapping function is derived by a Gaussian Process using the mean and covariance of the noisy RSS values of the training objects as input. 3. The method of claim 2, wherein the parameters of the optimised coordinate mapping function are determined by iteratively feeding small batches of training data sets containing noisy training data of the training objects to a stochastic gradient descent process. 4. The method of one or more of claims 1 to 3, wherein the wireless signals are wireless communication signals and wherein the at last two receivers (400) are adapted to determine identities of the one or more objects, which identities are transmitted in the respective wireless communication signals, 202302178 -26- and to transmit the identities to the common computing unit (500) along with the respective RSS values. 5. A receiver (400) of a wireless communication system comprising an antenna (402) and associated receiving circuitry, one or more microprocessors (450), volatile (452) and non-volatile memory (454), and an interface (404) for communicatively coupling with a common computing unit (500), wherein the non-volatile memory (454) stores computer program instructions which, when executed by the microprocessor (450), configure the receiver (400) to at least determine RSS values of wireless signals of one or more objects and to communicate the RSS values to the common computing unit (500). 6. The receiver of claim 5, wherein the computer program instructions, when executed by the microprocessor (450), configure the receiver (400) to determine an identifier of the one or more objects and to communicate the identifier along with the RSS values to the common computing unit (500). 7. A common compute unit (500) of a wireless communication system comprising two or more receivers (400) in accordance with claim 5 or 6, the common compute unit (500) comprising one or more microprocessors (450), volatile (452) and non-volatile memory (454), and an interface (404) for communicatively coupling with two or more receivers (400), wherein the non-volatile memory (454) stores computer program instructions which, when executed by the microprocessor (450), configure the common compute unit (500) to execute the method of one or more of claims 1 to 4. 8. Computer program product comprising computer program instructions which, when executed by a microprocessor, cause a computer and/or control hardware blocks, modules or components of a receiver (400) in accordance with claim 5 or 6 to at least determine RSS values of wireless signals of one or more objects and to communicate the RSS values to the common computing unit (500), or cause a computer and/or control hardware blocks, modules or components of a of a common compute unit (500) in 202302178 -27- accordance with claim 7 to execute the method of one or more of claims 1 to 4. 9. Computer readable medium or data carrier retrievably transmitting or storing the computer program product of claim 8. 10. A wireless communication system comprising two or more receivers (400) in accordance with claims 5 or 6, which are communicatively connected to a common compute unit (500) in accordance with claim 7.