Positioning method and device for implementing same

Abstract

It is proposed a method of locating an object transmitting a wireless signal in an environment having at least two receivers adapted to determine RSSI values of the wireless signal of the object. The receiver has a known location in the environment and is communicatively connected to a common computing unit. The method includes determining, at the common computing unit, an optimized RSSI value-based coordinate mapping function for the environment using known positions of the receiver and the training object while taking into account shadow noise. RSSI values for the object and from each receiver are aggregated. The aggregated RSSI values are arranged into a received signal power vector that includes a sum of the RSSI values determined at all receivers for each individual object. For each object, a vector containing RSSI values received by the receiver is mapped onto x-coordinates and y-coordinates of the environment using an optimized mapping function.

Description

Technical Field

[0001] This invention relates to the field of object localization using wireless signals (particularly wireless communication signals) emitted by an object.

[0002] mark

[0003] In this specification, bold symbols represent vectors or matrices. Scalar values ​​are represented in italic lowercase letters, such as x. Superscripts T and H denote the transpose and complex conjugate transpose of a vector or matrix, respectively. Background Technology

[0004] Over the past few decades, wireless positioning technology has received significant attention and development, particularly in the field of autonomous vehicles, where knowing the vehicle's location is crucial for safe and efficient operation. Location information can be further used to track vehicles and predict their paths, which can aid in collision prevention or detection. Other applications of wireless positioning include near-field radio frequency identification (RFID) positioning in smart factories, homes, and other applications, as well as Internet of Things (IoT) sensor networks.

[0005] Traditional positioning technologies typically rely on Global Navigation Satellite Systems (GNSS) to obtain satellite-based geolocation and timing information. However, such methods exhibit poor power efficiency, accuracy, latency, and robustness in dense urban scenarios, especially for applications exceeding the expected requirements of fifth-generation (B5G) communication.

[0006] Therefore, alternative positioning systems have been investigated to utilize wireless signals from closer environments, such as wireless sensors, devices, and access points. These systems use captured signal metrics, such as time of arrival (ToA), angle of arrival (AoA), or received signal strength information (RSSI) values, to estimate the corresponding location of the signal source. Due to the distributed nature of such positioning scenarios, the required methods typically must solve a multidimensional, multivariate optimization problem based on the signal metrics received at the sensors, where the location information of the signal source or target is the solution.

[0007] To alleviate such challenging optimization problems, recently proposed methods utilize machine learning (ML) techniques.

[0008] For example, in "Autonomous 3d UAV localization using Taylor series linearized TDoA-based approach with machine learning algorithms" (13th International Conference on Convergence of Information and Communication Technologies (ICTC), 2022, pp. 783-785), V. Tilwari and S. Pack suggest using supervised ML methods to evaluate Taylor series linearized Time Difference of Arrival (TDoA) measurements for the localization of autonomous UAVs. In "A deep learning based AoA estimation method in NLOS environments" (IEEE Globecom Workshop (GC Wkshps), 2021, pp. 1-6), YMT Wang and Y. Shen use deep residual networks to evaluate AoA measurements in single-sensor non-line-of-sight (NLOS) indoor environments.

[0009] NTAMI Al Hajri and RM Shubair, in their paper "Indoor localisation for IoT using adaptive feature selection: A cascaded machine learning approach" (IEEE Antennas & Radio Propagation Letters, Vol. 18, No. 11, pp. 2306-2310, November 2019), propose a method for integrating heterogeneous sensor information. Specifically, they use the K-Nearest Neighbor (KNN) algorithm to adaptively select and combine various signal radio frequency (RF) features for indoor localization.

[0010] A growing trend is to operate solely using RSSI values ​​at sensors, where the advantageous feature is that the encoded information of the wireless signal itself is uncorrelated, making it usable for other applications such as communications or channel estimation. Furthermore, there is no need to embed specific information for localization purposes into the wireless signal. For example, in “RSS-based multiple sources localization with unknown log-normal shadow fading” (arXiv:2110.10435v1, 2021), Y. Chu, W. Guo, K. You, L. Zhao, T. Peng, and W. Wang proposed detecting RSSI values ​​at distributed sensors and using this information to localize targets transmitting signals on a discrete grid. The target's location is initially estimated via sparse dictionary updates and K-means clustering, and iteratively refined through dynamic dictionary updates.

[0011] While existing technological methods offer feasible solutions for specific environments and scenarios, they provide suboptimal accuracy in the presence of noise and are mostly only applicable to limited indoor environments. Summary of the Invention

[0012] Therefore, it is desirable to provide a positioning method and an apparatus for implementing the method that exhibits improved robustness and accuracy in noisy environments.

[0013] This need is addressed by the method of claim 1, the receiver of claim 6, the common computing unit of claim 8, and the computer program product of claim 9. A corresponding computer-readable storage medium is provided in claim 10. Embodiments and improvements of the method and apparatus are provided in the respective dependent claims.

[0014] According to a first aspect of the invention, a noise-resistant localization method is proposed, which estimates the two-dimensional (2D) location of one or more objects using only the RSSI values ​​of wireless signals emitted by the objects and received at a distributed receiver. Specifically, to improve the robustness of noise estimation, an optimized Gaussian process regression (GPR) model is proposed and trained using noisy RSSI data from previously trained locations via a mini-batch stochastic gradient descent (SGD) scheme, wherein the gradients are given in closed-form. Furthermore, a pair of robust marginalization procedures for estimating the target location is also provided.

[0015] The invention will be described below, assuming a multi-user (MU) distributed massively multi-input multiple-output (DM-MIMO) scenario consisting of K single-antenna transmission devices (also called objects or targets), each served by M single-antenna remote radio heads (RRHs) (also called receivers or sensors), the receivers being centrally connected to a computing unit (CU) via an error-free fronthaul link with infinite rate, as follows. Figure 1 The image is depicted schematically.

[0016] No. The receiver and the first The two-dimensional position of each object (where and Each is described by a 2D coordinate vector.

[0017]

[0018] in and These are the x and y coordinates of the m-th receiver and the k-th object, respectively.

[0019] Based on the above, the Euclidean distance between the m-th receiver and the k-th object is given by the following formula.

[0020]

[0021] The signal vector received at the m-th receiver in T consecutive transmission instances is given by the following formula.

[0022]

[0023] in, It is the channel gain between the m-th receiver and the k-th object, assumed to remain constant over T transmissions. and These are the transmission power from the k-th object and the arbitrary transmission symbol vector, respectively. XN This is the additive white Gaussian noise (AWGN) received at the m-th receiver. In this specification, it is assumed that the transmitted power of all objects is uniform, such that... .

[0024] The flat fading uplink channel gain coefficient in equation (3) Further modeling using the following formula

[0025]

[0026] in, It is a small-scale fading factor, and It is the large-scale fading factor, which is given by the following formula:

[0027]

[0028] in This represents the reference path loss coefficient, i.e., the path loss at the reference distance, and This represents the path loss index determined by environmental assumptions. and These are the distance defined in equation (2) and the channel gain caused by the shadowing of the path between the m-th receiver and the k-th object, respectively.

[0029] Given the above, the RSSI value of the signal received by each k-th object at the m-th receiver is obtained by the following formula.

[0030]

[0031] Semi-blind estimation can be performed using short orthogonal pilot sequences and independent payload data, as illustrated by KNRSV Prasad, E. Hossain, and VK Bhargava in "Machine learning methods for RSSI-based user positioning in distributed massive MIMO" (IEEE Transactions on Wireless Communications, Vol. 17, No. 12, 2018), or by HQ Ngo et al. in "Cell-free massive MIMO versus small cells" (IEEE Transactions on Wireless Communications, Vol. 16, No. 3, 2017). Alternatively, it can be performed blindly by utilizing the sparsity caused by intermittent user activity, such that only a relatively small subset of random transmitters share the channel at each transmission time, as illustrated by H. Djelouat, M. Leinonen, and M. Juntti in "Joint estimation of clustered user activity and correlated channels with unknown covariance in mmTC". As shown in “mmtc” (ICASSP 2023 - IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2023, pp. 1-5), based on the following relationship

[0032]

[0033] Among them, W [ω1 … ω K ] and p m [p m1 … p mK ] T These represent the matrices that collect transmitted signals and power from all K transmitters at the m-th sensor.

[0034] p mK It can be equivalent to decibels Scale is expressed as

[0035]

[0036] in and ,and It refers to radio sensitivity.

[0037] Therefore, the RSSI values ​​from all objects and from all M receivers are aggregated at CU and stacked into a vector (in order to...). (in units), as shown below

[0038]

[0039] The multi-object problem presented above requires a suitable solution to achieve a feasible implementation. According to the present invention, an ML-based solution to the multi-object localization problem is proposed, which effectively transforms... For the optimization problem of real-valued 2D coordinates, given The aggregated RSSI value at each RRH and The known locations of the RRHs. Specifically, the proposed solution is described in three sections:

[0040] - Object coordinate model based on Gaussian process regression (GPR)

[0041] - A training method using noisy training data via mini-batch SGD, and

[0042] - The process of approximating unknown coordinates using the GPR method.

[0043] It should be noted that some aspects of the GPR-based coordinate model, SGD training process, and GPR localization process are discussed in German patent application no. 10 2023 204 636.9, filed by the same applicant and specifying the same inventors, which is hereby incorporated herein by reference in its entirety. Furthermore, the method presented herein can be used with both perfect and noisy training data.

[0044] In the following sections, we will discuss coordinate models based on GPR, considering two arbitrary functions. and They respectively map the received signal power vector of any k-th object to its x and y coordinates, i.e.

[0045]

[0046] This means that if in Given function and If the aggregated RSSI value is known, then the location of any object can be obtained.

[0047] Note: Since the expressions for the x-coordinate and y-coordinate functions and their derivatives are the same, subscripts and scalars will be omitted from now on for the sake of brevity. and Unless otherwise stated, the following expressions are assumed to apply equally to both x-coordinates and y-coordinates. The letter 'c' can sometimes be used to indicate any subscript, and these are interchangeable.

[0048] In the proposed method, GPR is used to model the coordinate mapping function, where it is first assumed that the objective function is extracted from a user-defined Gaussian process (GP) prior, i.e.

[0049]

[0050] in, This represents a matrix with zero mean and covariance. The GP prior, whose elements in the k-th row and q-th column are determined by the covariance function This is given, depending on the RSSI value between the k-th object and the q-th object.

[0051] To accurately model the relationship between RSSI values ​​and coordinates, a covariance function must be designed to carefully capture the covariance between any two objects in the region of relevance (ROI) of the system under consideration. The proposed method follows the covariance function proposed in "Machine learning methods for RSSI-based user positioning in distributed massive MIMO" (ibid.), which is designed to capture pairs of stationary and non-stationary transmitter objects, as follows:

[0052]

[0053] in, and These are the RSSI vectors of the k-th and q-th objects, respectively. It is the variance of the measurement error. It is an indicator variable (if) Then the value is 1, and if Then the value is 0), and the parameter These are the weight parameters to be learned, where

[0054]

[0055] in M is the weight corresponding to each RSSI vector in the exponential term of the covariance function defined in equation (12).

[0056] Based on the above, it can be seen that having an RSSI vector that yields the covariance matrix can be used to evaluate the GP in equation (11). To obtain the actual coordinate values, this requires the covariance function. One unknown weight parameter This section describes the optimization of the covariance function.

[0057] For convenience, the covariance matrix is ​​collected. A vector of unknown weight parameters is defined as

[0058]

[0059] In addition, a coordinate set c corresponding to the K training positions is defined. K×1 and the associated training RSSI vector set p k M×1, where k = 1, …, K.

[0060] Similarly, a corresponding training covariance matrix is ​​defined that is associated with the K training locations and their corresponding RSSI values. K×K And the cross-covariance matrix between the K training locations and the K target locations, constructed from the corresponding RSSI value sets. K×K .

[0061] According to the conventional GP method, the joint distribution of the coordinate vectors of the training position and the target position is given by the following equation:

[0062]

[0063] in K×K The kth row and kth column are defined by ϕ(p) k , p k The result is given by equation (12).

[0064] Having the joint distribution in equation (15), the conditional distribution of c is given by the following equation.

[0065]

[0066] Where the conditional mean vector µ K×1 The covariance matrix C K×K Obtained by the following formula

[0067]

[0068] Finally, the edge distribution of individual object coordinates can be obtained as follows:

[0069]

[0070] Among them, c k and v k Let be the marginal mean and variance of the estimated coordinates of the k-th target, respectively, given by the following formula.

[0071]

[0072] in,[·] k and[·] k,i Let c represent the k-th element of the vector and the matrix elements at the k-th row and i-th column, respectively. kIt is Gaussian distributed, so the marginal mean c k It's directly x k The maximum a posteriori estimate is thus the final predicted coordinate of the k-th object. From the above procedure, it can be inferred that the performance of the GPR-based RSSI localization algorithm is highly dependent on the accuracy of the covariance matrix model given in equation (13), which is essentially determined by the parameter vector θ. In other words, the core step of this method is to optimally determine θ given a certain amount of training data.

[0073] The authors of "Machine learning methods for RSSI-based user positioning in distributed massive MIMO" (ibid.) propose using maximum likelihood fitting of the distribution of training coordinates c, given K RSSI vectors p k The corresponding set is assumed to be error-free. This assumption is not only almost impossible to satisfy in practice, because assuming that RSSI values ​​can be obtained without any error implies the need for extremely high-power or extremely large numbers of pilot signals, which is already idealized in the case of a single transmitter-sensor pair, let alone in multi-target-multi-sensor and multi-path scenarios; it is also the reason for poor performance in practical applications, because the design cannot mitigate the inevitable error in the collected RSSI values.

[0074] The embodiments of this invention address this unrealistic assumption by proposing a noise-resistant training solution to determine the parameter vector θ, thus providing feasibility and robustness even for known methods, and significantly improving the multi-target localization problem described above. The noise-resistant training solution effectively transforms into an optimization problem for K pairs of real-valued 2D coordinates, given the aggregated RSSI values ​​of M receivers and the known positions of the M receivers, which is solved via SGD.

[0075] The implementations of these proposed methods adapt to random shading noise in the true RSSI values ​​by assuming that such random shading noise also exists in the training data. Therefore, the training RSSI vector used to obtain the optimal parameter vector θ is also modeled as...

[0076]

[0077] in .

[0078] This is equivalent to not treating the coordinates c of the training points as deterministic, but rather as random variables with a certain distribution. In the GPR model, this distribution can be assumed to be approximated by the following equation.

[0079]

[0080] Wherein, the covariance matrix Ψ ∈ K×K The elements are determined by equation (12), that is

[0081]

[0082] in Indicates subject to specific weight parameters Constrained covariance function.

[0083] Given the distribution in equation (21), the optimal weight parameter θ can be determined as the solution to the maximum likelihood problem.

[0084]

[0085] Wherein, the target g(θ; p1, …, p) K ) is implicitly defined, and for training purposes, it is a function of the parameter vector θ, as highlighted by the notation, and given the Gaussian approximation in equation (21), it can be modeled as

[0086]

[0087] Where |·| represents the determinant of the independent variable matrix. It is clear from equations (12), (22), and (24) that g(θ; p1, …, p K The matrix Ψ is not convex with respect to the optimization variable θ. In fact, from the perspective of optimization theory, the determinant operation and inverse operation of Ψ, and the latter with respect to the parameters β collected in matrix B, are not convex. m The nonlinear dependence of this makes the problem extremely difficult to solve. The authors of "Machine learning methods for RSSI-based user positioning in distributed massive MIMO" (ibid.) turned their attention to other matters and largely failed to solve this problem, limiting the discussion to citing gradient-based methods and classic literature on the subject.

[0088] As mentioned above, according to the present invention, this problem is solved via the SGD method, for example, as discussed by S. Ruder in “An overview of gradient descent optimization algorithms” (arXiv preprint arXiv: 1609.04747, 2016). For this purpose, we first consider g(θ; p 1, …, p K The partial derivative with respect to α is given by the following formula.

[0089]

[0090] Next, we will use the matrix derivative identity.

[0091]

[0092] The expression in equation (25) is simplified to

[0093]

[0094] It is observed that equation (24) with respect to β m and The partial derivatives of are in the same form as those in equation (27). The derivation details corresponding to the parameters of the latter are omitted here, and only information about is provided. β m and The expression for each element of the partial derivative Ψ is given by the following formula.

[0095]

[0096]

[0097] in yes The m-th element, and the notation This represents the matrix element located at the k-th row and i-th column.

[0098] Then, the gradients of the objective function in equation (24) can be put together to obtain...

[0099]

[0100] This allows the optimal parameter vector θ to be optimized via gradient descent (GD) according to the update equation.

[0101]

[0102] Where, θ (i-1) and θ (i)These are the parameter vectors for the (i-1)th and i-th SGD iterations, respectively, while λ is the learning rate. To ensure convergence, the learning rate is constrained by the Lipschitz condition.

[0103]

[0104] Where L represents the Lipschitz constant, given by the following equation.

[0105]

[0106] While the above training procedure can be performed on large datasets consisting of multiple data snapshots collected from numerous training locations, this can result in highly complex training algorithms, as the complexity of the training algorithm is fundamentally determined by the covariance matrix. The inverse determination is as shown in equation (29).

[0107] Therefore, this invention further proposes a variation of the general training scheme based on mini-batch SGD, as described in the following section. In the proposed mini-batch SGD method, for multiple applications of the SGD process, the total training data is divided into several mini-batches of size S, which results in a significantly lower complexity for the implementation compared to the implementation using large datasets.

[0108] First, define a training data cube. It includes each and all RSSI vectors. S noisy snapshots, of which And s ∈ {1, …, S}. Mini-batch Depend on training RSSI vectors Composition, the vector is from Randomly selected from among them, with equal and mutually exclusive probabilities, such that and .

[0109] For ease of notation, the training position corresponding to the given b-th mini-batch is relabeled as... And relabel the corresponding RSSI vector as This allows the small batch to be described as .

[0110] Next, consider a structure similar to that of equation (22) but only for the training position vector. The covariance matrix to be constructed, i.e.

[0111]

[0112] Then, under the SGD method, small batches are obtained through the strain type of equations (29) and (31). parameter vector The update, i.e.

[0113]

[0114]

[0115]

[0116] Figure 2 An exemplary data cube is shown. The exemplary data cube Δ corresponds to the case where the number of receivers is M = 5, the number of training locations is K = 7, and the total number of snapshots of the RSSI vector at each training location is S = 8. The gray column shows the mini-batch Δ. b Examples, where The exemplary mini-batch includes those corresponding to the training positions. A series of random RSSI vectors, such that Taken from snapshots respectively ,get

[0117]

[0118] Figure 3 The parameters for the mini-batch implementation using data cubes via mini-batch SGD are given in the document. A schematic diagram of the optimization method. Figure 4 The schematic flowchart further illustrates this optimization method. It should be noted that this method requires processing each coordinate... and Running independently allows its execution to be optimized (i.e., trained) by parameters. and .

[0119] The input to the training process is a data cube. (with each and all RSSI vectors) S snapshots, where k ∈ {1, …, K} and s ∈ {1, …, S}), the number B of mini-batches, and their size. Number of SGD iterations per mini-batch and initial parameter vector They are received in step 110. In step 120, from the data cube... Obtain small batches Each small batch includes Mutually exclusive training RSSI vectors ,in In step 130, a mini-batch is fed into the iterative calculation process. In step 140, the covariance matrix is ​​constructed according to equation (32). And in step 150, the gradient is calculated via equation (33). ( ; p1, …, p K In step 160, update according to equation (34). The process of calculating the gradient and updating the intermediate optimized values ​​is repeated iteratively until a termination criterion is met, which is checked in step 170. If the termination criterion is not met, i.e., the "No" branch of step 170, the next iteration is executed. Suitable termination criteria include, in particular, a predetermined maximum number of iterations. Or intermediate optimized values The convergence occurs below a predetermined threshold. The convergence criterion may also include that this convergence is stable over a predetermined number of subsequent iterations. Once the termination criterion is satisfied in step 170 (the "Yes" branch of step 170), step 180 checks whether the last of the B mini-batches has been fed into the computation process. If not, i.e., the "No" branch of step 180, the process returns to step 120 and repeats. If all mini-batches have been fed into the computation process, i.e., the "Yes" branch of step 180, the training phase is complete, and the weight parameters are output in step 190. The optimized value.

[0120] Next, we will describe RSSI-based localization via GPR. This will be done using the parameter vectors obtained through training as discussed above. In the case of a given online RSSI measurement value Offline obtained noise-free training RSSI vectors and the associated covariance matrix The RSSI-based localization algorithm via GPR discussed in “Machine learning methods for RSSI-based user positioning in distributed massive MIMO” (ibid.) simplifies to the evaluation equation (19a) for each k-th target.

[0121] In addition to using the optimized parameter vectors obtained in some implementations through the aforementioned "noisy" training methods, In addition, another difference between the proposed robust method and known methods is that it does not use noise-free training RSSI vectors, but instead uses vectors containing training RSSI vectors. The entire data cube of multiple snapshots This leads to different alternatives for calculating GPR-based location estimates.

[0122] For example, one alternative is to use a data cube. Each RSSI vector in These are considered as clear, noise-free data points, and corresponding KS values ​​are constructed. KS covariance matrix

[0123]

[0124] in

[0125]

[0126] Then, the training position vector c is stacked S times, which can be done via the Kronecker product. In short, the position of an object can be obtained by a variation of the following equation (19a).

[0127]

[0128] The complexity of evaluating equation (37) is As the number of training points K and / or snapshots S increases, this complexity quickly becomes unacceptable, making the method described here for completeness unrecommended and not to be pursued further.

[0129] A lower-complexity alternative to the latter approach is obtained by independently performing location estimation on each snapshot of the data cube using the covariance matrix from the corresponding vectors, and then averaging the results. This will be referred to below as the 'Estimate Then Average' (EA) method, and can be concisely expressed as follows:

[0130]

[0131] The method summarized by equation (38) requires S snapshots K K covariance matrices Find the inverse so that its complexity is O(n). The order, while much less complex than equation (37), may still be too high for larger S.

[0132] In this case, an alternative with lower complexity (of order 1) The method, referred to below as the 'Average Then Estimate' (AE) method, utilizes the sample covariance matrix.

[0133]

[0134] The location estimate was determined in the following manner.

[0135]

[0136] Among them, expected Taken from data cube S data snapshots are taken. Here, all covariance matrices are first constructed, and their average is used for location estimation. Similarly, the RSSI vectors are averaged before determining the location based on the RSSI vectors.

[0137] The RSSI-based localization schemes proposed by the AE-GPR and EA-GPR methods are summarized in pseudocode below, and are divided into alternative scheme 2a) and alternative scheme 2b, respectively.

[0138] Input: Data cube Having each and all RSSI vectors S snapshots, and and RSSI values ​​measured for all objects ; and the optimized parameter vector .

[0139] Output: Estimated target x and y coordinate vectors or .

[0140] repeat

[0141] 1: Calculate the covariance matrix of all snapshots via equation (36) ;

[0142] 2a) EA positioning method:

[0143] 2: Calculate and return the estimated object position via equation (38). ;

[0144] 2b) AE positioning method:

[0145] 2: Calculate the sample covariance matrix using equation (39) ;

[0146] 3: Calculate and return the estimated object position via equation (40). ;

[0147] In the following sections, the effectiveness of the proposed SGD-based robust training mechanism and the corresponding RSSI-based robust localization method via EA / AE-GPR are evaluated through computer simulations and comparisons with known methods presented in "Machine learning methods for RSSI-based user positioning in distributed massive MIMO" (ibid.).

[0148] Figure 5 It shows different mini-batch sizes A comparison of the average convergence behavior of the proposed robust training algorithm based on mini-batch SGD as a function of the gradient descent epoch. This is to compare the convergence behavior of the algorithm used for optimizing the parameter vector. To maintain fairness in the comparison regarding the total amount of training data, the number of mini-batch Bs varies, making... The same applies to all curves.

[0149] The results show that smaller mini-batches lead to slower convergence, but also result in lower points in the objective function, while larger mini-batches lead to faster convergence, but result in higher local minima. This is a typical trade-off between convergence speed and optimality found in mini-batch-based SGD schemes.

[0150] Next, the proposed EA / AE-GPR-based localization method is evaluated, and its performance is compared with that of known RSSI-based GPR schemes proposed in "Machine learning methods for RSSI-based user positioning in distributed massive MIMO" (ibid.).

[0151] The scenarios under consideration include A street intersection with a target, where ROI is... placed along the roadside 56 sensor services. (For example...) Figure 6 As shown, the distribution within a regular grid within the region Training is performed on a training location grid. Environmental parameters such as reference path loss coefficient and exponent are set according to the 3GPP City Micro-Propagation Model described in 3GPP "Evolved Universal Terrestrial Radio Access (E-UTRA); Further advances for E-UTRA physical layer aspects" (3GPP, Technical Report (TR) 36.814, 032017, Version 9.2.0 [online]). Accessible at: https: / / portal.3gpp.org / desktopmodules / Specifications / SpecificationDetails.aspx?specificationId=2493.

[0152] Radio parameters such as transmit / noise power and radio sensitivity are set according to the LTE standard, for example, as discussed in "Practical introduction to LTE radio planning" by J. Salo, M. Nur-Alam, and K.-K. Chang in 2010, and the final SGD parameters are based on... Figure 5 The results show that the optimized objective function achieves a low convergence point with small batch sizes. Path loss parameters. ,and Defined by the 3GPP city micro-propagation model, as defined in 3GPP "Evolved Universal Terrestrial Radio Access (E-UTRA); Further advancements for E-UTRA physicallayer aspects" (ibid.), and Transmission power Defined by the LTE standard, for example, as discussed in "Practical introduction to LTE radioplanning" (ibid.). Additionally, the noise power in the system is defined as... The receiver sensitivity is This means that if the RSSI at the receiver is lower than the receiver sensitivity, the signal is assumed to have noise power.

[0153] The following table summarizes these parameters:

[0154]

[0155] Figure 6 The estimates obtained by running the proposed method and known methods multiple times are shown. The measurement noise variance is... = 1, and the proposed AE-GPR algorithm uses a parameter vector. The parameter vector is trained in the manner described above, where the mini-batch size is... = 5 and B = 200.

[0156] To facilitate comparison with known methods used for this purpose, and for visibility, the proposed method is represented only by a robust AE-GPR alternative of lower complexity, as shown below, which exhibits slightly inferior performance compared to the EA-GPR alternative. The point cloud representation of the location estimates demonstrates that the proposed robust method indeed outperforms known methods.

[0157] By comparing the performance of the root mean square error (RMSE), a more quantitative evaluation of the gains achieved by the proposed method compared to known methods can be made. RMSE is defined as...

[0158]

[0159] in, Let represent the true coordinates of the k-th target, and These are the corresponding estimated values ​​obtained through appropriate methods.

[0160] To provide a lower bound reference, it also includes location estimates corresponding to those obtained via the genie-assisted (GA)-GPR scheme. The result is calculated via the following expression.

[0161]

[0162] in It is a noise-free RSSI vector generated by the following

[0163]

[0164] and This is the corresponding noise-free covariance matrix, which is obtained using an optimized parameter vector. The optimized parameter vector was constructed using the noise-resistant mini-batch training method proposed above, i.e.

[0165]

[0166] The results are as follows Figure 7 As shown, where Figure 7 a) shows small batch sizes ( = 5) result, and Figure 7 b) shows large small batches ( = 50). It is evident that the proposed robust EA / AE-GPR method lags significantly behind the known methods proposed in "Machine learning methods for RSSI-based user positioning in distributed massive MIMO" (ibid.). It should also be noted that the proposed alternative with the lowest computational complexity, the AE-GPR scheme, is slightly superior to the computationally more computationally demanding proposed EA-GPR method.

[0167] It is equally evident that both the proposed AE-GPR and EA-GPR robust algorithms achieve RMSE performance very close to that of the (infeasible) genie-assisted lower bound reference. This is because the GA-GPR reference scheme also uses parameter vectors obtained through the noise-resistant training method proposed in this paper. The results show that most of the gains obtained are actually due to the proposed SGD-based training method, and the remaining gap between the EA / AE-GPR method and the GA-GPR reference is only due to the amount of available data.

[0168] Figure 7 The results in b) confirm the latter finding that the proposed robust AE-GPR and EA-GPR algorithms asymptotically approach the same performance as the genie-assisted reference, indicating that when using a larger mini-batch size... At that time, the performance of these schemes was indeed very similar.

[0169] To further evaluate the proposed method, Figure 8 The CDF curve of the RMSE of the location estimate is given in the figure, where Figure 8 a) is and Figure 8 b) is And the noise variance is It needs to be emphasized that... This choice is disadvantageous to the proposed method because the latter's gain relative to known methods is... Figure 7 The figure shows that the improvement achieved with this parameter increases. Nevertheless, the results clearly demonstrate that the improvement achieved with the proposed method is not only significant in terms of the average value, but also significant across the entire RMSE range. Of particular note is that for larger mini-batch sizes, the performance of the proposed method overlaps with that of the ideal GA reference in the low RMSE range.

[0170] Finally, the number of sensors was evaluated. The impact on the performance of GPR-based methods. Therefore, in order to... Its influence is isolated from other factors (such as the geometry of the scene), in Figure 9 The solution was tested in a highly symmetrical single-target scenario as depicted in the paper, where the target is located at the center of the ROI and the sensor is symmetrically positioned in the surrounding environment, like it is installed on the side of a road at an intersection.

[0171] Figure 10 The diagram shows the number of sensors. The average RMSE of the function is given by the results, and it is further demonstrated that the proposed method not only always outperforms known methods, but also tends to approach GA performance as the number of sensors increases, especially the EA-GPR scheme.

[0172] The mini-batch, SGD-based, noise-resistant training process for optimizing the parameters of the GPR model for RSSI-based multi-target localization, along with either the alternative AE or EA marginalization procedure for computing the proposed corresponding location estimates, significantly outperforms the best known alternatives utilizing similar GPR-based methods, while approaching the performance of the genie-assisted (GA) scheme, which employs a training method combined with an infeasible marginalization procedure based on the true covariance matrix of RSSI data. It should be noted that the GA scheme is infeasible because it assumes an infinite amount of data.

[0173] It should be noted that although the invention has been described above using anti-training (i.e., assuming noisy training data), the AE and EA localization methods can also be used, assuming ideal, noise-free training data.

[0174] In view of the foregoing discussion, according to a first aspect of the invention, a method is proposed for locating one or more objects transmitting wireless signals in an environment having at least two receivers, the at least two receivers being adapted to at least determine the RSSI values ​​of the wireless signals of the one or more objects. The at least two receivers have known locations in the environment and are communicatively connected to a common computing unit. The method includes: at the common computing unit, determining an optimized RSSI-based coordinate mapping function for the environment using the known locations of the receivers and training objects, taking into account RSSI training values. Training objects and their signals can be simulated. The method further includes aggregating RSSI values ​​for each of the one or more objects and from each of two or more receivers, and arranging the aggregated RSSI values ​​into a received signal power vector, the received signal power vector representing the RSS values ​​of all one or more objects determined in each receiver. According to the invention, determining the optimized RSSI-based coordinate mapping function includes: establishing RSSI training values ​​between each of a first plurality of receivers at known locations and each of a second plurality of known training transmitter locations, establishing a plurality of values ​​for each pair of receivers and training transmitters, and arranging these values ​​into a series of snapshots, the snapshots representing the training RSSI vector for each training location. The elements of the vector are the trained RSSI values ​​between each receiver and its corresponding training location. Finally, to determine the location of the object, the method includes constructing all trained RSSI vectors for all snapshots. covariance matrix Then, in the first alternative of the two alternatives, the method includes using the corresponding covariance matrix for each object and each snapshot. A vector containing RSSI values ​​received by two or more receivers is mapped to the x and y coordinates of the environment, and the mean or median is calculated from all obtained locations. In a second alternative to the two alternatives, the method includes calculating multiple covariance matrices. The mean or median of each element is used, and the covariance matrix is ​​expected using the obtained mean or median. For each object, a vector containing RSSI values ​​received by two or more receivers (400) is mapped to the x and y coordinates of the environment.

[0175] In one or more embodiments of this method, an optimized parameter vector of the coordinate mapping function is derived via a Gaussian process using the mean and / or covariance of the RSS values ​​of the training objects as input. A Gaussian process can include a gradient descent process.

[0176] In an implementation of this method, determining the coordinate mapping function includes determining the conditional distribution of coordinates for the training transmitter and the actual transmitter, and using weight parameters determined during the training phase to determine the marginal distribution of the coordinates based on this conditional distribution.

[0177] In one or more embodiments of this method, the optimized parameter vector of the coordinate mapping function is determined by iteratively feeding a mini-batch training dataset containing training data of the training objects into the gradient descent process. .

[0178] In one or more embodiments of this method, the RSSI values ​​of the training objects are arranged in a data cube. In this data cube, the training RSSI vectors are contained. Multiple snapshots are taken, and the training vectors are arbitrarily selected from the data cube.

[0179] In one or more embodiments of the method, the wireless signal is a wireless communication signal, and at least two receivers are adapted to determine the identifier of one or more objects transmitted in the respective wireless communication signal, and transmit the identifier together with the corresponding RSSI value to a common computing unit.

[0180] According to a second aspect of the invention, a receiver is provided for use in a wireless communication system with the method described above. The receiver includes one or more software and / or hardware blocks configured to receive wireless signals from one or more objects transmitting such signals, to at least determine the RSSI value of the received signals, and to transmit the signals to a common computing unit.

[0181] The receiver includes one or more antennas and associated receiving circuitry for receiving wireless signals from one or more objects, one or more microprocessors, volatile and non-volatile memory, and an interface for communicatively connecting to a common computing unit. Elements or components of the receiver are connected or communicatively linked via one or more communication lines or buses. The non-volatile memory stores computer program instructions that, when executed by one or more microprocessors, configure the one or more microprocessors to control software or hardware blocks or modules or combinations thereof to at least determine the RSSI value of the wireless signals from one or more objects and at least transmit the RSSI value to the common computing unit.

[0182] In one or more embodiments, the receiver's non-volatile memory stores computer program instructions that configure the receiver to determine an identifier for one or more objects and transmit that identifier, along with an RSSI value, to a common computing unit.

[0183] According to a third aspect of the invention, a common computing unit is proposed for a wireless communication system comprising two or more receivers according to a second aspect of the invention. The common computing unit includes one or more microprocessors, volatile and non-volatile memory, and an interface for communicatively connecting to the two or more receivers. Elements or components of the common computing unit are connected or communicatively linked via one or more communication lines or buses. The non-volatile memory stores computer program instructions that, when executed by one or more microprocessors, configure the common computing unit (500) to perform the method according to the first aspect of the invention.

[0184] The method described above can be represented by computer program instructions. Therefore, the computer program product includes computer program instructions that, when executed by a microprocessor of a receiver according to the second aspect of the invention, cause the receiver's microprocessor and / or control hardware blocks, modules, or components to at least determine the RSSI value of a wireless signal of one or more objects and transmit the RSSI value to a common computing unit. When executed by a microprocessor of a common computing unit according to the third aspect of the invention, the computer program instructions cause the common computing unit's microprocessor and / or control hardware blocks, modules, or components to perform an embodiment of the method according to the first aspect of the invention.

[0185] The computer program instructions may be retrievably stored on or transmitted on a computer-readable medium or data carrier. This medium or data carrier may be physically embodied, for example, in the form of a hard disk, solid-state drive, flash memory device, etc. However, the medium or data carrier may also include modulated electromagnetic, electrical, or optical signals, which are received by the computer via a corresponding receiver and transmitted to and stored in the computer's memory.

[0186] According to another aspect of the invention, a wireless communication system is proposed. The wireless communication system includes two or more receivers according to a second aspect of the invention, which are communicatively connected to a common computing unit according to a third aspect of the invention.

[0187] The method and apparatus presented in this paper provide a foundation for robust object localization in noisy environments based on RSSI values ​​of wireless signals emitted from objects (particularly vehicles, autonomous or manually controlled vehicles). Improved performance is achieved, especially in the presence of noise, particularly by performing training using noisy training signals.

[0188] The methods and devices proposed in this paper can be used in any wireless communication system environment, especially 6G and beyond 6G communication systems, and can be used in indoor and outdoor environments, including industrial scenarios.

[0189] In addition to deterministic (i.e. noise-free) training RSSI values, the variance of shadow noise is incorporated into the training phase, resulting in a more noise-resistant ML prediction model than existing techniques that do not incorporate noise during the training phase.

[0190] The derived closed-form expression of the target Hessian matrix optimized during the training phase reduces the complexity of the implementation by avoiding numerical estimation of the matrix derivative.

[0191] The noise-resistant RSSI-based localization method via GPR brings robustness to the training of location estimates and the calculation of the covariance matrix. Brief description of the attached diagram

[0193] The figures in the accompanying drawings are used to illustrate various aspects of the invention.

[0194] Figure 1 A schematic diagram of a system according to the present invention is shown, the system including a common computing unit, multiple receivers, and multiple objects.

[0195] Figure 2 An exemplary data cube Δ is shown.

[0196] Figure 3 The noise immunity parameters via mini-batch SGD are shown. A schematic diagram of the optimization method.

[0197] Figure 4 The optimized noise immunity parameters obtained via mini-batch SGD are shown. A schematic flowchart of the method.

[0198] Figure 5 It shows different mini-batch sizes A comparison of the average convergence behavior of the proposed robust training algorithm based on mini-batch SGD as a function of the gradient descent epoch.

[0199] Figure 6 A comparison of position estimates obtained from multiple runs of the method according to the invention and known methods is shown.

[0200] Figure 7 The proposed positioning method and known methods are compared in terms of noise variance for various small batch sizes of RSME.

[0201] Figure 8 The comparison of CDF curves for RSME with different methods and parameters is shown.

[0202] Figure 9 This illustrates an ideal scenario for determining the impact of the number of receivers on the performance of the proposed method.

[0203] Figure 10 This illustrates the different methods used as sensors. Comparison of the average RMSE of functions of quantity

[0204] Figure 11 A schematic block diagram of a method for locating one or more objects transmitting wireless signals according to the present invention is shown.

[0205] Figure 12 An exemplary schematic block diagram of a receiver according to the present invention is shown, and

[0206] Figure 13 An exemplary schematic block diagram of a common computing unit according to the present invention is shown.

[0207] In the accompanying drawings, the same or similar elements may be referenced using the same reference numerals. Detailed Implementation

[0208] Figures 1 to 10 This has already been described above and will not be discussed again.

[0209] Figure 11 A schematic block diagram and flowchart illustrating the main steps of the localization process according to the present invention are shown. The inputs to this process are the measured RSSI value of the object, the coordinates of the sensor or receiver and training points, optimized parameters, and values ​​from the data cube. These inputs are used to calculate the covariance matrix of the corresponding samples, which is then fed into the conditionalization and marginalization steps, ultimately outputting the estimated coordinates of the object.

[0210] Figure 12 An exemplary schematic block diagram of a receiver 400 according to the present invention is shown. The receiver 400 includes: 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 computing unit 500. The aforementioned elements are communicatively connected via one or more signal or data lines or buses 458. The non-volatile memory 454 stores computer program instructions that, when executed by the microprocessor 450, configure one or more microprocessors to control software or hardware blocks or modules or combinations thereof of the receiver 400 to at least determine the RSSI value of the wireless signals from one or more objects, and to at least transmit the RSSI value to the common computing unit 500.

[0211] Figure 13An exemplary schematic block diagram of a common computing unit 500 according to the present invention is shown. The common computing unit 500 includes 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 lines or buses 458. The non-volatile memory 454 stores computer program instructions that, when executed by the microprocessor 450, cause the common computing unit 500 to perform the method of the present invention as described above.

[0212] List of reference numerals (part of the instruction manual)

[0213]

Claims

1. A method of locating one or more objects emitting a wireless signal in an environment having at least two receivers (400) adapted to determine at least RSSI values of the wireless signal of the one or more objects, 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 optimized RSSI value based coordinate mapping function for the environment using the known positions of the receivers (400) and of a training object, taking into account RSSI training values, - aggregating RSSI values for each of the one or more objects and from each of the two or more receivers (400), - arranging the aggregated RSSI values into a received signal power vector representing RSSI values of all the one or more objects determined in each receiver, wherein determining the optimized RSSI value based coordinate mapping function comprises: - establishing RSSI training values between each receiver of a first plurality of receivers at known locations and each training transmitter of a second plurality of known training transmitter locations, establishing a plurality of values for each pair of receiver and training transmitter and arranging these values into a succession of snapshots, said snapshots representing a training RSSI vector for each training location ( ), the elements of said vector being the training RSSI values between each receiver and the corresponding training location,​ wherein the method further comprises: - Construct all training RSSI vectors for each snapshot. The covariance matrix of ) ), and - For each object and each snapshot, use the corresponding covariance matrix ( The vector containing the RSSI values ​​received by the two or more receivers (400) is mapped onto the x and y coordinates of the environment, and - computing a mean or median value from all resulting positions, or - calculating the mean or median of each element of a plurality of covariance matrices ) and - mapping a vector containing RSSI values received by the two or more receivers (400) for each object onto x and y coordinates of the environment using a resulting mean or median value or an expected covariance matrix.

2. The method of claim 1, wherein an optimized parameter vector of the coordinate mapping function is derived by a Gaussian process using a mean and / or a covariance of RSSI values of training objects as input. )​ 3. The method of claim 2, wherein the optimized parameter vector of the coordinate mapping function is determined by iteratively feeding a mini-batch training data set comprising training data of the training objects into a gradient descent process. )​ 4. The method of claim 2 or 3, wherein the RSSI values of the training objects are arranged in a data cube ( ) containing a plurality of snapshots of a training RSSI vector ( ) arbitrarily selected from the data cube.​​ 5. The method of one or more of claims 1 to 4, wherein the wireless signal is a wireless communication signal, and wherein the at least two receivers (400) are adapted to determine identifiers of the one or more objects transmitted in the respective wireless communication signal and to transmit the identifiers together with the respective RSSI values to the common computing unit (500).

6. A receiver (400) of a wireless communication system, the receiver comprising one or more antennas (402) and associated receiving circuitry (456), one or more microprocessors (450), volatile memory (452) and non-volatile memory (454), and an interface (404) for communicatively coupling with a common computing unit (500), the elements or components of the receiver (400) being communicatively connected via one or more signal lines and / or data lines and / or buses (458), wherein the non-volatile memory (454) stores computer program instructions which, when executed by the one or more microprocessors (450), configure the receiver (400) to determine at least RSSI values of a wireless signal of one or more objects and to transmit at least the RSSI values to the common computing unit (500).

7. The receiver of claim 6, wherein the computer program instructions, when executed by the microprocessor (450), configure the receiver (400) to determine identifiers of the one or more objects and to transmit the identifiers together with RSSI values to the common computing unit (500).

8. A common computing unit (500) of a wireless communication system, the common computing unit comprising two or more receivers (400) according to claim 6 or 7, the common computing unit (500) comprising one or more microprocessors (450), volatile memory (452) and non-volatile memory (454) and an interface (404) for communicatively coupling to the two or more receivers (400), elements or components of the common computing unit (500) being communicatively connected via one or more signal lines and / or data lines and / or buses (458), wherein the non-volatile memory (454) stores computer program instructions which, when executed by the one or more microprocessors (450), configure the common computing unit (500) to perform the method of one or more of claims 1 to 5.

9. A computer program product comprising computer program instructions which, when executed by a microprocessor of a receiver (400) according to claim 6 or 7, cause the microprocessor and / or control hardware blocks, modules or components of the receiver (400) to at least determine RSSI values of wireless signals of one or more objects and to transmit the RSSI values to a common computing unit (500) according to claim 8, or which, when executed by a microprocessor of a common computing unit (500) according to claim 8, cause the microprocessor and / or control hardware blocks, modules or components of the common computing unit (500) to perform the method of one or more of claims 1 to 5.

10. A computer readable medium or data carrier which retrievably transmits or stores the computer program product of claim 9.

11. A wireless communication system comprising two or more receivers (400) according to claim 6 or 7, the two or more receivers being communicatively connected to a common computing unit (500) according to claim 8.

Images