A method for joint estimation of emitter location and channel state parameters under uncertain path loss conditions

Abstract

The present application relates to a kind of under uncertain path loss condition radiation source position and channel state parameter joint estimation method, belong to passive location technical field.The method first establishes the signal strength model based on channel state parameter, and positioning system model is constructed on this basis;Based on positioning system model, construct radiation source position and channel state parameter joint estimation cost function;Based on joint estimation cost function, disclose a kind of radiation source position and channel state parameter joint estimation method based on alternating optimization.The present application is superior in that: under uncertain path loss condition radiation source position and channel state parameter joint estimation system model is established, and the connection between radiation source position and channel state parameter and signal observation is clear;Proposed a kind of radiation source position and channel state parameter joint estimation method based on alternating optimization, can realize the low complexity fast estimation of radiation source position and channel state parameter.

Description

Technical Field

[0001] This invention relates to a passive positioning system for radiation sources, and more particularly to a time difference positioning system, specifically to a method for jointly estimating the location of a radiation source and channel state parameters under uncertain path loss conditions. Background Technology

[0002] Traditional passive localization methods typically involve two steps. First, signal parameters related to the location of the radiation source are extracted from the received electromagnetic signal, such as angle of arrival, time of arrival, time difference of arrival, and frequency difference of arrival. Then, the radiation source is located based on the extracted signal parameters. Because traditional two-step localization algorithms ignore the potential constraint that the extracted signal parameters correspond to a single radiation source, they are often not optimal.

[0003] To further improve the accuracy of passive positioning under low signal-to-noise ratio conditions, a novel method—direct positioning—has been proposed in recent years. Direct positioning refers to a passive positioning method in which a group of observation stations directly estimate the location of a radiation source based on the received electromagnetic signals, without parameter extraction. In the past few years, due to its higher robustness and positioning accuracy compared to traditional positioning algorithms, it has attracted a large number of scholars to participate in related research and applications.

[0004] Currently, most direct positioning methods utilize the angle of arrival, time difference of arrival, or frequency difference of arrival information inherent in the signal from the observation station, with few considering the use of signal amplitude information. In fact, when signal propagation loss follows a certain pattern, the signal amplitude is also related to the propagation distance from the radiation source to the observation station, thus providing information related to the location of the radiation source given the location of the observation station. Therefore, by additionally utilizing signal amplitude information in direct positioning methods, it is hoped that positioning performance can be further improved. The literature (M.-Y.You, A.–N.Lu, Y.–X.Ye, K.Huang, C.Lou. “Directposition determination using compressive sensing measurements without reconstruction,” IEEE Transactions on Aerospace and Electronic Systems, vol.59, no.2, pp.2036-2043, Apr.2023.) considers using signal radiation information in a compressed sensing direct positioning model to further improve positioning accuracy. The literature (M.–Y.You, W.Wang, L.Gao, Y.–X.Ye, K.Huang, A.–N.Lu, C.Lou. “Joint direct estimation of emitter location and antenna beam direction based on baseband reconstruction,” IEEE Sensors Journal, vol.23, no.9, pp.9607-9619, May 2023.) improves the accuracy of transmitter antenna beam direction estimation and positioning by further utilizing the signal strength of the radiating source during the radiating source location estimation process. However, current direct positioning methods using signal amplitude information all assume that signal propagation conforms to the free space propagation loss model. In reality, the radiating source signal may propagate in a more complex channel, and the channel parameters may be unknown or partially unknown. In this case, there is currently no relevant research to answer the following questions: 1) Does signal amplitude information still help improve the accuracy of radiating source positioning under uncertain path loss conditions? 2) Can the signal state parameters and radiating source location be jointly estimated under uncertain path loss conditions, so as to obtain the radiating source location estimate and simultaneously grasp the state of the current propagation channel?

[0005] In view of this, this patent discloses a joint estimation method for radiation source location and channel state parameters under uncertain path loss conditions. The method first establishes a signal strength model based on channel state parameters (including path loss factor and shadowing fading factor), and then constructs a positioning system model based on this model. Based on the positioning system model, a joint estimation cost function for radiation source location and channel state parameters is constructed. Based on the joint estimation cost function, a joint estimation method for radiation source location and channel state parameters based on alternating optimization is disclosed. To evaluate the performance of the method, the Cramér-Rao lower bound (CRLB) for radiation source location and unknown channel parameters under unknown and known path loss factors is also derived. Summary of the Invention

[0006] Based on the above analysis, the embodiments of the present invention aim to provide a method for jointly estimating the location of a radiation source and channel state parameters under uncertain path loss conditions. This method addresses the questions of whether signal amplitude information under existing uncertain path loss conditions can still help improve the accuracy of radiation source positioning, and whether it is possible to jointly estimate signal state parameters and radiation source location under uncertain path loss conditions, thereby obtaining the radiation source location estimate while simultaneously understanding the current propagation channel state.

[0007] On one hand, embodiments of the present invention provide a method for jointly estimating the location of a radiation source and channel state parameters under uncertain path loss conditions, including:

[0008] A positioning system will be established using no fewer than three time-frequency synchronized motion observation stations to observe unknown radiation sources.

[0009] One observation station is designated as the main station, and the rest are auxiliary stations.

[0010] All observation stations synchronously sample the radiation source signal, and all auxiliary stations transmit the obtained sampling data to the main station through inter-station communication links;

[0011] Construct a signal strength model related to channel state parameters, and build a positioning system model based on this model;

[0012] Based on the signal strength model and the positioning system model, a joint estimation cost function related to the radiation source location and channel parameters is established using the maximum likelihood criterion.

[0013] Based on the joint estimation cost function, the aggregated sampled data is iteratively optimized. After the iteration stopping condition is met, a fast estimation result of the radiation source location and channel state parameters is obtained, wherein the channel state parameters include path loss factor and shadow fading factor.

[0014] Based on a further improvement of the above method, the signal strength model related to the channel state parameters is specifically as follows:

[0015] In the formula,

[0016]

[0017] ε l Let be the shadowing fading factor of each auxiliary station, and let be the value with zero mean and variance σ. 2 The Gaussian-distributed independent and identically distributed variables, ε1 being the shadowing fading factor of the main station. w l (t) is zero-mean statistically independent complex Gaussian noise;

[0018] δ l The shadow fading factor difference between each auxiliary station and the main station is δ = [δ2, ..., δ]. L ] T To satisfy the condition that the mean is zero, the covariance matrix is ​​Σ δ =σ 2 (I L-1 +1 L-1 The multidimensional Gaussian distribution of )

[0019] Among them, I L-1 It is an (L-1) order identity matrix, 1 L-1 It is an all-one matrix of size (L-1)×(L-1).

[0020] η0 is the reference power.

[0021] l represents the observation station number.

[0022] L represents the number of observation stations.

[0023] d l The distance from which the radiation source signal propagates to observation station l.

[0024] α is the path loss factor.

[0025] Based on a further improvement of the above method, the positioning system model is expressed as the following vector equation:

[0026] In the formula,

[0027] z represents the acquired signal vector of N points collected by each observation station.

[0028] s = [s[0], s[1], ..., s[N-1]] T This is a signal sampling sequence with N points;

[0029] The zero-mean statistical complex Gaussian noise of the sampled signal;

[0030] Q represents a Fast Fourier Transform and an Inverse Fourier Transform of z.

[0031]

[0032]

[0033] n = [0, 1, ..., N-1] T , in,

[0034] Δ is the sampling interval.

[0035] τ l The time it takes for the signal to travel from the radiation source to the observation station l.

[0036] v l =2πf dl , where πf dl The Doppler frequency shift of the signal observed at observation station l;

[0037] The signal strength amplitude matrix is ​​represented as follows: In the formula,

[0038] I N It is an N-order identity matrix. w represents the Gaussian noise of the observed signal l The covariance matrix.

[0039] Based on a further improvement of the above method, the joint estimation cost function is expressed as:

[0040]

[0041] in,

[0042] To reflect the channel fading variables for each observation station, where,

[0043]

[0044]

[0045] The magnitude matrix of the channel fading variables is represented as follows: Among them, I N It is an N-order identity matrix.

[0046]

[0047] ‖·‖ is used to perform L2 norm operations.

[0048] The Gaussian noise w represents the observed signal that follows the same distribution. l variance

[0049] σ 2 θ represents the variance of the difference δ between the shadow fading factor of the auxiliary station and the main station, which follows the same distribution, θ = [u T ,λ0,α,δ T ] T Represents a vector of unknown parameters.

[0050] Based on a further improvement of the above method, based on the sampled data, an iterative optimization process is performed using a joint estimation cost function. After the iteration stopping condition is met, a fast estimation result of the radiation source location and channel state parameters is obtained, specifically including:

[0051] First, a priori value of the shadow fading factor difference between each auxiliary station and the main station is set, with an initial value of 0, to obtain the initial value of the radiation source location;

[0052] Initiate the iteration, taking the previous round's radiation source location estimate and the previous round's shadow fading factor difference estimate between all auxiliary stations and the main station as known quantities, and substitute them into the joint estimation cost function to obtain the current round's path loss factor estimate;

[0053] Using the previous round of radiation source location estimation value and the current round of path loss factor estimation value as known quantities, deep iteration is performed on the sampling data of each observation station to obtain the shadow fading factor difference between all observation stations in this round and the main station;

[0054] Using the estimated path loss factor value for this round and the difference in shadow fading factor between all observation stations and the main station for this round as known quantities, and substituting them into the joint estimation cost function, the estimated location of the radiation source for this round is obtained;

[0055] The iteration ends when the iteration stopping condition is met, and the final result is the estimated value of the radiation source location, the estimated value of the path loss factor, and the estimated value of the difference in shadow fading factor between all auxiliary stations and the main station in the last round.

[0056] Based on a further improvement of the above method, the initial value of the radiation source location is obtained using the following equation:

[0057] In the formula,

[0058] Ω represents the set containing all possible locations of the radiation source.

[0059] Based on a further improvement to the above method, the initial value of the radiation source location is obtained by applying the following equation:

[0060] In the formula,

[0061] Ω represents the set containing all possible locations of the radiation source.

[0062] Based on a further improvement of the above method, using the previous round's radiation source location estimate and the current round's path loss factor estimate as known quantities, deep iteration is performed on the sampling data of each observation station to obtain the shadowing fading factor difference between all observation stations and the main station in this round, including:

[0063] In the current iteration round, initiate an inner iteration to estimate the difference in shadow fading factor between each auxiliary station and the primary station, specifically:

[0064] S10. Take the estimated values ​​of the radiation source location in the previous round, the estimated values ​​of the path loss factor in this round, and the estimated values ​​of the shadow fading factor difference between the auxiliary stations other than the current auxiliary station and the main station in the previous round as known quantities, substitute them into the joint estimation cost function, and calculate the estimated value of the shadow fading factor difference between the current auxiliary station and the main station in this round.

[0065] S11. Replace the previous round's estimated value for the shadow fading factor difference between the current auxiliary station and the master station with the estimated value for the shadow fading factor difference between the current auxiliary station and the master station in the previous round's shadow fading factor difference estimation value sequence to form an updated shadow fading factor difference estimation value sequence for the previous round. Return to step S10 until the shadow fading factor difference between all auxiliary stations and the master station in this round is obtained; wherein the shadow fading factor difference estimation value sequence is a sequence formed by the estimated values ​​for the shadow fading factor difference between each auxiliary station and the master station.

[0066] Based on a further improvement of the above method, the estimated value of the current-round path loss factor is obtained by applying the following calculation through the joint estimation cost function, and is expressed as follows:

[0067]

[0068] Based on a further improvement of the above method, the estimated location of the radiation source in this round is obtained by applying the following calculation through the joint estimation cost function, and is expressed as follows:

[0069]

[0070] Based on a further improvement of the above method, the stopping condition is to calculate the ratio of the difference between the estimated location of the radiation source in the current round and the estimated location of the radiation source in the previous round to the estimated location of the radiation source in the current round, and stop when the ratio is less than a preset threshold.

[0071] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0072] 1. A joint estimation system model of radiation source location and channel state parameters under uncertain path loss conditions was established, clarifying the relationship between radiation source location and channel state parameters, especially the path loss factor and the shadow fading factor of each observation station and the signal observations.

[0073] 2. A joint estimation method for radiation source location and channel state parameters based on alternating optimization is proposed, which can achieve low-complexity and fast estimation of radiation source location and channel state parameters.

[0074] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0075] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0076] Figure 1 This is the overall flow of the technical solution of the present invention.

[0077] Figure 2 This is an iterative joint estimation process based on the acquired signals and the joint estimation cost function.

[0078] Figure 3 This is a schematic diagram showing the location of the radiation source and three observation stations at the initial moment of the embodiment.

[0079] Figure 4 The cost function plot within the region of interest when estimating the initial location of the radiation source.

[0080] Figure 5 For the corresponding Figure 4 Contour plot of the cost function.

[0081] Figure 6 The results show the root mean square localization error based on statistics of all samples under different signal-to-noise ratio conditions. Detailed Implementation

[0082] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0083] A specific embodiment of the present invention discloses a method for jointly estimating the location of a radiation source and channel state parameters under uncertain path loss conditions, such as... Figure 1As shown, a positioning system is established using no fewer than three time-frequency synchronized motion observation stations to observe unknown radiation sources.

[0084] One observation station is designated as the main station, and the rest are auxiliary stations.

[0085] All observation stations synchronously sample the radiation source signal, and all auxiliary stations transmit the obtained sampling data to the main station through inter-station communication links;

[0086] Construct a signal strength model related to channel state parameters, and build a positioning system model based on this model;

[0087] Based on the signal strength model and the positioning system model, a joint estimation cost function related to the radiation source location and channel parameters is established using the maximum likelihood criterion.

[0088] Based on the joint estimation cost function, the aggregated sampled data is iteratively optimized. After the iteration stopping condition is met, a fast estimation result of the radiation source location and channel state parameters is obtained, wherein the channel state parameters include path loss factor and shadow fading factor.

[0089] In this embodiment, a positioning system is established comprising l time-frequency synchronized motion observation stations to observe a stationary radiation source whose location and parameters are unknown.

[0090] At time t, consider a stationary radiation source located at u = [x, y]. T ,

[0091] Let u∈Ω, where Ω represents the set containing all possible locations of the radiation source.

[0092] The position vector of observation station l is p l (t)=[x l (t),y l (t)] T l = 1, 2, ..., L

[0093] The velocity vector of observation station l is

[0094] Observation station 1 is designated as the main station, and the rest are designated as auxiliary stations.

[0095] All observation stations simultaneously sampled the radiation source signal at 50 signal points, and all auxiliary stations transmitted the obtained sampling data to the main station through inter-station communication links.

[0096] Furthermore, the signal strength model related to the channel state parameters is specifically as follows:

[0097] In the formula,

[0098]

[0099] ε l Let be the channel parameter of the observation station, the shadowing fading factor, which has zero mean and variance σ. 2 Independent and identically distributed variables under a Gaussian distribution.

[0100] δ l The shadow fading factor difference between each auxiliary station and the primary station is δ = [δ2,...,δ]. L ] T To satisfy the condition that the mean is zero, the covariance matrix is ​​Σ δ =σ 2 (I L-1 +1 L-1 The multidimensional Gaussian distribution of )

[0101] Among them, I L-1 It is an (L-1) order identity matrix, 1 L-1 It is an all-one matrix of size (L-1)×(L-1).

[0102] η0 is the reference power.

[0103] l represents the observation station number.

[0104] L represents the number of observation stations.

[0105] d l The distance from the radiation source signal to the observation station l is...

[0106] α is the path loss factor, a channel parameter.

[0107] In this embodiment, at time t, let the propagation time of the signal from the radiation source to the observation station be...

[0108] τ l (t)=||up l (t)|| / c=d l / c

[0109] In the formula, c is the signal propagation speed.

[0110] Assuming the signal at time t is s(t), the signal received by observation station l can be expressed by the equation:

[0111] z l (t)=a l (t)s(t-τ l (t))+w l (t),

[0112] In the formula, the signal strength a l (t) is independent of time t; therefore, from this point onward, the specification will no longer include the parameter t in the representation of signal strength, such as: al ,

[0113] w l (t) is zero-mean statistically independent complex Gaussian noise, and its variance is expressed as...

[0114] For signal strength a l It is usually assumed that the propagation distance is ||up l (t)||, the path loss factor α is related to the reference power η0. The path loss factor is related to the propagation environment and varies over a wide range. The reference power is defined as the signal power received at 1m from the observation station and the radiation source. Further considering the small-scale effects of shadow fading, the following signal strength expression is obtained:

[0115]

[0116] In the formula, ε l The shadowing fading factor, representing the channel parameters from each observation station to the radiation source, is a parameter that has zero mean and variance σ. 2 Independent and identically distributed variables under a Gaussian distribution.

[0117] To more concisely describe the subsequent derivation process, the signal strength expression is simplified to:

[0118]

[0119] in

[0120] but

[0121] Define δ = [δ2, ..., δ] L ] T Then δ satisfies the condition that the mean is zero and the covariance matrix is ​​Σ. δ =σ 2 (I L-1 +1 L-1 The multi-frequency Gaussian distribution of I, where I L-1 It is an (L-1) order identity matrix, 1 L-1 It is an all-1 matrix of size (L-1)×(L-1).

[0122] Therefore, a signal strength model that includes the location of unknown radiation sources, path loss factor, and shadow fading factor is defined.

[0123] Furthermore, the establishment of the positioning system model includes:

[0124] According to the signal strength equation, when the narrowband model holds, the equation for the received signal at the l-th observation station is obtained as follows:

[0125] In the formula,

[0126] s is the sampled signal,

[0127] j is the imaginary unit.

[0128] w l (t) is zero-mean statistically independent complex Gaussian noise.

[0129] t is time, t0 is the sampling start time.

[0130] τ l0 Let τ be the time it takes for the signal to travel from the radiation source to the observation station l at an initial time t0. l0 =τ l (t0),

[0131] f d The Doppler frequency shift is represented as: In the formula,

[0132] f c For the signal carrier frequency,

[0133] c is the signal propagation speed

[0134] u represents the signal position vector.

[0135] p l (t0) represents the position vector of observation station l at time t0.

[0136] This represents the velocity vector of observation station l at time t0;

[0137] With Δ as the sampling interval, the discretized sampled signal received by observation station l is represented as:

[0138] In the formula,

[0139] w l [n] = w l (nΔ+t0) represents the zero-mean statistical complex Gaussian noise over n sampling intervals starting from the sampling time.

[0140] Each observation station collects N signals, and the vector equation of the collected signals is:

[0141] In the formula,

[0142] z is the acquired signal vector of N points collected by each observation station;

[0143] s = [s[0], s[1], ..., s[N-1]] T Given an N-point signal sampling sequence,

[0144] Q represents a Fast Fourier Transform and an Inverse Fourier Transform of z, specifically:

[0145]

[0146] The Fourier transform equation is...

[0147] For Fourier time delay,

[0148] For Fourier frequency shift,

[0149] v l =2πf dl , where πf dl The Doppler frequency shift of the signal observed at observation station l;

[0150] Q is the signal strength amplitude matrix, represented as In the formula,

[0151] I N It is an N-order identity matrix. w represents the Gaussian noise of the observed signal l The covariance matrix.

[0152] In this embodiment, when the narrowband signal model holds true, the signal equation received by observation station l can be expressed as follows:

[0153] z l (t)=a l (t)s(t-τ l (t))+w l (t)

[0154] Simplified to:

[0155]

[0156] In the formula f d The Doppler frequency shift is defined as follows:

[0157]

[0158] In the formula f c τ is the signal carrier frequency. l0 =τ l (t0), where t0 is the sampling start time.

[0159] Let Δ be the sampling interval, then the discretized continuous sampled signal can be represented by the equation:

[0160]

[0161] In the formula wl [n] = w l (nΔ+t0).

[0162] Assuming each station collects signals from N points, the collected signal vector can be represented as:

[0163] z l =[z l [0],z l [1],...,z l [N-1] T .

[0164] The observed signal can be represented as:

[0165] s = [s[0], s[1], ..., s[N-1]] T .

[0166] z l It can be expressed as an equation in s using a Fast Fourier Transform (FFT) and an Inverse FFT (IFFT):

[0167]

[0168] In the formula,

[0169] n = [0, 1, ..., N-1] T ,

[0170]

[0171]

[0172]

[0173]

[0174] The above are some common mathematical expressions for Fourier transform and inverse transform.

[0175] v l =2πf dl This is a variable substitution performed to simplify the representation of the formula.

[0176] w l =[w l [0],w l [1],...,w l [N-1] T This represents the Gaussian noise sequence of signals collected at N points by observation station l.

[0177] The vector representation of all signals collected by the observation stations is as follows:

[0178] Gaussian noise is represented as:

[0179] The Fourier transform is expressed as:

[0180] The signal strength amplitude matrix is ​​represented as follows: The localization model that corresponds to the acquired signal vector, the unknown radiation source, and the channel parameters can then be obtained, expressed as the following equation:

[0181]

[0182] In the formula, E{w}=0 LN×1 , The observed signal is Gaussian noise w with zero mean l The covariance matrix.

[0183] Meanwhile, the prior information of δ can be expressed as an equation relating the signal vector acquired by the observation station, the difference in shadow fading factors between the main and auxiliary observation stations, and Gaussian noise:

[0184] z δ =δ+w δ ,

[0185] In the formula, w δ The mean is zero, and the covariance matrix is ​​Σ. δ =σ 2 (I L-1 +1 L-1 The multidimensional Gaussian distribution of ).

[0186] Furthermore, the joint estimation cost function is expressed as:

[0187]

[0188] in,

[0189] To reflect the channel fading variables for each observation station, where,

[0190]

[0191]

[0192] The magnitude matrix of the channel fading variables is represented as follows: Among them, I N It is an N-order identity matrix.

[0193]

[0194] ‖·‖ is used to perform L2 norm operations.

[0195] I represents the Gaussian noise w of the observed signal that follows the same distribution. l variance

[0196] σ 2 θ represents the variance of the difference δ between the shadow fading factor of the auxiliary station and the main station, which follows the same distribution. T ,λ0,α,δ T ] T Represents a vector of unknown parameters.

[0197] In this embodiment, the unknown parameter vector θ is first defined as follows:

[0198] θ=[u T ,λ0,α,δ T ] T ,

[0199] In the formula, ε = [ε1,...ε L ] T Then the likelihood function of θ is expressed as:

[0200]

[0201] Based on u T ,α,ε T All variables are independent, and there is no prior information about u and α. By substituting them into the localization model equation and the signal strength equation, we have:

[0202]

[0203] Taking the natural logarithm of the above equation and ignoring terms irrelevant to θ, we obtain the simplified likelihood function C1(θ) as follows:

[0204]

[0205] Based on the above equation, the maximum likelihood function of θ can be expressed as:

[0206]

[0207] To simultaneously perform joint estimation of the channel between each observation station and the unknown radiation source, it is necessary to first establish the relationship between the unknown signal s and the signal strength a. l The correspondence between the acquired signal vector z and the signal vector z is expressed by the following equation:

[0208]

[0209] in,

[0210] Substituting the previous equation into the simplified likelihood function C1(θ), s can be eliminated. This allows us to derive the joint estimation cost function, which reflects the relationship between the acquired signal and the location of the unknown radiation source, the path loss factor, and the shadow fading factor, as shown below:

[0211]

[0212] in,

[0213] To reflect the channel fading variables for each observation station, where,

[0214]

[0215]

[0216] The magnitude matrix of the channel fading variables is represented as follows: Among them, I N It is an N-order identity matrix.

[0217] Furthermore, based on the sampled data, an iterative optimization process is performed using a joint estimation cost function. After the iteration stopping condition is met, a fast estimation result of the radiation source location and channel state parameters is obtained, specifically including:

[0218] First, a priori value of the shadow fading factor difference between each auxiliary station and the main station is set, with an initial value of 0, to obtain the initial value of the radiation source location;

[0219] Initiate the iteration, taking the previous round's radiation source location estimate and the previous round's shadow fading factor difference estimate between all auxiliary stations and the main station as known quantities, and substitute them into the joint estimation cost function to obtain the current round's path loss factor estimate;

[0220] Using the previous round of radiation source location estimation value and the current round of path loss factor estimation value as known quantities, deep iteration is performed on the sampling data of each observation station to obtain the shadow fading factor difference between all observation stations in this round and the main station;

[0221] Using the estimated path loss factor value for this round and the difference in shadow fading factor between all observation stations and the main station for this round as known quantities, and substituting them into the joint estimation cost function, the estimated location of the radiation source for this round is obtained;

[0222] The iteration ends when the iteration stopping condition is met, and the final result is the estimated value of the radiation source location, the estimated value of the path loss factor, and the estimated value of the difference in shadow fading factor between all auxiliary stations and the main station in the last round.

[0223] Furthermore, the initial value of the radiation source location is obtained using the following equation:

[0224] In the formula,

[0225] Ω represents the set containing all possible locations of the radiation source.

[0226] Furthermore, using the previous round's estimated radiation source location value and the current round's estimated path loss factor value as known quantities, deep iteration is performed on the sampling data of each observation station to obtain the shadowing fading factor difference between all observation stations and the main station in this round, including:

[0227] In the current iteration round, initiate an inner iteration to estimate the difference in shadow fading factor between each auxiliary station and the primary station, specifically:

[0228] S10. Take the estimated values ​​of the radiation source location in the previous round, the estimated values ​​of the path loss factor in this round, and the estimated values ​​of the shadow fading factor difference between the auxiliary stations other than the current auxiliary station and the main station in the previous round as known quantities, substitute them into the joint estimation cost function, and calculate the estimated value of the shadow fading factor difference between the current auxiliary station and the main station in this round.

[0229] S11. Replace the previous round's estimated value for the shadow fading factor difference between the current auxiliary station and the master station with the estimated value for the shadow fading factor difference between the current auxiliary station and the master station in the previous round's shadow fading factor difference estimation value sequence to form an updated shadow fading factor difference estimation value sequence for the previous round. Return to step S10 until the shadow fading factor difference between all auxiliary stations and the master station in this round is obtained; wherein the shadow fading factor difference estimation value sequence is a sequence formed by the estimated values ​​for the shadow fading factor difference between each auxiliary station and the master station.

[0230] Furthermore, the estimated value of the path loss factor for this round is obtained by applying the following calculation through the joint estimation cost function, and is expressed as follows:

[0231]

[0232] Furthermore, the estimated location of the radiation source in this round is obtained by applying the following calculation through the joint estimation cost function, and is expressed as follows:

[0233]

[0234] Furthermore, the stopping condition is to calculate the ratio of the difference between the estimated location of the radiation source in this round and the estimated location of the radiation source in the previous round to the estimated location of the radiation source in this round, and to stop when the ratio is less than a preset threshold.

[0235] In this embodiment, a joint estimation cost function is applied to jointly estimate the unknown radiation source and channel parameters. Since there are many locations and multi-point signal processing involving multiple observation stations is involved, directly using grid search would involve extremely complex high-dimensional optimization operations. Therefore, a method similar to block coordinate descent is adopted to achieve rapid estimation of unknown radiation sources and channel parameters. The difference is that, apart from the prior information of δ, it is not necessary to give prior estimates of the initial values ​​of the radiation source location u and α.

[0236] Once all L observation stations have collected signals from N points, with observation station 1 as the master station and the others as auxiliary stations, the joint estimation cost function can be applied to initiate the iteration, such as... Figure 2 As shown, it includes the following steps:

[0237] Step S1: Initialization, let the iteration round number k = 0. Treating the channel state as a whole and ignoring terms unrelated to u, the initial value of the radiation source position can be obtained:

[0238]

[0239] Based on the prior δ, let δ l initial value That is, the initial value of the shadow fading factor of the master observation station is set to 0.

[0240] Step S2: Start the iteration, set the iteration round k = k + 1, and set the current round's... and Substituting into the joint cost estimation function, the estimated path loss factor for the current round can be calculated using the following formula.

[0241]

[0242] Step S3: This step uses the estimated radiation source location from the previous round, the estimated path loss factor for this round, and the sequence of shadow fading factors between each auxiliary station and the main station from the previous round as known quantities. After obtaining the shadow fading factor difference between the first auxiliary station and the main drilling station in this round, the difference sequence is updated. This step is repeated to solve the shadow fading factor difference between each auxiliary station and the main station in this round and update the difference sequence until the shadow fading factor difference between all auxiliary stations and the main drilling station in this round is finally obtained.

[0243] Specifically,

[0244] First, apply the radiation source location estimates from the previous round. The path loss factor estimate obtained in step S2 for the current round Substitute into the following formula to estimate the distance between the main station and the first auxiliary station. Shadow fading factor difference:

[0245]

[0246] From step S1, we can know As the first known quantity, it can be known from step S2. The second known quantity is the sequence of differences between the shadow fading factors of each auxiliary station and the main station. This sequence is derived from the differences between the shadow fading factors of the auxiliary station and the main station calculated in the previous round. Since this is the first iteration, δ is taken from the prior δ in step S1. l initial value Using the difference in shadow fading factors between each auxiliary station and the main station in the previous round as the third known quantity, and substituting these three known quantities into the joint estimation cost function, we first calculate the difference in shadow fading factors between the first auxiliary station and the main station in this round.

[0247] by Replace the shadow fading factor difference between the auxiliary station and the main station in the previous round in the difference sequence to form a new difference sequence. Then, using this sequence as a known quantity, compare it with... As a known quantity, continue to estimate the difference in shadow fading factor between the next auxiliary station and the main station in this round; repeat the above steps to calculate the difference in shadow fading factor between each auxiliary station and the main station in this round, and obtain δ for this round.

[0248] Step S4: Path loss factor for this round obtained from step S2 The valuation is the first known quantity. Step S3 obtains the difference in shadow fading factor between each auxiliary station and the main station in this round. As the second known quantity, it is substituted into the joint estimation cost function, and the estimated location of the radiation source in this round is obtained through the following formula.

[0249]

[0250] Step 5: Repeat the iteration until the stopping condition is met. In the formula, γ is a given update stopping parameter.

[0251] Preferably, γ is set to a typical value of 10. -3 ~10 -4 ,

[0252] Take the last round The radiation source location u, path loss factor α, and the difference in shadow fading factor between each auxiliary station and the main station are respectively represented as radiation source location u, path loss factor α, and shadow fading factor difference δ between each auxiliary station and the main station. l The estimated value.

[0253] Specifically, this embodiment designs a scenario including a stationary radiation source and three moving observation stations. The radiation source is located at u = [14.5, 102.6]. T (km), the locations of the observation stations are respectively located at p1=[40,1] T(km), p2 = [0,0] T (km) and p3 = [20, 100] T (km), and their speeds are respectively (m / s) (km / s) and (km / s). The radiation source signal waveform modulation style is BPSK, with a bandwidth of 25kHz. The carrier frequency is set to 403MHz, and the sampling frequency is 100kHz. 1024 signal data points are collected at each station for radiation source localization. In this example, α = 1 is considered, and ε1 = 0.8099, ε2 = 0.5819, and ε3 = 1.3340 are randomly generated according to a Gaussian distribution with a mean of 0 and a variance of 1.

[0254] The initial scenario of the embodiment is as follows: Figure 3 As shown.

[0255] First, we analyze the CRLB under various typical conditions. Table 1 shows the results under different signal-to-noise ratios. and For comparison, the following baseline is also provided: lower bound of positioning error when both α and δ are known. Channel state a l Lower bound of positioning error when parameters are unknown as a whole Lower bound of traditional two-step positioning error As can be seen from the results in the table, regardless of whether the channel parameters are known or not, the lower bound of the positioning error is significantly smaller than that of the traditional two-step method. The best performance indicates that when the channel model is fully known, utilizing RSS information can help further improve the accuracy of radiation source localization. Table 1 shows... Performance and This consistency is easily understood because when both α and δ are unknown, it is essentially equivalent to the model structure in equation (2) being completely unknown. However, while the method described cannot further improve positioning accuracy, it can simultaneously provide channel parameters α and δ, offering more information for understanding the channel state. Note that... Performance between and This indicates that understanding the path loss factor α is also beneficial for improving positioning accuracy, and in practice, the path loss information already available should be fully utilized.

[0256] Table 1. CRLB of positioning error under typical conditions

[0257]

[0258] Secondly, the convergence of the joint estimation algorithm is analyzed. Under a signal-to-noise ratio of -5dB, the table below shows the optimal cost function value max{C2(θ)} for the last iteration under different iteration numbers for 50 samples. As can be seen from the results in Table 2, max{C2(θ)} tends to stabilize as the number of iterations increases, indicating that the algorithm converges, and that 5 iterations allow the objective function to converge to near its optimal value.

[0259] Table 2. CRLB of positioning error under typical conditions

[0260] <![CDATA[rms{max[C2(θ)]}(10 -7 )]]> 440.1456 440.1462 440.1463 440.1464 440.1464 440.1464

[0261] Finally, for the scenario defined above, the root mean square localization error of 50 samples was statistically analyzed under different signal-to-noise ratio conditions.

[0262] For each sample, after the radiation source signals are collected and aggregated at each observation station, a cost function for estimating the initial value of the radiation source location can be constructed. The joint estimation cost function C2(θ) is calculated, and the radiation source location and channel parameters are iteratively solved based on the joint estimation algorithm. For example... Figure 4 , Figure 5 As shown, taking a single sample in a 5dB signal-to-noise ratio scenario as an example, the figure first presents the cost function plot and its corresponding contour plot within the region of interest when estimating the initial value of the radiation source location. The location corresponding to the maximum value and the initial value of the radiation source are then taken. (km).

[0263] Based on the initial value of the radiation source location, the channel parameters and radiation source location are estimated in 5 iterations. The signal parameters and radiation source location estimation results of each iteration are shown in the table below.

[0264]

[0265] Figure 6 The results show the root mean square (RMS) localization error based on statistics from all samples under different signal-to-noise ratios. As can be seen from the figures, regardless of whether α is known or not, the RMS localization error of both joint estimation algorithms is lower than [previous value]. Furthermore, the advantages are particularly significant under low signal-to-noise ratio (SNR) conditions, demonstrating the advantages and application potential of the proposed method in improving positioning accuracy. In addition, under low SNR conditions, the root mean square (RMS) positioning error of various positioning algorithms still deviates from its CRLB; however, as the SNR increases, the RMS positioning error gradually approaches its CRLB. During simulations, the RMS positioning error when α is known is lower than that when α is unknown, further illustrating that partial understanding of the signal state helps improve positioning accuracy.

[0266] Tables 3 and 4 present the root mean square estimation errors of channel parameters under different signal-to-noise ratios (CRLs) for scenarios where α is unknown and known. Similar to the positioning error, when the CRL is low, the root mean square estimation error of the parameters deviates far from its CRLB. However, as the CRL increases, the root mean square estimation error of the parameters gradually approaches its CRLB, which also demonstrates the effectiveness of the joint estimation algorithm.

[0267] Table 3. Root mean square estimation error of channel parameters and its CRLB under different signal-to-noise ratio conditions in the unknown α scenario.

[0268]

[0269] Table 4α shows the root mean square estimation error of channel parameters and its CRLB under different signal-to-noise ratios in a known scenario.

[0270]

[0271] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0272] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for jointly estimating the location of a radiation source and channel state parameters under uncertain path loss conditions, characterized in that, include: A positioning system will be established using no fewer than three time-frequency synchronized motion observation stations to observe unknown radiation sources. One observation station is designated as the main station, and the rest are auxiliary stations. All observation stations synchronously sample the radiation source signal, and all auxiliary stations transmit the obtained sampling data to the main station through inter-station communication links; A signal strength model related to channel state parameters is constructed, and a positioning system model is established based on this model. The signal strength model related to the channel state parameters is specifically as follows: In the formula, ， Let be the shadowing fading factor of each auxiliary station, and let be the value with zero mean and variance. Independent and identically distributed variables under a Gaussian distribution. The shadow decay factor of the main site. = , It is a zero-mean statistically independent complex Gaussian noise; This represents the difference in shadow fading factor between each auxiliary station and the main station. To satisfy the condition that the mean is zero, the covariance matrix is: Multidimensional Gaussian distribution, in, for An identity matrix of order 1. For size A matrix of all 1s For reference power, l represents the observation station number. L represents the number of observation stations. The distance from which the radiation source signal propagates to observation station l. This refers to the path loss factor. Based on the signal strength model and the positioning system model, a joint estimation cost function related to the radiation source location and channel parameters is established using the maximum likelihood criterion. The positioning system model is expressed as the following vector equation: In the formula, The acquired signal vector is the signal vector collected from N points at each observation station. ; This is a signal sampling sequence with N points; The zero-mean statistical complex Gaussian noise of the sampled signal; To The matrix obtained after performing a Fast Fourier Transform and an Inverse Fourier Transform. ; , , ,in, The sampling interval is... The time it takes for the signal to travel from the radiation source to the observation station l. ,in, The Doppler frequency shift of the signal observed at observation station l; The signal strength amplitude matrix is ​​represented as follows: In the formula, for An identity matrix of order 1. = , = Indicates Gaussian noise in the observed signal The covariance matrix; Based on the joint estimation cost function, the aggregated sampled data is iteratively optimized. After the iteration stopping condition is met, a fast estimation result of the radiation source location and channel state parameters is obtained, wherein the channel state parameters include path loss factor and shadow fading factor.

2. The method for jointly estimating radiation source location and channel state parameters under uncertain path loss conditions according to claim 1, characterized in that, The joint estimation cost function is expressed as follows: in, To reflect the channel fading variables for each observation station, where, ， The magnitude matrix of the channel fading variables is represented as follows: ,in, for An identity matrix of order 1. ， || To perform L2 norm operations, Gaussian noise representing observed signals that follow the same distribution variance This represents the difference in shadow fading factor between the auxiliary station and the primary station, both of which follow the same distribution. variance It is the difference in shadow fading factor between the auxiliary station and the main station. Represents a vector of unknown parameters.

3. The method for jointly estimating radiation source location and channel state parameters according to claim 2, characterized in that, Based on the sampled data, an iterative optimization process is performed using a joint estimation cost function. After the iteration stopping condition is met, a fast estimation result of the radiation source location and channel state parameters is obtained, specifically including: First, a priori value of the shadow fading factor difference between each auxiliary station and the main station is set, with an initial value of 0, to obtain the initial value of the radiation source location; Initiate the iteration, taking the previous round's radiation source location estimate and the previous round's shadow fading factor difference estimate between all auxiliary stations and the main station as known quantities, and substitute them into the joint estimation cost function to obtain the current round's path loss factor estimate; Using the previous round of radiation source location estimation value and the current round of path loss factor estimation value as known quantities, deep iteration is performed on the sampling data of each observation station to obtain the shadow fading factor difference between all observation stations in this round and the main station; Using the estimated path loss factor value for this round and the difference in shadow fading factor between all observation stations and the main station for this round as known quantities, and substituting them into the joint estimation cost function, the estimated location of the radiation source for this round is obtained; The iteration ends when the iteration stopping condition is met, and the final result is the estimated value of the radiation source location, the estimated value of the path loss factor, and the estimated value of the difference in shadow fading factor between all auxiliary stations and the main station in the last round.

4. The method for jointly estimating radiation source location and channel state parameters under uncertain path loss conditions according to claim 3, characterized in that, The initial value of the radiation source location is obtained using the following equation: In the formula, This represents the set containing all possible locations of the radiation source.

5. The method for jointly estimating radiation source location and channel state parameters according to claim 3, characterized in that, Using the previous round's estimated radiation source location value and the current round's estimated path loss factor value as known quantities, deep iteration is performed on the sampled data of each observation station to obtain the shadowing fading factor difference between all observation stations and the main station in this round, including: In the current iteration round, initiate an inner iteration to estimate the difference in shadow fading factor between each auxiliary station and the primary station, specifically: S10. Take the estimated values ​​of the radiation source location in the previous round, the estimated values ​​of the path loss factor in this round, and the estimated values ​​of the shadow fading factor difference between the auxiliary stations other than the current auxiliary station and the main station in the previous round as known quantities, substitute them into the joint estimation cost function, and calculate the estimated value of the shadow fading factor difference between the current auxiliary station and the main station in this round. S11. Replace the previous round's estimated value for the shadow fading factor difference between the current auxiliary station and the master station with the estimated value for the shadow fading factor difference between the current auxiliary station and the master station in the previous round's shadow fading factor difference estimation value sequence to form an updated shadow fading factor difference estimation value sequence for the previous round. Return to step S10 until the shadow fading factor difference between all auxiliary stations and the master station in this round is obtained; wherein the shadow fading factor difference estimation value sequence is a sequence formed by the estimated values ​​for the shadow fading factor difference between each auxiliary station and the master station.

6. The method for jointly estimating radiation source location and channel state parameters according to claim 3, characterized in that, The estimated value of the path loss factor for this round is obtained by applying the following calculation to the joint estimation cost function, and is expressed as follows: 。 7. The method for jointly estimating radiation source location and channel state parameters according to claim 3, characterized in that, The estimated location of the radiation source in this round is obtained by applying the following calculation through the joint estimation cost function, and is expressed as follows: 。 8. The method for jointly estimating radiation source location and channel state parameters according to claim 3, characterized in that, The stopping condition is calculated as the ratio of the difference between the current round of radiation source location estimation value and the previous round of radiation source location estimation value to the current round of radiation source location estimation value. The process stops when the ratio is less than a preset threshold.

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