Weak target signal level positioning method for non-reference channel passive radar networking cooperation

Abstract

The invention discloses a non-reference channel passive radar networking cooperative weak target signal level positioning method, and the method comprises the steps: firstly initializing system parameters, and building a target echo model, which is polluted by noise and direct wave interference, of a non-reference channel passive radar; then, a complete data set is established in combination with a distributed multi-station target echo model and an unknown signal of a non-cooperative external radiation source, a conditional likelihood function of the complete data set is derived, and finally, based on an expectation maximization principle, an expectation step and a maximum step of the conditional likelihood function are executed in a loop iteration mode so as to continuously update target position estimation and suppress direct wave interference. And the maximum likelihood estimation of the target position is obtained until the convergence condition of the expectation maximization algorithm is met, and combined direct wave suppression and target position estimation updating are realized. The method provided by the invention solves the problems that the current passive radar system is low in positioning precision, easy to be interfered by direct waves, unknown in non-cooperative external radiation source signal, strong in dependence on a reference channel and the like in weak target detection.

Description

Technical Field

[0001] The invention belongs to the technical field of passive radar target positioning, and in particular relates to a weak target signal level positioning method of passive radar networking collaboration without a reference channel. Background Art

[0002] Passive radar refers to the acquisition of target status by detecting the reflected echo radiated from the external radiation source to the target. Compared with active radars that need to be equipped with dedicated radiation sources, passive radars have the advantages of weak electromagnetic pollution, low power consumption and strong concealment. With the widespread deployment of digital video / audio broadcasting base stations, cellular communication base stations and communication / navigation satellites, the application of detection technology based on passive radar in the civilian field has gradually increased. In order to cope with the problems of high computational complexity and limited detection accuracy caused by the unknown signals of non-cooperative external radiation sources, passive radars are currently divided into two categories according to whether they are equipped with a reference channel. The first category is dual-channel passive radar. In addition to the monitoring channel for observing the target echo, a reference channel pointing to the external radiation source is also equipped to receive the direct wave from the external radiation source as a reference signal. Dual-channel passive radar mainly uses the correlation between the target echo and the reference signal to obtain target status information. Therefore, this type of method relies heavily on high-quality reference channel signals. In contrast, passive radars without reference channels are usually equipped with only one monitoring channel, which uses the correlation between target echoes from the same external radiation source observed by different radars to detect targets. Passive radar without reference channel avoids the harsh conditions of deploying high-quality reference channel and reduces the hardware cost and complexity of the system. However, the separate deployment of the receiver and external radiation source of the passive radar leads to the inevitable superposition of the received target echo with the direct wave, which refers to the signal emitted by the external radiation source and directly reaches the passive radar receiver. Since the direct wave is not reflected and attenuated by the target, it does not contain target information and is usually much stronger than the target echo, also known as direct wave interference. Previous studies have shown that direct wave interference can reduce the probability of target detection and the accuracy of target parameter estimation.

[0003] Passive radar network collaboration refers to combining multiple widely distributed passive radars and external radiation sources to build a distributed passive collaborative detection network to conduct multi-level, multi-angle three-dimensional detection of targets. Compared with a single radar system, widely distributed passive radar network collaborative detection can accumulate more samples to improve signal gain, and suppress the flicker of the target radar cross-sectional area through multi-angle observation, thereby obtaining spatial diversity gain. Therefore, passive radar network collaboration has unique advantages in anti-interference, anti-stealth and low-altitude target detection.

[0004] Target positioning is one of the core tasks of passive radar network cooperative detection, which can generally be divided into two categories. The first category is the two-step positioning method, also known as data-level positioning: First, each passive radar independently estimates the data parameters related to the target state, such as the echo arrival time and arrival time difference, based on the received target echo. Subsequently, the target position is estimated by combining these data parameters. The advantage of this method is that the required transmission bandwidth is small and the computational complexity is low. However, the data parameter estimation error generated in the first step may accumulate to the second step, affecting the final positioning accuracy, especially in small samples or low signal-to-noise ratio environments. In addition, since each passive radar independently processes the target echo, it is difficult to effectively accumulate the signal-to-noise ratio of weak target echoes, thereby limiting the detection capability of weak targets. With the improvement of communication bandwidth and computing power, direct positioning, that is, signal-level positioning, has gradually attracted widespread attention. This method obtains the maximum likelihood estimate of the target position by directly maximizing the joint likelihood function constructed by all passive radar echoes, bypassing the data parameter estimation link. In theory, it can achieve higher positioning accuracy and robustness, especially in weak target detection.

[0005] Although some research progress has been made in signal-level target positioning based on passive radar network collaboration, most of them ignore the direct wave interference that is stronger than the target echo, or assume that the direct wave interference has been completely suppressed. In addition, some studies rely on high-quality reference channels, which increases the deployment cost and complexity of the system. Therefore, there is currently a lack of effective solutions to the problem of high-precision signal-level target positioning in passive radar network collaboration without reference channels in a direct wave interference environment with unknown signals from non-cooperative external radiation sources.

[0006] The document "Direct Target Localization for Distributed Passive Radars With Direct-Path Interference Suppression, IEEE Transactions on Signal Processing, 2024, vol.72, pp.3611-3625" designs a direct target localization algorithm by combining the reference channel and monitoring channel observations of a distributed passive radar, and simultaneously suppresses direct wave interference. However, this work is highly dependent on reference channel observations and is not suitable for signal-level target localization of passive radars without reference channels; CN108519586A discloses a distributed passive radar system and its target localization method, which first uses a reference signal to extract the echo arrival time difference, and then uses the echo arrival time difference estimated by multiple passive radars to realize target localization. This work is essentially a two-step positioning, and its positioning performance is limited in a small sample point and low signal-to-noise ratio environment. In particular, it ignores the direct wave interference superimposed on the target echo, making it unable to work in a strong direct wave interference environment; CN117872342A discloses a distributed passive radar signal-level robust positioning method with direct wave suppression. First, the reference channel observation signal is used to estimate the emission signal waveform of the external radiation source, and then it is substituted into the direct target position positioning algorithm established by the monitoring channel observation signal, thereby realizing the signal-level target positioning of a low-complexity distributed dual-channel passive radar. This method is suitable for the target positioning problem of a dual-channel distributed passive radar equipped with an additional reference channel, but is not applicable to scenarios such as direct wave suppression and signal-level positioning of a radar without a reference channel.

[0007] In summary, the existing distributed passive radar related target detection or positioning algorithms are not fully applicable to the direct wave suppression and weak target signal level target positioning problems of passive radar without reference channel. Summary of the invention

[0008] To solve the above technical problems, the present invention provides a weak target signal-level positioning method for passive radar networking without reference channels, which can achieve low-complexity and high-precision robust positioning of weak target signal-level by passive radar without reference channels in a direct wave interference environment.

[0009] The technical solution adopted by the present invention is: a weak target signal level positioning method of passive radar networking without reference channel, and the specific steps are as follows:

[0010] S1. Initialize system parameters;

[0011] Initialize the number N and position coordinates of external radiation sources Initialize the number M and position coordinates of passive radar receivers Target position coordinates p = [x, y] T .

[0012] Among them, the superscript (·) T Indicates transpose.

[0013] For a passive dual-base pair consisting of the nth external radiation source and the mth passive radar receiver, the signal amplitudes of the direct wave interference and the target echo in the received signal are expressed as α and m,n and β m,n ; Set the number of passive radar sampling points to K and the sampling period to T s ; The noise superimposed by the echo received by each passive radar receiver has a mean of 0 and a variance of of complex circularly symmetric white Gaussian distribution, and are independent of each other.

[0014] S2. Establish a passive radar echo model without reference channel contaminated by direct waves and noise, and construct a joint observation model of passive radar network collaboration to obtain spatial diversity gain;

[0015] S3. Based on the maximum likelihood principle, a signal-level likelihood function for cooperative observation of passive radar networks is constructed to enhance the detection capability of weak targets, thereby forming a non-convex and nonlinear high-dimensional target position estimation problem;

[0016] S4. Treat the unknown signals of non-cooperative external radiation sources as unobservable hidden variables, and conduct collaborative observations with passive radar networks to construct a complete data set and derive its conditional likelihood function;

[0017] S5. Design an iterative estimation algorithm for weak target signal level for direct wave interference suppression based on the expectation maximization principle. Each iteration first calculates the conditional expectation of the likelihood function about the unknown external radiation source signal, and then maximizes the expectation based on the joint optimization mechanism of sequential and Newton iterations to achieve joint direct wave suppression and target position estimation update.

[0018] Furthermore, the step S2 is specifically as follows:

[0019] The target echo contaminated by direct waves and noise from the nth external radiation source received by the mth passive radar receiver The expression is as follows:

[0020]

[0021] Among them, the superscript (·) d and(·) e Represent the direct path and target echo path respectively, α m,n and β m,n Represent the complex amplitudes of the direct wave and the target echo respectively; represents the baseband transmission signal of the nth external radiation source at time t; represents the direct path propagation delay from the nth external radiation source to the mth passive radar receiver; represents the propagation delay of the echo path from the nth external radiation source through the target to the mth passive radar receiver, and c0 represents the propagation speed of electromagnetic waves; The variance is is a complex circularly symmetric white Gaussian random variable.

[0022] Assuming that the noises of different passive radar receivers are independent of each other and white in space and time, the expression is as follows:

[0023]

[0024] Among them, the symbol Indicates time, symbol (·) * and δ(·) denote the statistical expectation, conjugate, and impulse functions, respectively.

[0025] set up and Respectively represent the time domain signal in equation (1) and The K-point discrete sampling vector with a sampling period of T s .

[0026] Among them, the superscript (·) d / e Indicates the direct path or target echo path.

[0027] Then, the frequency domain expressions of the discrete vectors are calculated to extract the delay of the direct wave interference and the target echo. represents the K-point discrete Fourier transform of the received signal, T represents the discrete Fourier transform matrix, and its (a, b)th element is expressed as Then the frequency domain expression of the discrete sampling vector of formula (1) is as follows:

[0028]

[0029] in, and The symbol diag{·} denotes a diagonal matrix whose diagonal elements are vectors or matrices.

[0030] The observation model of MN passive dual-base pairs composed of M passive radars without reference channels and N external radiation sources is combined. The expression of the joint observation r of the passive radar network without reference channels is as follows:

[0031]

[0032] Furthermore, the step S3 is specifically as follows:

[0033] Based on the Gaussian characteristics of the joint observation signal, the logarithmic expression of the likelihood function of the joint observation r in formula (4) is as follows:

[0034]

[0035] in,

[0036]

[0037] and,

[0038]

[0039] Among them, the symbol represents the Kronecker product, the symbol det(·) represents the determinant of the matrix, (·) Η represents the conjugate transpose, (·) -1 Represents the inverse operation, matrix I K and I M Represents K-dimensional and M-dimensional identity matrices, respectively. and Respectively represent the noise w m,n and signal n The covariance matrix of .

[0040] Maximum Likelihood Estimation of Target Location It is obtained by maximizing the log-likelihood function lnp(r) in equation (5), and the expression is as follows:

[0041]

[0042] Among them, the unknown parameter vector θ = [p T ,α T ,β T ] T , α=[α 1,1 ,…,α M,N ] T , β=[β 1,1 ,…,β M,N ] T .

[0043] Furthermore, the step S4 is specifically as follows:

[0044] Unknown external radiation source signal is considered to be an unobservable hidden vector. Then the observation r in equation (4) is considered to be an incomplete data set, and the expression of the complete data set y is defined as follows:

[0045] y=[r T ,s T ] T (9)

[0046] According to Bayesian theory, the conditional log-likelihood function expression of the complete data set y is as follows:

[0047]

[0048] Among them, the function p(r,s,θ) represents the joint likelihood function of r, s and θ; the function p(s,θ) represents the joint likelihood function of s and θ; and the function p(θ) represents the likelihood function of θ.

[0049] The functions lnp(r|s,θ) and lnp(s|θ) represent the conditional log-likelihood functions of the network cooperative joint observation r and the non-cooperative external radiation source signal s, respectively, and the expressions are as follows:

[0050]

[0051] in, represents the covariance matrix of the external radiation source signal s, μ represents the conditional mean of the observation r, and the specific expression is as follows:

[0052]

[0053] Combining equations (11) and (12), the conditional log-likelihood function expression of the complete data set y in equation (10) is as follows:

[0054] lnp(y|θ)=f1(s)+f2(s,θ) (14)

[0055] in,

[0056]

[0057] Furthermore, the step S5 is specifically as follows:

[0058] S51, executing the expectation step, that is, finding the conditional expectation of the likelihood function of the complete data set;

[0059] The conditional expectation of the likelihood function lnp(y|θ) of the complete data set y in formula (14) is The expression is as follows:

[0060]

[0061] Among them, the superscript (·) (l) represents the lth iteration, Represents the parameter estimation of the lth iteration. Discarding the term f1(s) that is irrelevant to the estimated parameter θ and calculating the conditional expectation of f2(s,θ), we get the following expression:

[0062]

[0063] in,

[0064]

[0065] The symbol Tr{·} represents the trace of the matrix; the vector and matrix Respectively represent s n The minimum mean square error estimate and conditional covariance matrix of .

[0066] Due to s n and r n They obey a joint Gaussian distribution with mean zero, then and The closed form expression is as follows:

[0067]

[0068] in,

[0069]

[0070] and,

[0071]

[0072] S52, executing the maximum step, that is, maximizing the conditional expectation of the likelihood function of the complete data set obtained in step S51 based on the joint optimization mechanism of sequential and Newton iteration;

[0073] By maximizing the conditional expectation of formula (16) The estimated parameter vector for the (l+1)th iteration The expression is as follows:

[0074]

[0075] Then maximize the function in (25) That is, the target position p and the signal amplitudes α and β are jointly optimized. Using the sequential estimation strategy, Transformed into two low-dimensional sub-estimation problems, the expressions are as follows:

[0076]

[0077] in, and They respectively represent the estimate of the signal amplitude given by the lth iteration.

[0078] The optimization problems of equations (26) and (27) are solved as follows:

[0079] A. Solve the optimization problem (26), i.e., Newton iterative estimation of the target position;

[0080] The solution of the optimization problem (26) is obtained by Newton iteration method, and the expression is as follows:

[0081]

[0082] Here, i represents the index of the Newton iteration. and Respectively represent functions About estimated location The first and second order derivatives of are as follows:

[0083]

[0084] in,

[0085]

[0086] In formula (30), the path delay Derivatives of the target position coordinates x and y and The expressions are as follows:

[0087]

[0088] In formula (30), the cost function Q1 is related to the path delay The derivative of The expression is as follows:

[0089]

[0090] in,

[0091]

[0092] and,

[0093]

[0094] The Newton iteration process of equation (28) continues until the difference between two consecutive estimates meets the convergence criterion:

[0095] Among them, ε Newton Indicates a smaller value, which is set according to the actual scenario and positioning accuracy.

[0096] B. Solve the optimization problem (27), i.e., estimate the signal amplitude;

[0097] Let function about and The conjugate partial derivatives of are equal to zero, and the expressions are as follows:

[0098]

[0099] By solving equation (35), the solution expression of the optimization problem (27) is as follows:

[0100]

[0101] Based on steps A and B, the updated estimated parameters for the l+1th iteration of problem (25) have all been obtained, namely, And in formula (36) and It will be used as the input for the l+2th iteration.

[0102] S53, repeating steps S51-S52 until the expectation maximization iteration convergence condition is met, thereby achieving joint direct wave suppression and target position estimation update;

[0103] The maximization iterative convergence condition is

[0104] Among them, ε EM Set according to the actual scenario and task accuracy requirements.

[0105] Furthermore, in step S5, the weak target signal level iterative estimation algorithm for direct wave interference suppression performs an initial estimation on unknown parameters, specifically as follows:

[0106] In problem (26), the unknown parameter and is initialized uniformly randomly on each trial, and then a coarse 2D grid search is performed on the target position to find an initial estimate of the target position that maximizes problem (26)

[0107] After the iterative estimation algorithm converges, that is, after reaching the maximum iterative convergence condition, the simplified expression of the target position estimation problem in equation (26) is as follows:

[0108]

[0109] Among them, Indicates that from the observation r m,n Subtract the estimated direct wave interference item Indicates the estimated target echo.

[0110] The beneficial effects of the present invention are as follows: the method of the present invention first initializes system parameters and establishes a target echo model of a passive radar without a reference channel that is contaminated by noise and direct wave interference, then combines the target echo models of distributed multiple stations and the unknown signals of non-cooperative external radiation sources to establish a complete data set, and derives its conditional likelihood function, and finally, based on the expectation maximization principle, iteratively executes the expected step and the maximum step of the conditional likelihood function to continuously update the target position estimation and suppress direct wave interference until the convergence condition of the expectation maximization algorithm is met to obtain the maximum likelihood estimation of the target position, thereby realizing joint direct wave suppression and target position estimation update. The method of the present invention can be applied to the field of passive radar target positioning. A non-cooperative external radiation source with unknown signals is used as a signal source, and a passive radar without a reference channel is used to perform weak target signal-level positioning of a weak target with direct wave interference suppression in a networking and collaborative manner. The method is particularly suitable for realizing low-complexity robust weak target signal-level positioning of a weak target in a direct wave interference environment by using a non-cooperative external radiation source with unknown signals, while getting rid of the dependence on a reference channel, reducing the system deployment cost and complexity, and solving the problems of low positioning accuracy, susceptibility to direct wave interference, unknown signals of non-cooperative external radiation sources, and strong dependence on reference channels in weak target detection of current passive radar systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0111] Figure 1 The present invention is a flow chart of a method for weak target signal level positioning by passive radar networking collaboration without reference channels.

[0112] Figure 2 It is a schematic diagram of a two-dimensional simulation scenario of passive radar networking without reference channels to coordinate target positioning in an embodiment of the present invention.

[0113] Figure 3 It is a likelihood plane diagram of the weak target signal level positioning method of the passive radar networking collaboration without reference channel in an embodiment of the present invention.

[0114] Figure 4 Schematic diagram of the comparison of positioning errors between the method of the present invention and other target positioning algorithms under different direct wave interference intensities under weak target echo intensity in an embodiment of the present invention.

[0115] Figure 5 Schematic diagram of the comparison of positioning errors between the method of the present invention and other target positioning algorithms under different direct wave interference intensities under strong target echo intensity in an embodiment of the present invention.

[0116] Figure 6 Schematic diagram of comparison of positioning errors between the method of the present invention and other target positioning algorithms under different target echo intensities in an embodiment of the present invention. DETAILED DESCRIPTION

[0117] In order to facilitate the description of the present invention, the following terms are first defined:

[0118] 1. Passive radar: It obtains the target status by receiving the reflected echo from the external radiation source to the target without the need for a dedicated transmitter.

[0119] 2. Passive radar network collaboration: Passive radars and external radiation sources are widely distributed to form a passive collaborative detection network, which can observe targets from multiple perspectives, suppress target radar cross-sectional area flicker, and obtain spatial diversity gain.

[0120] 3. External radiation sources: various signal emission sources widely existing in space, including but not limited to commercial radiation sources such as broadcasting / communication base stations, navigation / communication satellites, and military signal emission sources such as active radar / interference.

[0121] 4. Non-cooperative external radiation source: The signal waveform and other working parameters of the external radiation source are unknown.

[0122] 5. Direct wave interference: The signal received by the radar that is superimposed on the target echo and comes directly from an external radiation source.

[0123] 6. Cramer-Rao lower bound: the lower bound of the variance of any unbiased estimator.

[0124] The present invention is mainly verified by simulation experiment, and all steps and conclusions are verified to be correct on Matlab R2020b. The method of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0125] like Figure 1 As shown, a flow chart of a weak target signal level positioning method for passive radar networking without reference channel of the present invention is shown, and the specific steps are as follows:

[0126] S1. Initialize system parameters;

[0127] Initialize the number N and position coordinates of external radiation sources Initialize the number M and position coordinates of passive radar receivers Target position coordinates p = [x, y] T .

[0128] Among them, the superscript (·) T Indicates transpose.

[0129] For a passive dual-base pair consisting of the nth external radiation source and the mth passive radar receiver, the signal amplitudes of the direct wave interference and the target echo in the received signal are expressed as α and m,n and β m,n ; Set the number of passive radar sampling points to K and the sampling period to T s ; The noise superimposed by the echo received by each passive radar receiver has a mean of 0 and a variance of of complex circularly symmetric white Gaussian distribution, and are independent of each other.

[0130] S2. Establish a passive radar echo model without reference channel contaminated by direct waves and noise, and construct a joint observation model of passive radar network collaboration to obtain spatial diversity gain;

[0131] S3. Based on the maximum likelihood principle, a signal-level likelihood function for cooperative observation of passive radar networks is constructed to enhance the detection capability of weak targets, thereby forming a non-convex and nonlinear high-dimensional target position estimation problem;

[0132] S4. Treat the unknown signals of non-cooperative external radiation sources as unobservable hidden variables, and conduct collaborative observations with passive radar networks to construct a complete data set and derive its conditional likelihood function;

[0133] S5. Design an iterative estimation algorithm for weak target signal level for direct wave interference suppression based on the expectation maximization principle. Each iteration first calculates the conditional expectation of the likelihood function about the unknown external radiation source signal, and then maximizes the expectation based on the joint optimization mechanism of sequential and Newton iterations to achieve joint direct wave suppression and target position estimation update.

[0134] In this embodiment, step S2 is specifically as follows:

[0135] The target echo contaminated by direct waves and noise from the nth external radiation source received by the mth passive radar receiver The expression is as follows:

[0136]

[0137] Among them, the superscript (·) d and(·) e Represent the direct path and target echo path respectively, α m,n and β m,n Represent the complex amplitudes of the direct wave and the target echo respectively; represents the baseband transmission signal of the nth external radiation source at time t; represents the direct path propagation delay from the nth external radiation source to the mth passive radar receiver; represents the propagation delay of the echo path from the nth external radiation source through the target to the mth passive radar receiver, and c0 represents the propagation speed of electromagnetic waves; The variance is is a complex circularly symmetric white Gaussian random variable.

[0138] Assuming that the noises of different passive radar receivers are independent of each other and white in space and time, the expression is as follows:

[0139]

[0140] The symbol t represents time, and the symbol (·) * and δ(·) denote the statistical expectation, conjugate, and impulse functions, respectively.

[0141] set up and Respectively represent the time domain signal in equation (1) and The K-point discrete sampling vector with a sampling period of T s .

[0142] Among them, the superscript (·) d / e Indicates the direct path or target echo path.

[0143] Then, the frequency domain expressions of the discrete vectors are calculated to extract the delay of the direct wave interference and the target echo. represents the K-point discrete Fourier transform of the received signal, T represents the discrete Fourier transform matrix, and its (a, b)th element is expressed as Then the frequency domain expression of the discrete sampling vector of formula (1) is as follows:

[0144]

[0145] in, and The symbol diag{·} denotes a diagonal matrix whose diagonal elements are vectors or matrices.

[0146] The observation model of MN passive dual-base pairs composed of M passive radars without reference channels and N external radiation sources is combined. The expression of the joint observation r of the passive radar network without reference channels is as follows:

[0147]

[0148] In this embodiment, step S3 is specifically as follows:

[0149] Based on the Gaussian characteristics of the joint observation signal, the logarithmic expression of the likelihood function of the joint observation r in formula (4) is as follows:

[0150]

[0151] in,

[0152]

[0153] and,

[0154]

[0155] A=diag{α1,…,αN},α n =[α 1,n ,…,α M,n ] T

[0156] B=diag{β1,…,β N},β n =[β 1,n ,…,β M,n ] T (7)

[0157] Among them, the symbol represents the Kronecker product, the symbol det(·) represents the determinant of the matrix, (·) Η represents the conjugate transpose, (·) -1 Represents the inverse operation, matrix I K and I M Represents K-dimensional and M-dimensional identity matrices, respectively. and Respectively represent the noise w m,n and signal n The covariance matrix of .

[0158] Maximum Likelihood Estimation of Target Location It is obtained by maximizing the log-likelihood function lnp(r) in equation (5), and the expression is as follows:

[0159]

[0160] Among them, the unknown parameter vector θ = [p T ,α T ,β T ] T , α=[α 1,1 ,…,α M,N ] T , β=[β 1,1 ,…,β M,N ] T .

[0161] The optimization problem of equation (8) is highly non-convex and nonlinear, so it is difficult to find an analytical solution. In addition, its computational complexity increases exponentially with the increase of the number of external radiation sources and passive radars N and M, and its computational workload is unbearable. In order to reduce the computational complexity, a weak target signal level iterative estimation algorithm based on the expectation maximization principle is adopted.

[0162] In this embodiment, step S4 is specifically as follows:

[0163] Unknown external radiation source signal is considered to be an unobservable hidden vector. Then the observation r in equation (4) is considered to be an incomplete data set, and the expression of the complete data set y is defined as follows:

[0164] y=[r T ,s T ] T (9)

[0165] According to Bayesian theory, the conditional log-likelihood function expression of the complete data set y is as follows:

[0166]

[0167] Among them, the function p(r,s,θ) represents the joint likelihood function of r, s and θ; the function p(s,θ) represents the joint likelihood function of s and θ; and the function p(θ) represents the likelihood function of θ.

[0168] The functions lnp(r|s,θ) and lnp(s|θ) represent the conditional log-likelihood functions of the network cooperative joint observation r and the non-cooperative external radiation source signal s, respectively, and the expressions are as follows:

[0169]

[0170] in, represents the covariance matrix of the external radiation source signal s, μ represents the conditional mean of the observation r, and the specific expression is as follows:

[0171]

[0172] Combining equations (11) and (12), the conditional log-likelihood function expression of the complete data set y in equation (10) is as follows:

[0173] lnp(y|θ)=f1(s)+f2(s,θ) (14)

[0174] in,

[0175]

[0176] In this embodiment, step S5 is specifically as follows:

[0177] S51, executing the expectation step, that is, finding the conditional expectation of the likelihood function of the complete data set;

[0178] The conditional expectation of the likelihood function lnp(y|θ) of the complete data set y in formula (14) is The expression is as follows:

[0179]

[0180] Among them, the superscript (·) (l)represents the lth iteration, Represents the parameter estimation of the lth iteration. Discarding the term f1(s) that is irrelevant to the estimated parameter θ and calculating the conditional expectation of f2(s,θ), we get the following expression:

[0181]

[0182] in,

[0183]

[0184] The symbol Tr{·} represents the trace of the matrix; the vector and matrix Respectively represent s n The minimum mean square error estimate and conditional covariance matrix of .

[0185] Due to s n and r n They obey a joint Gaussian distribution with mean zero, then and The closed form expression is as follows:

[0186]

[0187] in,

[0188]

[0189] and,

[0190]

[0191] S52, executing the maximum step, that is, maximizing the conditional expectation of the likelihood function of the complete data set obtained in step S51 based on the joint optimization mechanism of sequential and Newton iteration;

[0192] By maximizing the conditional expectation of formula (16) The estimated parameter vector for the (l+1)th iteration The expression is as follows:

[0193]

[0194] Then maximize the function in (25) That is, the target position p and the signal amplitudes α and β are jointly optimized. This is also a high-dimensional optimization problem with high computational complexity. Here, a sequential estimation strategy is adopted. Transformed into two low-dimensional sub-estimation problems, the expressions are as follows:

[0195]

[0196] in, and They respectively represent the estimate of the signal amplitude given by the lth iteration.

[0197] The optimization problems of equations (26) and (27) are solved as follows:

[0198] A. Solve the optimization problem (26), i.e., Newton iterative estimation of the target position;

[0199] The solution of the optimization problem (26) is obtained by Newton iteration method, and the expression is as follows:

[0200]

[0201] Here, i represents the index of the Newton iteration. and Respectively represent functions About estimated location The first and second order derivatives of are as follows:

[0202]

[0203] in,

[0204]

[0205] In formula (30), the path delay Derivatives of the target position coordinates x and y and The expressions are as follows:

[0206]

[0207] In formula (30), the cost function Q1 is related to the path delay The derivative of The expression is as follows:

[0208]

[0209] in,

[0210]

[0211] and,

[0212]

[0213] The Newton iteration process of equation (28) continues until the difference between two consecutive estimates meets the convergence criterion:

[0214] Among them, ε Newton Indicates a smaller value, which is set according to the actual scenario and positioning accuracy.

[0215] B. Solve the optimization problem (27), i.e., estimate the signal amplitude;

[0216] The optimization problem (27) has an analytical solution, which is because the function It is a quadratic function of the unknown parameters α and β, as shown in formula (17).

[0217] Let function about and The conjugate partial derivatives of are equal to zero, and the expressions are as follows:

[0218]

[0219] By solving equation (35), the solution expression of the optimization problem (27) is as follows:

[0220]

[0221] Based on steps A and B, the updated estimated parameters for the l+1th iteration of problem (25) have all been obtained, namely, And in formula (36) and It will be used as the input for the l+2th iteration.

[0222] S53, repeating steps S51-S52 until the expectation maximization iteration convergence condition is met, thereby achieving joint direct wave suppression and target position estimation update;

[0223] The maximization iterative convergence condition is

[0224] Among them, ε EM Set according to the actual scenario and task accuracy requirements.

[0225] In this embodiment, in step S5, the weak target signal level iterative estimation algorithm for direct wave interference suppression performs an initial estimation on unknown parameters, specifically as follows:

[0226] In problem (26), the unknown parameter and is initialized uniformly randomly on each trial, and then a coarse 2D grid search is performed on the target position to find an initial estimate of the target position that maximizes problem (26)

[0227] After the signal-level iterative algorithm converges, that is, after reaching the maximum iterative convergence condition, the simplified expression of the target position estimation problem in equation (26) is as follows:

[0228]

[0229] Among them, Indicates that from the observation r m,n Subtract the estimated direct wave interference item represents the estimated target echo. In essence, the target position estimation is based on the observation of With the estimated target echo The correlation between them is used to continuously update the estimated target position and suppress direct wave interference during the iteration process.

[0230] Considering that the target echo in the passive radar observation without reference channel is polluted by noise and direct wave interference, a high-dimensional joint direct target positioning algorithm involving the target position and other unknown parameters is first designed. However, due to the highly nonlinear nature of the algorithm, there is no closed-form solution. This embodiment designs a weak target signal-level positioning method for passive radar networking without reference channel collaboration based on the weak target signal-level iterative estimation algorithm for direct wave interference suppression based on the expectation maximization principle. The weak target signal-level positioning method iteratively estimates the target position and other unknown parameters, significantly reducing the computational complexity. In addition, a sequential estimation strategy is adopted to transform the high-dimensional estimation problem into several low-dimensional estimation problems, further reducing the computational burden. The weak target signal-level positioning method continuously subtracts the estimated direct wave interference from the received signal during the entire iterative process, and then updates the estimate of the target position until convergence, thereby achieving joint direct wave suppression and target position estimation. In addition, unlike the two-step method of data-level positioning, the weak target signal-level positioning method of the present invention directly combines the received signals of multiple stations to estimate the target position, which can effectively deal with the problem of limited estimation performance caused by weak echoes of weak targets, and also get rid of the dependence of existing passive radars on reference channels, reduce hardware costs, avoid the strict requirements for deploying high-quality reference channels, and have wider applicability. Based on this, the weak target signal-level positioning method of the present invention can use non-cooperative external radiation sources with unknown signals to achieve signal-level low-complexity robust target positioning of passive radar networking without reference channels in a direct wave interference environment, and can be applied to the target positioning of passive radars and other fields.

[0231] The target position estimation accuracy is evaluated by the root mean square error RMSE (Root Mean Square Error), which is expressed as follows:

[0232]

[0233] Wherein, L represents the number of Monte Carlo experiments. In this embodiment, L=300; represents the target position estimate of the lth Monte Carlo trial.

[0234] In this embodiment, the direct wave interference intensity ratio INR to the target echo and the target echo intensity ratio SNR are defined as follows:

[0235]

[0236] The weak target signal-level positioning method designed in this embodiment is a signal-level target positioning based on the expectation maximization algorithm, so it is called EMDL (expectation maximization-based direct localization). In order to prove the direct wave suppression performance and positioning performance of the positioning algorithm EMDL of the present invention, three positioning algorithms are given for comparison: the positioning algorithm EMDL-NDPI (expectation maximization-based direct localization with nodirect-path interference), that is, signal-level target positioning based on the expectation maximization algorithm but without considering direct wave interference; the positioning algorithm CCTSL (cross-correlation-based two-step localization), that is, two-step target positioning that first estimates the intermediate parameters and then estimates the target position. In addition, it also includes a theoretical lower bound of the estimation error that can be obtained by the positioning algorithm under the observation model described in the present invention, namely RCRLB (square root of the Cramer-Rao lower bound CRLB).

[0237] The simulation scenario of this embodiment is as follows Figure 2 As shown, it includes M = 4 passive radars, located at and N = 1 external radiation source, located at One at p = [5,6] T Km of target to be located.

[0238] By traversing the 2D grid plane of the monitoring area, the likelihood planes of the positioning algorithms EMDL-NDPI and EMDL under different direct wave interference intensities are obtained, as shown in Figure 3 As shown (the maximum likelihood point corresponds to the point with the minimum value in the figure). Figure 3 (a) and 3(b) are the likelihood function planes of the positioning algorithm EMDL-NDPI when INR = -10dB and INR = 15dB, respectively; Figure 3 (c) and 3(d) are the likelihood function planes of the positioning algorithm EMDL when INR = -10dB and INR = 15dB, respectively. Figure 3(a) and 3(c) show that when INR = -10dB, the maximum likelihood points of the positioning algorithms EMDL-NDPI and EMDL both appear at the true target position. When the intensity of the direct wave interference increases to INR = 15dB, as shown in Figure 3 As shown in (b) and 3(d), the maximum likelihood point of the positioning algorithm EMDL-NDPI is far away from the true target position, while the maximum likelihood point of the positioning algorithm EMDL is still at the true target position, indicating that the invented positioning algorithm can work normally in a strong direct wave interference environment and estimate the target position.

[0239] Under the condition of target echo intensity SNR=5dB, the direct wave interference intensity INR is changed, and steps S1-S5 of the method of the present invention are repeatedly executed to obtain Figure 4 .from Figure 4 It can be seen that as the intensity of direct wave interference increases, the positioning algorithms EMDL-NDPI and CCTSL quickly deviate from RCRLB, and positioning fails. However, the positioning error RMSE of the positioning algorithm EMDL of the method of the present invention gradually decreases and always converges to RCRLB until the INR exceeds the tolerance threshold of 10dB. This means that the positioning algorithm of the present invention has good tolerance to direct wave interference, and the direct wave interference of appropriate intensity helps to improve the positioning performance of the target.

[0240] Under the condition of target echo intensity SNR=10dB, the direct wave interference intensity INR is changed, and steps S1-S5 of the method of the present invention are repeatedly executed to obtain Figure 5 .contrast Figure 4 and 5 It can be seen that as the target echo intensity increases, the direct wave interference tolerance threshold of the positioning algorithm EMDL of the method of the present invention is increased from INR=10dB to INIR=15dB, and it has a stronger direct wave interference tolerance capability.

[0241] When the direct wave interference intensity INR = -5dB, the target echo intensity SNR is changed, and steps S1-S5 of the present invention are repeated to obtain Figure 6 .from Figure 6 It can be seen that with the enhancement of SNR, the positioning algorithm EMDL of the method of the present invention can first converge to RCRLB, which is effective. However, the positioning algorithms EMDL-NDPI and CCTSL require a larger SNR to converge to RCRLB.

[0242] In summary, the method of the present invention can be applied to the field of passive radar target positioning. A non-cooperative external radiation source with unknown signal is used as a signal source, and a passive radar without a reference channel is used to perform weak target signal-level positioning with direct wave interference suppression on weak targets in a networked collaborative manner. The method is particularly suitable for realizing signal-level low-complexity robust weak target positioning in a direct wave interference environment by using a non-cooperative external radiation source with unknown signal. At the same time, the method gets rid of the dependence on the reference channel, reduces the system deployment cost and complexity, and solves the problems of low positioning accuracy, susceptibility to direct wave interference, unknown signals of non-cooperative external radiation sources, and strong dependence on reference channels in weak target detection of current passive radar systems.

[0243] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for weak target signal level positioning without reference channel passive radar network collaboration, the specific steps are as follows: S1. Initialize system parameters; Initialize the number N and position coordinates of external radiation sources n=1,…,N;Initialize the number M and position coordinates of passive radar receivers m=1,…,M, target position coordinates in, Superscript represents transpose; For a passive dual-base pair consisting of the nth external radiation source and the mth passive radar receiver, the signal amplitudes of the direct wave interference and the target echo in the received signal are expressed as α and m,n and β m,n ; Set the number of passive radar sampling points to K and the sampling period to T s ; The noise superimposed by the echo received by each passive radar receiver has a mean of 0 and a variance of The complex circularly symmetric white Gaussian distribution of and are independent of each other; S2. Establish a passive radar echo model without reference channel contaminated by direct waves and noise, and construct a joint observation model of passive radar network collaboration to obtain spatial diversity gain; S3. Based on the maximum likelihood principle, a signal-level likelihood function of weak targets in passive radar network collaborative observation is constructed to enhance the detection capability of weak targets, thereby forming a non-convex and nonlinear high-dimensional target position estimation problem; S4. Treat the unknown signals of non-cooperative external radiation sources as unobservable hidden variables, and conduct collaborative observations with passive radar networks to construct a complete data set and derive its conditional likelihood function; S5. Design an iterative estimation algorithm for weak target signal level for direct wave interference suppression based on the expectation maximization principle. Each iteration first calculates the conditional expectation of the likelihood function about the unknown external radiation source signal, and then maximizes the expectation based on the joint optimization mechanism of sequential and Newton iterations to achieve joint direct wave suppression and target position estimation update.

2. According to claim 1, a method for weak target signal level positioning by passive radar networking without reference channel, It is characterized in that The step S2 is specifically as follows: The target echo contaminated by direct waves and noise from the nth external radiation source received by the mth passive radar receiver The expression is as follows: Among them, the superscript (·) d and(·) e Represent the direct path and target echo path respectively, α m,n and β m,n Represent the complex amplitudes of the direct wave and the target echo respectively; represents the baseband transmission signal of the nth external radiation source at time t; represents the direct path propagation delay from the nth external radiation source to the mth passive radar receiver; represents the propagation delay of the echo path from the nth external radiation source through the target to the mth passive radar receiver, c 0 It represents the propagation speed of electromagnetic waves; The variance is A complex circularly symmetric white Gaussian random variable; Assuming that the noises of different passive radar receivers are independent of each other and white in space and time, the expression is as follows: Among them, the symbol Indicates time, symbol (·) * and δ(·) represent the statistical expectation, conjugate, and impulse functions, respectively; set up and Respectively represent the time domain signal in equation (1) and The K-point discrete sampling vector with a sampling period of T s ; Among them, the superscript (·) d / e Indicates the direct path or target echo path; Then, the frequency domain expressions of the discrete vectors are calculated to extract the delay of the direct wave interference and the target echo. represents the K-point discrete Fourier transform of the received signal, T represents the discrete Fourier transform matrix, and its (a, b)th element is expressed as a,b=0,…,K-1,f Δ =1 / T s K; then the frequency domain expression of the discrete sampling vector of formula (1) is as follows: in, and The symbol diag{·} denotes a diagonal matrix whose diagonal elements are vectors or matrices; The observation model of MN passive dual-base pairs composed of M passive radars without reference channels and N external radiation sources is combined. The expression of the joint observation r of the passive radar network without reference channels is as follows:

3. According to claim 1, a method for weak target signal level positioning by passive radar networking without reference channel, It is characterized in that The step S3 is specifically as follows: Based on the Gaussian characteristics of the joint observation signal, the logarithmic expression of the likelihood function of the joint observation r in formula (4) is as follows: in, and, Among them, the symbol represents the Kronecker product, the symbol det(·) represents the determinant of the matrix, (·) Η represents the conjugate transpose, (·) -1 Represents the inverse operation, matrix I K and I M Represents K-dimensional and M-dimensional identity matrices respectively, and the matrices and Respectively represent the noise w m,n and signal n The covariance matrix of Maximum Likelihood Estimation of Target Location It is obtained by maximizing the log-likelihood function lnp(r) in equation (5), and the expression is as follows: Among them, the unknown parameter vector 4. According to claim 1, a method for weak target signal level positioning by passive radar networking without reference channel, It is characterized in that The step S4 is specifically as follows: Unknown external radiation source signal is considered to be an unobservable hidden vector; then the observation r in equation (4) is considered to be an incomplete data set, and the expression of the complete data set y is defined as follows: According to Bayesian theory, the conditional log-likelihood function expression of the complete data set y is as follows: Among them, the function p(r,s,θ) represents the joint likelihood function of r, s and θ; the function p(s,θ) represents the joint likelihood function of s and θ; the function p(θ) represents the likelihood function of θ; The functions lnp(r|s,θ) and lnp(s|θ) represent the conditional log-likelihood functions of the network cooperative joint observation r and the non-cooperative external radiation source signal s, respectively, and the expressions are as follows: in, represents the covariance matrix of the external radiation source signal s, μ represents the conditional mean of the observation r, and the specific expression is as follows: Combining equations (11) and (12), the conditional log-likelihood function expression of the complete data set y in equation (10) is as follows: lnp(y|θ)=f 1 (s)+f 2 (s,θ) (14) in, 5. According to claim 1, a method for weak target signal level positioning by passive radar networking without reference channel, It is characterized in that The step S5 is specifically as follows: S51, executing the expectation step, that is, finding the conditional expectation of the likelihood function of the complete data set; The conditional expectation of the likelihood function lnp(y|θ) of the complete data set y in formula (14) is The expression is as follows: Among them, the superscript (·) (l) represents the lth iteration, represents the parameter estimate of the lth iteration; discard the term f that is not related to the estimated parameter θ 1 (s), calculate f 2 The conditional expectation of (s,θ) can be expressed as follows: in, The symbol Tr{·} represents the trace of the matrix; the vector and matrix Respectively represent s n The minimum mean square error estimate and conditional covariance matrix of ; Due to s n and r n They obey a joint Gaussian distribution with mean zero, then and The closed form expression is as follows: in, and, S52, executing the maximum step, that is, maximizing the conditional expectation of the likelihood function of the complete data set obtained in step S51 based on the joint optimization mechanism of sequential and Newton iteration; By maximizing the conditional expectation of formula (16) The estimated parameter vector for the (l+1)th iteration The expression is as follows: Then maximize the function in (25) That is, the target position p and the signal amplitudes α and β are jointly optimized; a sequential estimation strategy is adopted to Transformed into two low-dimensional sub-estimation problems, the expressions are as follows: in, and They represent the estimation of the signal amplitude given by the lth iteration respectively; The optimization problems of equations (26) and (27) are solved as follows: A. Solve the optimization problem (26), i.e., Newton iterative estimation of the target position; The solution of the optimization problem (26) is obtained by Newton iteration method, and the expression is as follows: Where i represents the index of Newton iteration; and Respectively represent functions About estimated location The first and second order derivatives of are as follows: in, In formula (30), the path delay Derivatives of the target position coordinates x and y and The expressions are as follows: In formula (30), the cost function Q 1 About path delay The derivative of The expression is as follows: in, and, The Newton iteration process of equation (28) continues until the difference between two consecutive estimates meets the convergence criterion: Among them, ε Newton Indicates a smaller value, which is set according to the actual scenario and positioning accuracy; B. Solve the optimization problem (27), i.e., estimate the signal amplitude; Let function about and The conjugate partial derivatives of are equal to zero, and the expressions are as follows: By solving equation (35), the solution expression of the optimization problem (27) is as follows: Based on steps A and B, the updated estimated parameters for the l+1th iteration of problem (25) have all been obtained, namely, And in formula (36) and It will be used as the input for the l+2th iteration; S53, repeating steps S51-S52 until the expectation maximization iteration convergence condition is met, thereby achieving joint direct wave suppression and target position estimation update; The maximization iterative convergence condition is Among them, ε EM Set according to the actual scenario and task accuracy requirements.

6. According to claim 1, a method for weak target signal level positioning by passive radar networking without reference channel, It is characterized in that In step S5, the weak target signal level iterative estimation algorithm for direct wave interference suppression performs an initial estimation on unknown parameters, specifically as follows: In problem (26), the unknown parameter and is initialized uniformly randomly on each trial, and then a coarse 2D grid search is performed on the target position to find an initial estimate of the target position that maximizes problem (26) After the iterative estimation algorithm converges, that is, after reaching the maximum iterative convergence condition, the simplified expression of the target position estimation problem in equation (26) is as follows: Among them, Indicates that from the observation r m,n Subtract the estimated direct wave interference item Indicates the estimated target echo.

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