Far-field target direct direction finding method, system, device and medium

Abstract

The invention relates to a far-field target direct direction finding method, system and device and a medium, and the method comprises the steps: arranging at least L sensor nodes in a two-dimensional or three-dimensional space, and carrying out the synchronous observation of a signal transmitted by a far-field target; the method comprises the following steps: eliminating dependence on irrelevant parameters such as a target distance through mathematical transformation by using original signals received by each sensor node, and constructing a maximum likelihood cost function only related to a target signal direction-of-arrival angle; directly determining the direction-of-arrival angle of the target signal by searching the maximum value of the cost function; the influence of an intermediate parameter estimation error on a final direction finding result caused by explicit extraction and estimation of an intermediate parameter (such as time difference of arrival (TDOA)) in a traditional two-step method is avoided; the system, the equipment and the medium realize the direct arrival angle determination of the far-field target based on the method. According to the invention, the direction finding precision under the conditions of low signal-to-noise ratio and short base line is improved, and the method is suitable for scenes with high requirements on direction finding performance; in a complex electromagnetic environment, all observation data are directly processed, so that the robustness of the system on direction finding of a single target is enhanced.

Description

Technical Field

[0001] This invention belongs to the field of radio direction finding technology, and particularly relates to a method, system, device and medium for direct direction finding of far-field targets. Background Technology

[0002] In the field of radio direction finding for far-field targets, positioning techniques based on Time Difference of Arrival (TDOA) are widely used due to their advantage of not requiring absolute time synchronization. Among them, the SUM-MPR and GTRS-MPR algorithms based on Modified Polar (MPR) coordinates achieve target azimuth estimation through a two-step method: the first step obtains the TDOA values ​​between sensor pairs using signal processing techniques such as mutual ambiguity function analysis; the second step substitutes the TDOA into a nonlinear equation system constructed in the MPR coordinate system and uses optimization methods such as successive unconstrained minimization or solving generalized trust region subproblems to calculate the azimuth angle. The MPR coordinate system attempts to improve the stability and convergence of the positioning solution under far-field conditions by introducing the reciprocal of the range parameter.

[0003] In recent years, significant progress has been made in optimizing TDOA direction finding technology. Patent application CN201910747347.5, entitled "Radar Signal Direction Finding Method, Device, and Computer Storage Medium Based on Improved Polar Coordinate Representation Model," proposes a radar signal direction finding method based on an improved polar coordinate representation. This method associates the TDOA estimation equation with MPR variables, transforms it into a generalized trust region subproblem (GTRS-MPR) through pseudo-linearization, and utilizes the Lagrange multiplier method to achieve high-precision direction finding for far-field targets. Patent application CN202211424566.8, entitled "A Target Direction Finding Method Based on a Short Baseline Unified Model," proposes a unified model based on MPR, combined with an improved successive unconstrained minimization (SUM-MPR) method. It solves for the target angle through a quadratic constrained optimization problem, effectively avoiding the threshold effect of short baseline positioning systems.

[0004] Although existing MPR-based TDOA direction finding techniques have made some progress, these methods mostly rely on two-step separation processing, and TDOA estimation errors are prone to accumulate in the azimuth calculation. In noisy environments, the positioning accuracy and stability still need to be improved. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention aims to provide a method, system, device, and medium for direct direction finding of far-field targets. At least three sensor nodes are arranged in a two-dimensional or three-dimensional space, and the known position coordinates of each node are determined using the centroid of all sensor nodes as the origin. Then, the sensor nodes synchronously sample signals from the far-field target to obtain the raw received signals of each node. The obtained raw received signals are transformed to the frequency domain, and based on the maximum likelihood estimation criterion, a covariance matrix related to the candidate incoming wave direction is constructed. Then, the properties of the common time delay component in the signal caused by the target distance corresponding to the unitary matrix in the frequency domain are utilized. The distance effect is eliminated, thereby establishing a cost function that is only related to the direction of arrival of the wave. The value of the cost function is determined by the largest eigenvalue of the covariance matrix. Finally, within a predetermined angle search space, the cost function is solved using search methods such as grid search and a strategy that can be combined with multiple rounds of iterative refinement. By finding the angle that maximizes the global value of the cost function, the direction of arrival of the wave of the target is directly estimated. The Direct Direction Finding (DAAD) method has stronger noise resistance and higher direction finding accuracy in far-field target direction finding. Its overall performance is significantly better than traditional parameter estimation methods, providing an effective solution for high-precision direction finding of far-field targets.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A direct direction finding method for far-field targets includes the following steps:

[0008] Step 1: Construct a direct direction finding scenario model for the far-field target. This involves establishing a geometric layout model between the sensor array and the far-field target, and, based on the far-field approximation, correlating the relative time delay of the received signals from each sensor with the direction-of-arrival angle of the target signal. Simultaneously sample the signal from the far-field target using L sensor nodes with known locations, where L≥3, to obtain the original received signal vector r of each sensor node. l (t);

[0009] Step 2: Construct a cost function for the target signal direction-of-arrival angle. Establish a cost function that depends only on the target signal direction-of-arrival angle. This cost function is obtained by transforming the far-field target direct direction-finding scenario model established in Step 1, and using the unitary matrix property and similarity transformation theory to decouple the target signal direction-of-arrival angle parameter to be estimated from other irrelevant variables. The change in the cost function value characterizes the likelihood of the target signal direction-of-arrival angle.

[0010] Step 3: Perform angle search and estimation: Solve the cost function constructed in Step 2 using numerical optimization methods; systematically traverse and evaluate the preset angle space to find the optimal angle that makes the cost function reach its global maximum value; this optimal angle is the final estimated value of the target signal direction of arrival angle.

[0011] The specific method for step 1 is as follows:

[0012] Suppose there are L sensor nodes with known positions in two-dimensional or three-dimensional space, with the centroid p0 of each sensor node's position as the origin of the coordinate system (hereinafter referred to as the centroid), and the coordinates of the l-th sensor node denoted as p. l =[x l ,y l ] T The sensor node coordinates satisfy the following relationship:

[0013]

[0014] Let the far-field target position be p. s =[x s ,y s ] T The distance ρ from the far-field target position to the center of gravity s =||p s || F The angle θ between the far-field target position and the centroid of the target's incoming wave direction is defined as the angle between the opposite direction of the signal incident direction and the positive x-axis. The distance from the far-field target position to the l-th sensor node is expressed as:

[0015]

[0016] The angle between the line connecting the l-th sensor node and the center of gravity and the positive x-axis is defined as... ρ l With p l The relationship is given by the following formula:

[0017]

[0018] Distance ρ between far-field target position and center of gravity s The distance ρ from the far-field target position to the l-th sensor node l The difference Δρ l Represented as:

[0019]

[0020] For far-field signals, ρ l <<ρ s It is approximately assumed that:

[0021]

[0022] When the target is in the far field, the distance ρ between the target position and the center of gravity is... s The distance ρ from the far-field target position to the l-th sensor node l The ratio approaches 0 on the right; using the approximate relationship of equation (5), we find the limit of equation (4):

[0023]

[0024] The physical meaning of equation (6) is: when the far-field target is far enough (i.e. ), the difference Δρ between the distance from the far-field target position to the centroid and the distance from the far-field target position to the l-th sensor node. l The time delay τ experienced by the far-field target signal to reach the l-th sensor node is a variable that depends only on the direction-of-arrival angle θ of the target signal. sl Decomposed into the following form:

[0025] τ sl =τ0+τ l (7)

[0026]

[0027] Where τ0 is the time delay experienced by the far-field target signal to reach the centroid, τ l Let be the relative time delay between the center of gravity and the l-th sensor node, and c be the electromagnetic wave propagation speed, usually set as a constant; assuming the far-field target signal starts at time 0, then the signal r received by the l-th sensor node... l (t) is expressed in the following form:

[0028] r l (t)=b l s(t-τ0-τ l )+n l (t)0≤t≤T (10)

[0029] Among them, b l It is the attenuation experienced by the far-field target signal as it propagates to the l-th sensor node, s(t) is the original waveform of the far-field target signal, and n l (t) is a normally distributed N(0,σ). 2 Gaussian white noise.

[0030] The specific method for step 2 is as follows:

[0031] By eliminating the irrelevant parameter of target distance ρ and retaining only the target signal direction-of-arrival angle θ, a maximum likelihood estimator for the target signal direction-of-arrival angle θ is provided, specifically:

[0032] The time delay τ between the far-field target signal and the l-th sensor node l (ps The formula can be decomposed as follows:

[0033] τ l (p s )=τ0(p s )+τ l (θ) (11)

[0034] in,

[0035]

[0036]

[0037] e(θ) = [cosθ, sinθ] T (14)

[0038] Wherein, τ0(p s τ represents the time delay τ takes for the far-field target signal to reach the centroid. l (θ) represents the relative time delay difference between the centroid and the l-th sensor node, and c is the electromagnetic wave propagation speed; e(θ) represents the direction vector with respect to the angle θ of the target signal's direction of arrival; the far-field target signal received by sensor node l is represented in the frequency domain as:

[0039]

[0040] in, They represent r respectively l (t), s n (t), n l (t) The data at the k-th frequency after undergoing a Discrete Fourier Transform (DFT) at K points, ω k It is the kth frequency, f0 is the signal start frequency, and T s Indicates the sampling interval time. This represents the phase change caused by the signal delay at the k-th frequency; further, based on the maximum likelihood criterion, the maximum likelihood function for all unknown parameters is given; the estimation model based on the maximum likelihood criterion can be expressed as:

[0041]

[0042] Where L(p,b) represents the total phase shift of the far-field target signal reaching the l-th sensor, and Γ(ρ) represents the phase shift determined by the target distance and is the same for all sensors. l (θ) represents the additional phase offset on the l-th sensor, determined by the direction-of-arrival angle θ of the target signal;

[0043] In equation (16) Γl,p Decomposed into:

[0044] Γ l,p =Γ(ρ)Γ l (θ) (17)

[0045]

[0046] Channel attenuation b l Both the direction of arrival angle θ of the target signal and the unknown channel attenuation b are unknown. l For the unknown problem, the partial derivative is obtained by minimizing equation (16):

[0047]

[0048] Setting equation (20) to 0, we obtain the channel attenuation b. l The maximum likelihood estimate is:

[0049]

[0050] In equation (21), Γ(ρ) and Γ l (θ) is a unitary matrix, therefore:

[0051]

[0052] The power of the far-field target signal received by the station is normalized.

[0053]

[0054] Substituting equations (22) and (23) into equation (21) yields

[0055]

[0056] Furthermore, substituting equation (24) into equation (20) yields:

[0057]

[0058] Equation (25) is equivalent to maximizing the following equation:

[0059]

[0060] Since Γ(ρ) is a unitary matrix, therefore, Having the same matrix eigenvalues ​​as Q(ρ,θ), the time delay matrix Γ(ρ) is introduced by ignoring the target distance ρ, thus eliminating the irrelevant parameter of target distance ρ, and providing an estimate of the direction of arrival angle θ of the weak target signal in the far field:

[0061]

[0062] When the waveform of the far-field target signal is known, then:

[0063]

[0064] C(θ) is the cost function we are looking for. The change in its function value can characterize the likelihood of the target signal's direction of arrival angle. To maximize the cost function value C(θ), the target signal direction of arrival angle θ, i.e., the optimal angle, is required.

[0065] The specific method for step 3 is as follows:

[0066] The optimal angle in equation (30) is solved using an angle search strategy. Specifically, through grid search, firstly, within a predetermined angle search space, all direction-of-arrival angles θ of the target signals to be measured are traversed at a set step size, undergoing multiple rounds of iterative refinement; for each direction-of-arrival angle θ of the target signal to be measured, its corresponding cost function value C(θ) is calculated; finally, all calculated cost function C(θ) values ​​are compared, and the optimal angle is found that maximizes the cost function C(θ) value. This is the final estimate of the direction of the incoming wave from the target.

[0067] Systems based on direct direction finding methods for far-field targets include:

[0068] The signal receiving module is used in step 1 to synchronously sample signals from a far-field target using L sensor nodes with known locations, where L≥3, to obtain the original received signal vector r of each sensor node. l (t);

[0069] The signal preprocessing and transformation module is used in step 2 to process the original received signal vector r output by the signal receiving module. l (t) Utilizing the properties of unitary matrices and the theory of similarity transformation, the output is transformed into the received target signals of each sensor node after angle and phase compensation;

[0070] The cost function construction module is used in step 2 to construct the final cost function for estimating the direction-of-arrival angle θ of the target signal, based on the received target signal from each sensor node after angle and phase compensation, output by the signal preprocessing and transformation module.

[0071] The target signal direction-of-arrival angle θ estimation module is used in step 3 to search for the cost function C(θ) output by the cost function construction module within a predetermined angle search space using a specified search strategy, through multiple rounds of iterative refinement, to find the angle that maximizes the global cost function value. that angle This is a precise estimate of the target signal's angle of arrival.

[0072] A device based on a direct direction finding method for far-field targets, specifically comprising:

[0073] Memory, used to store computer programs;

[0074] A processor is used to implement the far-field target direct direction finding method described in steps 1 to 3 when executing the computer program.

[0075] A computer-readable storage medium storing a computer program, which, when executed by a processor, is capable of performing direct orientation finding of a far-field target based on the far-field target direct orientation finding method described in steps 1 to 3.

[0076] Compared with the prior art, the present invention has the following advantages:

[0077] (1) Higher direction finding accuracy

[0078] Under the same signal-to-noise ratio (SNR), the mean square error (RMSE) of the method of this invention is about 3 dB lower than that of the SUM-MPR and GTRS-MPR methods, indicating that its direction-finding accuracy is higher. When the SNR is above 0 dB, the error variance level of the method of this invention is significantly lower than that of the comparative methods, and it is closer to the Cramer-Rao lower bound (CRLB) under high SNR conditions.

[0079] The fundamental reason lies in the fact that the Direct Direction Finding (DAAD) method proposed in this invention fundamentally avoids the inherent defects of traditional "two-step methods" (such as SUM-MPR and GTRS-MPR). Traditional methods require first accurately estimating the time difference of arrival (TDOA) between each sensor. This step is highly sensitive to noise and small TDOA values ​​in the far field, easily introducing initial errors. Subsequently, these erroneous TDOA values ​​are substituted into a nonlinear positioning equation system for solution, further amplifying the initial errors.

[0080] This invention constructs a direct maximum likelihood estimation model for the direction-of-arrival angle θ of the target signal, using the target signal's direction-of-arrival angle θ as the quantity to be estimated. Through mathematical derivation, this method cleverly incorporates the distance p from the target... s The relevant time delay term τ0(p) s The error is eliminated from the final cost function C(θ), thus avoiding the estimation process of the intermediate parameter TDOA. Since there is no error propagation and amplification between steps, this method directly uses the raw signal information received by all sensors for joint processing, preserving the integrity of the angle information to the greatest extent. Therefore, its direction finding accuracy is superior to the "two-step method" in principle, and the result is closer to the theoretical performance limit (CRLB).

[0081] (2) Stronger noise immunity

[0082] SUM-MPR and GTRS-MPR exhibit a "threshold effect" that degrades performance when the signal-to-noise ratio is below -2dB, while the DAAD method maintains stable performance even when the signal-to-noise ratio is as low as -6dB, without exhibiting the threshold effect.

[0083] The "threshold effect" typically occurs because at low signal-to-noise ratios (SNR), the signal is severely overwhelmed by noise, causing the estimation of the key parameter (TDOA in comparative methods) to completely fail. Traditional methods become extremely difficult to accurately measure small TDOA values ​​at low SNRs, leading to a rapid performance collapse.

[0084] The direct direction finding method of this invention is more robust to noise because it does not rely on the measurement of a single, weak TDOA value. Instead, as shown in equation (27), it constructs a covariance matrix... The received signals from all L observation stations are jointly processed. This process is equivalent to effectively integrating the weak signal energy distributed across multiple channels and using it collectively for the target signal's direction of arrival angle θ. This joint processing method has inherent noise suppression and signal enhancement effects, enabling the method to extract effective angle information from noise even in environments with extremely low signal-to-noise ratios (e.g., -6dB), thereby significantly lowering the performance threshold and exhibiting stronger robustness.

[0085] (3) Robustness to actual errors

[0086] Self-localization error: As the node self-localization error increases (0-20 meters), the direction finding error of the DAAD method increases more slowly, and its accuracy is always better than that of the traditional method.

[0087] Clock synchronization error: The DAAD method is more tolerant of clock synchronization errors and can still maintain a low error when the error reaches 400 nanoseconds, while the performance of the comparison method is significantly reduced.

[0088] For self-localization error: the coordinates p of the sensor node l This is the known input to the model of this invention (as in equation (3)). In the traditional "two-step method", p l Errors can directly and severely affect the calculation of TDOA, thereby disrupting the entire solution process. However, under the global optimization framework of this invention, the slight positional error of a single node has a smooth and distributed effect on the final cost function C(θ). The optimization process (such as arg max in equation (30)) searches for the optimal solution in the entire angle space, which has a certain "averaging" or "passivation" effect on such local disturbances, thus the error growth is more gradual.

[0089] Regarding clock synchronization error: Clock synchronization error is fatal in the TDOA method because it directly manifests as a huge deviation in the TDOA measurement. A synchronization error of 400 ns is much larger than the true TDOA value of the far-field target signal, leading to a completely incorrect TDOA estimation. The method of this invention focuses on the path difference Δρ... l The resulting relative time delay τ l (θ)(as in equation (9)), and transform it into the phase term Γ in the frequency domain. l (θ) is processed. Although clock synchronization error also introduces a common phase offset, the joint processing and maximum value search mechanism of this method have a stronger tolerance for this systematic, θ-independent error, and therefore the performance degrades more slowly when there is a large synchronization error. Attached Figure Description

[0090] Figure 1 This is a plan view of the sensor node and target radiation source of the present invention.

[0091] Figure 2 This is a simulation diagram showing the impact of the signal-to-noise ratio on the direction-finding accuracy of this invention.

[0092] Figure 3 This is a simulation diagram showing the effect of target distance on direction finding accuracy under free fading conditions according to the present invention.

[0093] Figure 4 This is a simulation diagram showing the impact of the site self-positioning error on the direction finding accuracy of the present invention.

[0094] Figure 5 This is a diagram of the far-field target direct direction finding model of the present invention. Detailed Implementation

[0095] The present invention will now be described in further detail with reference to the accompanying drawings.

[0096] A direct direction finding method for far-field targets includes the following steps:

[0097] Step 1, as follows Figure 5 A scenario model for direct direction finding of far-field targets is constructed. This step aims to formalize the direction finding problem physically and mathematically. Its core lies in establishing a geometric layout model between the sensor array and the far-field target, and based on the far-field approximation, correlating the relative time delay of the signals received by each sensor with the direction of arrival angle of the target signal, providing a theoretical premise for subsequent algorithm derivation.

[0098] Step 2: Construct the cost function for angle estimation. The core task of this step is to derive a cost function that depends only on the direction-of-arrival angle of the target signal. This is achieved by performing a series of mathematical transformations on the signal model established in Step 1, utilizing the properties of unitary matrices and similarity transformation theory to decouple the angle parameter to be estimated from other irrelevant variables (such as the target distance). This ultimately results in a cost function whose changes characterize the likelihood of the target signal's direction-of-arrival angle.

[0099] Step 3: Perform angle search and estimation. This step aims to solve the cost function constructed in Step 2 using numerical optimization methods. By systematically traversing and evaluating the preset angle space, a specific angle is found that makes the cost function reach its global maximum. This optimal angle is determined as the final estimated value of the target signal's direction of arrival angle.

[0100] The specific method for step 1 is as follows:

[0101] Suppose there are L sensor nodes with known positions in two-dimensional or three-dimensional space, with the centroid p0 of each sensor node's position as the origin of the coordinate system (hereinafter referred to as the centroid), and the coordinates of the l-th sensor node denoted as p. l =[x l ,y l ] T Therefore, the sensor node coordinates satisfy the following relationship:

[0102]

[0103] Let the far-field target position be p. s =[x s ,y s ] T The distance ρ from the far-field target position to the center of gravity s =||p s || F The angle θ between the far-field target position and the centroid of the target's incoming wave direction is defined as the angle between the opposite direction of the signal incident direction and the positive x-axis. The distance from the far-field target position to the l-th sensor node is expressed as:

[0104]

[0105] The angle between the line connecting the l-th sensor node and the center of gravity and the positive x-axis is defined as... ρ l With p l The relationship is given by the following formula:

[0106]

[0107] Distance ρ between far-field target position and center of gravity s The distance ρ from the far-field target position to the l-th sensor nodel The difference Δρ l Represented as:

[0108]

[0109] For far-field signals, ρ l <<ρ s It is approximately assumed that:

[0110]

[0111] When the target is in the far field, the distance ρ between the target position and the center of gravity is... s The distance ρ from the far-field target position to the l-th sensor l The ratio approaches 0 on the right. Using the approximate relationship of equation (5), we find the limit of equation (4):

[0112]

[0113] The physical meaning of equation (6) is that when the far-field target is far enough away, the difference Δρ between the distance from the far-field target position to the centroid and the distance from the far-field target position to the l-th sensor node is... l Let τ be a variable that depends only on the direction-of-arrival angle θ of the unknown target signal, then the time delay τ experienced by the far-field target signal to reach the l-th sensor node is... sl Decomposed into the following form:

[0114] τ sl =τ0+τ l (7)

[0115]

[0116]

[0117] Where τ0 is the time delay experienced by the far-field target signal to reach the centroid, τ l Let be the relative time delay between the center of gravity and the l-th sensor node, and c be the electromagnetic wave propagation speed, usually set as a constant; assuming the far-field target signal starts at time 0, then the signal r received by the l-th sensor node... l (t) can be expressed in the following form:

[0118] r l (t)=b l s(t-τ0-τ l )+n l (t)0≤t≤T (10)

[0119] Among them, b l It is the attenuation experienced by the far-field target signal as it propagates to the l-th sensor node, s(t) is the original waveform of the far-field target signal, and n l(t) is a normally distributed N(0,σ). 2 Gaussian white noise.

[0120] The specific method for step 2 is as follows:

[0121] By eliminating the irrelevant parameter of target distance ρ and retaining only the target signal direction of arrival angle θ, a maximum likelihood estimator for the target signal direction of arrival angle θ is given; the specific derivation process is as follows.

[0122] The time delay τ between the far-field target signal and the l-th sensor node l (p s The formula can be decomposed as follows:

[0123] τ l (p s )=τ0(p s )+τ l (θ) (11)

[0124] in,

[0125]

[0126] e(θ) = [cosθ, sinθ] T (14)

[0127] Wherein, τ0(p s τ represents the time delay τ takes for the far-field target signal to reach the centroid. l (θ) represents the relative time delay difference between the centroid and the l-th sensor node, and c is the electromagnetic wave propagation speed; e(θ) represents the direction vector with respect to the angle θ of the target signal's direction of arrival; the far-field target signal received by sensor node l can be represented in the frequency domain as:

[0128]

[0129] in, They represent r respectively l (t), s n (t), n l (t) The data at the k-th frequency after undergoing a Discrete Fourier Transform (DFT) at K points, ω k It is the kth frequency, f0 is the signal start frequency, and T s Indicates the sampling interval time. This represents the phase change caused by the signal delay at the k-th frequency. Furthermore, based on the maximum likelihood criterion, the maximum likelihood function for all unknown parameters is given. The estimation model based on the maximum likelihood criterion can be expressed as:

[0130]

[0131] Where L(p,b) represents the total phase offset of the far-field target signal reaching the l-th sensor. Γ(ρ) represents the phase offset, which is determined by the target distance and is the same for all sensors. l (θ) represents the additional phase offset on the l-th sensor, determined by the direction-of-arrival angle θ of the target signal.

[0132] In equation (16) Γ l,p Decomposed into:

[0133] Γ l,p =Γ(ρ)Γ l (θ) (17)

[0134]

[0135] Channel attenuation b l Both the direction of arrival angle θ of the target signal and the unknown channel attenuation b are unknown. l For the unknown problem, the partial derivative is obtained by minimizing equation (16):

[0136]

[0137] Setting equation (20) to 0, we obtain the channel attenuation b. l The maximum likelihood estimate is:

[0138]

[0139] In equation (21), Γ(ρ) and Γ l (θ) is a unitary matrix, therefore:

[0140]

[0141] The power of the far-field target signal received by the station is normalized:

[0142]

[0143] Substituting equations (22) and (23) into equation (21), we get:

[0144]

[0145] Furthermore, substituting equation (24) into equation (20) yields:

[0146]

[0147] Equation (25) is equivalent to maximizing the following equation:

[0148]

[0149] Since Γ(ρ) is a unitary matrix, therefore, Having the same matrix eigenvalues ​​as Q(ρ,θ), the time delay matrix Γ(ρ) is introduced by ignoring the distance ρ, thus eliminating the irrelevant parameter ρ, and giving an estimate of the direction of arrival angle θ of the weak far-field target signal only:

[0150]

[0151] When the waveform of the far-field target signal is known, then:

[0152]

[0153] In the above formula, C(θ) is the cost function to be sought, and the change of its function value can characterize the likelihood of the target signal direction of arrival angle.

[0154] The specific method for step 3 is as follows:

[0155] In order to solve for the optimal angle in equation (30) in practice This invention employs an efficient angle search strategy. Specifically, this process is typically implemented through a grid search. First, within a predetermined angle search space (e.g., [0°, 360°)), all possible candidate angles θ are traversed at a set step size. For each candidate angle, its corresponding cost function value C(θ) is calculated. Finally, by comparing all calculated C(θ) values, the candidate angle that maximizes the global value is found; this angle is the final estimate of the target signal's direction of arrival angle.

[0156] A system based on a direct direction finding method for far-field targets includes:

[0157] The signal receiving module is used in step 1 to synchronously sample signals from the far-field target using L (L≥3) distributed observation stations, obtaining the original received signal vector r of each observation station. l (t);

[0158] The signal preprocessing and transformation module is used in step 2 to perform necessary processing on the raw received signal vector output by the signal receiving module. This module aims to transform the raw signal into a form suitable for angle correlation analysis.

[0159] The cost function construction module is used in step 2 to construct the final cost function for estimating the direction of arrival angle of the target signal, based on the angle and phase compensated signals from each observation station output by the signal preprocessing and transformation module. The core function of this module is to calculate matrices. And extract its largest eigenvalue.

[0160] The target signal direction-of-arrival angle estimation module is used in step 3 to search the cost function C(θ) output by the cost function construction module within a predetermined angle search space using a specified search strategy (such as grid search, which can be iteratively refined in multiple rounds) to find the angle that maximizes the global value of the cost function. that angle This is a precise estimate of the direction of arrival angle of the target signal wave.

[0161] Simulation experiment

[0162] This embodiment uses four observation stations with known locations and one UAV target that needs to be located in two-dimensional space as an example. The position coordinates of the three observation stations are (200, 200), (-200, 200), (-200, -200), and (200, -200) (unit: meters); the target radiation source is 200 kilometers away from the origin of the coordinate system, and the target signal wave direction of arrival angle is 28.65°. The scenario state in this embodiment is as follows: Figure 2 As shown.

[0163] To comprehensively evaluate the direction-finding performance of the method of this invention in practical applications, a systematic experimental design was adopted, and the following steps were used to quantitatively test and analyze various influencing factors:

[0164] The observation stations are set to be located at arbitrary positions in two-dimensional space. The number of observation stations is initialized to 4, and the coordinates of each observation station are determined to be (200,200), (-200,200), (-200,-200) and (200,-200) (unit: meters). The sampling rate of all observation stations is set to 1 GHz and the number of observation samples is set to 32768.

[0165] The signal-to-noise ratio (SNR) of the received signals at each receiving station was set to range from -6dB to 24dB, with an interval of 2dB, for a total of 16 groups. The Monk Carlo simulation was performed 1000 times, and the results were compared with existing technologies to obtain a diagram illustrating the impact of SNR on direction-finding accuracy. For example... Figure 3 As shown.

[0166] By changing the signal source position, the impact of target distance on direction finding is examined. The target distance is set from 2 km to 40 km, with 2 km intervals. The signal source is flown from near to far, considering the attenuation of signal strength with increasing propagation distance during actual signal propagation. The signal strength gradually decreases within the received signal band. Assuming the signal received power is P0 at distance d0, then at distance d... r The received power P at the location r It can be represented as:

[0167]

[0168] Assuming the noise power is constant, then for a distance d r The received signal-to-noise ratio at that location can be expressed as:

[0169]

[0170] In this experiment, we assume that the signal-to-noise ratio (SNR) at a distance of 1 km is 20 dB. The target distance is set from 2 km to 40 km, with intervals of 2 km. The SNR of the received signal at each distance is calculated according to equation (33). 1000 Monte Carlo simulations are performed and compared with existing technologies. The results are as follows: Figure 3 As shown.

[0171] Considering that in practical positioning or direction finding scenarios, the coordinates of distributed nodes usually need to be obtained using other positioning methods, such as GPS or BeiDou satellites for self-positioning, and that node coordinate self-positioning typically has varying degrees of error (generally, the error of GPS or BeiDou satellite positioning is less than 20 meters), in this experiment, we assume the node self-positioning error to be Δp. l =[Δx l ,Δy l ] T Δx l and Δy l All follow a Gaussian distribution σ s The value was set to 0 meters to 20 meters, with an interval of 1 meter, and 1000 Monte Carlo simulations were performed. The simulation results are as follows: Figure 4 As shown.

[0172] From above Figure 2 As can be seen from the figure, the Direct Direction Finding (DAAD) method exhibits superior direction finding performance for far-field targets. Compared to the SUM-MPR and GTRS-MPR methods, DAAD reduces the variance of target direction estimation error by 3dB at signal-to-noise ratios (SNR) above 0dB. Furthermore, while SUM-MPR and GTRS-MPR gradually exhibit a severe performance degradation threshold effect at an SNR of -2dB, the method of this invention demonstrates superior performance at low SNR conditions, showing no performance degradation threshold effect even at an SNR of -6dB. The figure shows a slight difference between DAAD and CRLB. This is because the scenario presented in this paper is a non-cooperative communication scenario, i.e., the prior waveform of the signal is unknown. Therefore, a solution method based on the given waveform is used, which results in a certain degree of performance loss compared to the case where the waveform is known. Through analysis of... Figure 3Analysis shows that when the distance exceeds a certain level, the direction-finding error performance of the SUM-MPR and GTRS-MPR methods deteriorates rapidly with increasing distance. This is because the signal-to-noise ratio of the received signal is too low, severely degrading the performance of the mutual ambiguity estimation method. However, the present invention maintains a more stable and accurate estimation effect within the experimental range. Under the same direction-finding error level, the direction-finding range of the proposed method is twice that of the SUM-MPR and GTRS-MPR methods. Through further analysis... Figure 4 Analysis shows that as the self-localization error increases, the direction finding error gradually increases. However, this method still has better direction finding accuracy than the SUM-MPR and GTRS-MPR methods.

[0173] In summary, the simulation results fully validate the significant advantages of the Direct Direction Finding (DAAD) method in far-field target direction finding: under the same signal-to-noise ratio (SNR), the DAAD method reduces the estimation error variance by 3 dB compared to traditional methods, and exhibits stronger noise resistance, maintaining stable performance even in SNR environments as low as -6 dB without any threshold effect. In long-range direction finding scenarios, the effective direction finding range of the DAAD method is twice that of the SUM-MPR and GTRS-MPR methods. These results demonstrate that the DAAD method possesses higher direction finding accuracy, stronger environmental adaptability, and superior engineering practicality, making it particularly suitable for target direction finding tasks in complex scenarios such as low SNR and long distances. Although there is some performance loss in non-cooperative communication scenarios, its overall performance is still significantly better than traditional parameter estimation methods, providing an effective solution for high-precision direction finding of far-field targets.

Claims

1. A direct direction finding method for far-field targets, characterized in that, Specifically, the following steps are included: Step 1: Construct a direct direction finding scenario model for the far-field target. This involves establishing a geometric layout model between the sensor array and the far-field target, and, based on the far-field approximation, correlating the relative time delay of the received signals from each sensor with the direction-of-arrival angle of the target signal. Simultaneously sample the signal from the far-field target using L sensor nodes with known locations, where L≥3, to obtain the original received signal vector r of each sensor node. l (t); Step 2, construct the cost function of the target signal direction of arrival angle: establish a cost function that depends only on the target signal direction of arrival angle. This cost function is obtained by transforming the far-field target direct direction finding scenario model established in Step 1, using the unitary matrix property and similarity transformation theory to decouple the target signal direction of arrival angle parameter to be estimated from other irrelevant variables. The change in the cost function value represents the likelihood of the target signal direction of arrival angle. Step 3: Perform angle search and estimation: Solve the cost function constructed in Step 2 using numerical optimization methods; systematically traverse and evaluate the preset angle space to find the optimal angle that makes the cost function reach its global maximum value; this optimal angle is the final estimated value of the target signal direction of arrival angle.

2. The method for direct direction finding of a far-field target according to claim 1, characterized in that, The specific method for step 1 is as follows: Suppose there are L sensor nodes with known positions in two-dimensional or three-dimensional space, with the centroid p0 of each sensor node's position as the origin of the coordinate system (hereinafter referred to as the centroid), and the coordinates of the l-th sensor node denoted as p. l =[x l ,y l ] T The sensor node coordinates satisfy the following relationship: Let the far-field target position be p. s =[x s ,y s ] T The distance ρ from the far-field target position to the center of gravity s =||p s || F The angle θ between the far-field target position and the centroid of the target's incoming wave direction is defined as the angle between the opposite direction of the signal incident direction and the positive x-axis. The distance from the far-field target position to the l-th sensor node is expressed as: The angle between the line connecting the l-th sensor node and the center of gravity and the positive x-axis is defined as... ρ l With p l The relationship is given by the following formula: Distance ρ between far-field target position and center of gravity s The distance ρ from the far-field target position to the l-th sensor node l The difference Δρ l Represented as: For far-field signals, ρ l <<ρ s It is approximately assumed that: When the target is in the far field, the distance ρ between the target position and the center of gravity is... s The distance ρ from the far-field target position to the l-th sensor node l The ratio approaches 0 on the right; using the approximate relationship of equation (5), we find the limit of equation (4): The physical meaning of equation (6) is: when the far-field target is far enough (i.e. ), the difference Δρ between the distance from the far-field target position to the centroid and the distance from the far-field target position to the l-th sensor node. l The time delay τ experienced by the far-field target signal to reach the l-th sensor node is a variable that depends only on the direction-of-arrival angle θ of the target signal. sl Decomposed into the following form: t sl =τ0+τ l (7) Where τ0 is the time delay experienced by the far-field target signal to reach the centroid, τ l Let be the relative time delay between the center of gravity and the l-th sensor node, and c be the electromagnetic wave propagation speed, usually set as a constant; assuming the far-field target signal starts at time 0, then the signal r received by the l-th sensor node... l (t) is expressed in the following form: r l (t)=b l s(t-τ0-τ l )+n l (t)0≤t≤T (10) Among them, b l It is the attenuation experienced by the far-field target signal as it propagates to the l-th sensor node, s(t) is the original waveform of the far-field target signal, and n l (t) is a normally distributed N(0,σ). 2 Gaussian white noise.

3. The method for direct direction finding of a far-field target according to claim 1, characterized in that, The specific method for step 2 is as follows: By eliminating the irrelevant parameter of target distance ρ and retaining only the target signal direction-of-arrival angle θ, a maximum likelihood estimator for the target signal direction-of-arrival angle θ is provided, specifically: The time delay τ between the far-field target signal and the l-th sensor node l (p s The formula can be decomposed as follows: t l (p s )=τ0(p s )+τ l (i) (11) in, e(θ)=[cosθ,sinθ] T (14) Wherein, τ0(p s τ represents the time delay τ takes for the far-field target signal to reach the centroid. l (θ) represents the relative time delay difference between the centroid and the l-th sensor node, and c is the electromagnetic wave propagation speed; e(θ) represents the direction vector with respect to the angle θ of the target signal's direction of arrival; the far-field target signal received by sensor node l is represented in the frequency domain as: in, They represent r respectively l (t), s n (t), n l (t) The data at the k-th frequency after undergoing a Discrete Fourier Transform (DFT) at K points, ω k It is the kth frequency, f0 is the signal start frequency, and T s Indicates the sampling interval time. This represents the phase change caused by the signal delay at the k-th frequency; further, based on the maximum likelihood criterion, the maximum likelihood function for all unknown parameters is given; the estimation model based on the maximum likelihood criterion can be expressed as: Where L(p,b) represents the total phase shift of the far-field target signal reaching the l-th sensor, and Γ(ρ) represents the phase shift determined by the target distance and is the same for all sensors. l (θ) represents the additional phase offset on the l-th sensor, determined by the direction-of-arrival angle θ of the target signal; In equation (16) Γ l,p Decomposed into: C l,p =Γ(ρ)Γ l (i) (17) Channel attenuation b l Both the direction of arrival angle θ of the target signal and the unknown channel attenuation b are unknown. l For the unknown problem, the partial derivative is obtained by minimizing equation (16): Setting equation (20) to 0, we obtain the channel attenuation b. l The maximum likelihood estimate is: In equation (21), Γ(ρ) and Γ l (θ) is a unitary matrix, therefore: The power of the far-field target signal received by the station is normalized: Substituting equations (22) and (23) into equation (21), we get: Furthermore, substituting equation (24) into equation (20) yields: Equation (25) is equivalent to maximizing the following equation: Since Γ(ρ) is a unitary matrix, therefore, Having the same matrix eigenvalues ​​as Q(ρ,θ), the time delay matrix Γ(ρ) is introduced by ignoring the target distance ρ, thus eliminating the irrelevant parameter of target distance ρ, and providing an estimate of the direction of arrival angle θ of the weak target signal in the far field: When the waveform of the far-field target signal is known, then: C(θ) is the cost function we are looking for. The change in its function value can characterize the likelihood of the target signal's direction of arrival angle. To maximize the cost function value C(θ), the target signal direction of arrival angle θ, i.e., the optimal angle, is required.

4. The method for direct direction finding of a far-field target according to claim 1, characterized in that, The specific method for step 3 is as follows: The optimal angle in equation (30) is solved using an angle search strategy. Specifically, through grid search, firstly, within a predetermined angle search space, all direction-of-arrival angles θ of the target signals to be measured are traversed at a set step size, undergoing multiple rounds of iterative refinement; for each direction-of-arrival angle θ of the target signal to be measured, its corresponding cost function value C(θ) is calculated; finally, all calculated cost function C(θ) values ​​are compared, and the optimal angle is found that maximizes the cost function C(θ) value. This is the final estimate of the direction of the incoming wave from the target.

5. The system based on the far-field target direct direction finding method according to any one of claims 1 to 4, characterized in that, include: The signal receiving module is used in step 1 to synchronously sample signals from a far-field target using L sensor nodes with known locations, where L≥3, to obtain the original received signal vector r of each sensor node. l (t); The signal preprocessing and transformation module is used in step 2 to process the original received signal vector r output by the signal receiving module. l (t) Utilizing the properties of unitary matrices and the theory of similarity transformation, the output is transformed into the received target signals of each sensor node after angle and phase compensation; The cost function construction module is used in step 2 to construct the final cost function for estimating the direction-of-arrival angle θ of the target signal, based on the received target signal from each sensor node after angle and phase compensation, output by the signal preprocessing and transformation module. The target signal direction-of-arrival angle θ estimation module is used in step 3 to search for the cost function C(θ) output by the cost function construction module within a predetermined angle search space using a specified search strategy, through multiple rounds of iterative refinement, to find the angle that maximizes the global cost function value. that angle This is a precise estimate of the target signal's angle of arrival.

6. A device based on a direct direction finding method for far-field targets, characterized in that, Specifically include: Memory, used to store computer programs; A processor, configured to implement the far-field target direct direction finding method according to any one of claims 1 to 4 when executing the computer program.

7. A computer-readable storage medium storing a computer program, which, when executed by a processor, is capable of performing direct orientation finding of a far-field target based on the direct orientation finding method for far-field targets as described in any one of claims 1 to 4.

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