Deviation compensation weighting tool variable method for target motion analysis
By introducing a penalty term and instrumental variable matrix into target motion analysis, and combining the weighted instrumental variable method for multiple iterative estimations, the bias problem caused by sensor noise and position error is solved, thereby improving the accuracy and robustness of target motion analysis.
Patent Information
- Application Number
- CN202511443654.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-10
- Publication Date
- 2026-01-09
AI Technical Summary
Existing target motion analysis methods suffer from severe biases due to sensor measurement noise and position errors, resulting in poor estimation accuracy and insufficient robustness, especially in complex scenarios.
By establishing a motion analysis model under pure azimuth measurement conditions, a pseudo-linear estimation method is used to compensate for the deviation of the initial state vector. An instrumental variable matrix and a weight matrix are constructed, and multiple iterative estimations are performed by combining a weighted instrumental variable method with a selection strategy and a weighted instrumental variable method with a penalty term to improve accuracy and stability.
It significantly improves the estimation accuracy and stability of target motion analysis, enhances model robustness through penalty term regularization, explicitly eliminates systematic errors, and improves the calculation results of target motion parameters.
Smart Images
Figure CN121301727A_ABST
Abstract
Description
Technical Field
[0001] This disclosure relates to the field of data processing technology, and in particular to a bias-compensated weighted instrumental variable method for target motion analysis. Background Technology
[0002] Currently, with the development of communication technology and wireless sensor networks, target motion analysis (TMA) technology has played an important role in many civilian and military fields such as marine engineering, aerospace electronics, and military reconnaissance.
[0003] The accuracy of TMA estimation is a key indicator for evaluating the performance of the TMA method, but in practical applications, the measurement noise of the sensor can have a serious impact on the performance of TMA.
[0004] Pseudolinear estimation is a technique that transforms a nonlinear model into a linear form through appropriate mathematical transformations. The basic idea is to approximate the originally nonlinear relationship as a linear model by applying mathematical transformations such as logarithms and exponentials, thus enabling the solution using classical linear estimation techniques such as linear regression or least squares. However, due to the correlation between the measurement matrix and the noise matrix, pseudolinear methods suffer from significant bias, which increases substantially with increasing measurement noise and is further exacerbated by sensor position errors.
[0005] The weighted instrumental variable method introduces an instrumental variable matrix to replace the measurement matrix and designs a weighting matrix to suppress the influence of noise. However, as noise increases, the correlation coefficient between the instrumental variable matrix and the measurement matrix weakens, leading to a decrease in estimation accuracy. The weighted instrumental variable method with a selection strategy builds upon this by introducing a selection strategy to balance bias and mean squared error, thereby improving the algorithm's robustness in complex scenarios. However, if the threshold value is too large, the weighted instrumental variable method with a selection strategy will degenerate into a weighted instrumental variable method, while if the threshold value is too small, it will degenerate into a weighted pseudolinear method.
[0006] It is evident that there is an urgent need for a bias-compensated weighted instrumental variable method for target motion analysis that can improve the accuracy of target motion analysis. Summary of the Invention
[0007] In view of this, the present disclosure provides a bias-compensated weighted instrumental variable method for target motion analysis, which at least partially solves the problem of poor analysis accuracy in the prior art.
[0008] This disclosure provides a bias-compensated weighted instrumental variable method for target motion analysis, including:
[0009] Step 1: Establish a motion analysis model under pure azimuth measurement conditions, and based on this, establish a pseudo-linear equation for the motion analysis of the target under pure azimuth and calculate the matrix related to the measured angle of arrival.
[0010] Step 2: Use a pseudo-linear estimation method to estimate the initial state vector of the target and perform bias compensation. Calculate the target-sensor distance and angle of arrival based on the bias compensation results.
[0011] Step 3: Based on the target-sensor distance and angle of arrival, construct the instrumental variable matrix and weight matrix, estimate the target initial state vector using the weighted instrumental variable method with selection strategy, and use it again as an approximation of the true parameters to recalculate the target-sensor distance and estimate the angle of arrival;
[0012] Step 4: Reconstruct the instrumental variable matrix and weight matrix. Construct a penalty term from the target initial state vector estimated by the weighted instrumental variable method with selection strategy in the form of column-row multiplication. Then, estimate the target initial state vector using the weighted instrumental variable method with penalty term and perform bias compensation.
[0013] According to a specific implementation of an embodiment of this disclosure, step 1 specifically includes:
[0014] Step 1.1: Establish motion models for the target and sensors, and define the initial state vector of the target. And based on this, the pure azimuth angle observation value of the sensor for the target at each moment within the total observation time is obtained;
[0015] Step 1.2: Establish pseudo-linear equations, calculate unit orthogonal vectors based on the observed values, and construct the measurement matrix accordingly. Observation vector and observation noise matrix .
[0016] According to a specific implementation of this disclosure, the pseudo-linear equation is:
[0017]
[0018] in, , Let the target position vector be... This is the sensor position vector.
[0019] According to a specific implementation of an embodiment of this disclosure, step 2 specifically includes:
[0020] Step 2.1: Estimate the target initial state vector using a pseudo-linear estimation method and perform bias compensation.
[0021]
[0022]
[0023]
[0024] in, The target initial state vector estimated by the pseudolinear method. The target initial state vector is estimated by the pseudolinear method after bias compensation. This is the deviation compensation item. The target transition matrix;
[0025] Step 2.2: Approximate the results of the bias-compensated pseudo-linear estimation method as the true parameters, and calculate the target-sensor distance and angle of arrival.
[0026]
[0027]
[0028]
[0029] in, and The target's x and y coordinates are estimated using the bias-compensated pseudolinear method. The target position vector is estimated using the deviation-compensated pseudolinear method. For the estimated target-sensor distance.
[0030] According to a specific implementation of an embodiment of this disclosure, step 3 specifically includes:
[0031] Step 3.1, based on target-sensor distance and angle of arrival Construct the instrumental variable matrix and weight matrix
[0032]
[0033]
[0034]
[0035] ;
[0036] Step 3.2: Estimate the target initial state vector using the weighted instrumental variable method with selection strategy, wherein the expression for the weighted instrumental variable method with selection strategy is:
[0037] ;
[0038] Step 3.3: The results of the weighted instrumental variable method with selection strategy are used again as an approximation of the true parameters to recalculate the target-sensor distance and angle of arrival.
[0039] According to a specific implementation of an embodiment of this disclosure, step 4 specifically includes:
[0040] Step 4.1: Based on the recalculated target-sensor distance and angle of arrival, construct the instrumental variable matrix. and weight matrix ;
[0041] Step 4.2, construct the penalty term matrix By introducing a penalty term into the general least squares problem, a pseudolinear method with a penalty term is obtained. Analogous to the relationship between the pseudolinear method and the weighted instrumental variable method with a choice strategy, [the following is discussed]. and Replace with and We obtain a weighted instrumental variable method with a penalty term and perform bias compensation.
[0042]
[0043]
[0044]
[0045]
[0046] in, It is a positive scalar penalty parameter. for The identity matrix.
[0047] According to a specific implementation of an embodiment of this disclosure, the penalty term matrix The optimal selection criterion is The optimal selection criterion for the penalty parameter is as follows: .
[0048] The bias-compensated weighted instrumental variable scheme for target motion analysis in this embodiment includes: Step 1, establishing a motion analysis model under pure azimuth measurement conditions, establishing a pseudo-linear equation for pure azimuth target motion analysis, and calculating a matrix related to the measured angle of arrival; Step 2, estimating the initial state vector of the target using a pseudo-linear estimation method, and performing bias compensation, calculating the target-sensor distance and angle of arrival based on the bias-compensated result; Step 3, constructing an instrumental variable matrix and a weight matrix based on the target-sensor distance and angle of arrival, estimating the initial state vector of the target using a weighted instrumental variable method with a selection strategy, and using it again as an approximation of the true parameters, recalculating the target-sensor distance and estimating the angle of arrival; Step 4, reconstructing the instrumental variable matrix and the weight matrix, constructing a penalty term from the initial state vector of the target estimated using the weighted instrumental variable method with a selection strategy in the form of column-to-row multiplication, and then estimating the initial state vector of the target using the weighted instrumental variable method with a penalty term, and performing bias compensation.
[0049] The beneficial effects of this disclosure are as follows: By introducing a penalty term into the least squares problem, a penalized least squares estimate is obtained. Furthermore, by introducing an instrumental variable matrix and a weighting matrix, a penalized weighted instrumental variable method is obtained. Finally, a bias-compensated weighted instrumental variable method with a penalty term is developed. This method relies on the penalty term to implicitly improve the model's robustness through regularization, while bias compensation explicitly eliminates systematic errors. The two work synergistically to significantly improve the estimation accuracy and stability of the target motion parameters. Attached Figure Description
[0050] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0051] Figure 1 A flowchart illustrating a bias-compensated weighted instrumental variable method for target motion analysis provided in this embodiment of the disclosure;
[0052] Figure 2 A motion model diagram provided for an embodiment of this disclosure. Detailed Implementation
[0053] The embodiments of this disclosure will now be described in detail with reference to the accompanying drawings.
[0054] The following specific examples illustrate the implementation of this disclosure. Those skilled in the art can easily understand other advantages and effects of this disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. This disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.
[0055] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.
[0056] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this disclosure. The illustrations only show the components related to this disclosure and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.
[0057] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.
[0058] This disclosure provides a bias-compensated weighted instrumental variable method for target motion analysis, which can be applied to motion analysis processes in scenarios such as marine engineering, aerospace electronics, and military reconnaissance.
[0059] See Figure 1 This is a flowchart illustrating a method for marine engineering, aerospace electronics, and military reconnaissance provided in an embodiment of this disclosure. Figure 1 As shown, the method mainly includes the following steps:
[0060] Step 1: Establish a motion analysis model under pure azimuth measurement conditions, and based on this, establish a pseudo-linear equation for the motion analysis of the target under pure azimuth and calculate the matrix related to the measured angle of arrival.
[0061] In practical implementation, a motion analysis model under pure azimuth measurement conditions can be established: the target moves at an approximately constant velocity, and its position is linearly represented by the initial state (initial position and velocity); the sensor measures the target's azimuth at each discrete time point, but the measured values are contaminated by Gaussian noise; a pseudo-linear equation for pure azimuth target motion analysis is established, and the matrix related to the measured angle of arrival is calculated. The specific process is as follows:
[0062] Step 1.1: Establish a motion analysis model under pure azimuth measurement conditions, define parameters and initialize them:
[0063] The trajectories of both the target and the sensor contain At discrete time points, the target and sensor at the th... The positions of the times are respectively by and Indicates. The target starts from the initial position. It begins, and at an approximately constant speed. Movement. Among them... and The moving target is in Position and velocity at any given moment For the sensor in Location at any given moment For sequence indexing Let the initial state vector of the target be... So in The position of the target at any given time can be represented as:
[0064]
[0065] In the formula The total motion time at the current moment. .
[0066] In the At any moment, recorded by sensors The measured noise-free azimuth is denoted as The calculation method is as follows:
[0067]
[0068] Pure azimuth angle measurement value of sensor measurement angle affected by noise as follows:
[0069]
[0070] in, It is zero-mean Gaussian noise with variance of
[0071] Step 1.2: Establish the pseudo-linear equations for target motion analysis using pure azimuth angle, define unit orthogonal vectors, and construct the measurement matrix, observation vector, and observation noise matrix:
[0072] The pseudolinear equation for target motion analysis based on pure azimuth angle is:
[0073]
[0074] in .
[0075] Calculate the unit orthogonal vector Measurement matrix , and observation noise matrix :
[0076]
[0077]
[0078]
[0079] .
[0080] Step 2: Use a pseudo-linear estimation method to estimate the initial state vector of the target and perform bias compensation. Calculate the target-sensor distance and angle of arrival based on the bias compensation results.
[0081] In practice, a pseudo-linear estimation method can be used to estimate the target's initial state vector, and bias compensation can be applied. The result of the bias-compensated pseudo-linear estimation method is used as an approximation of the true parameters. The target-sensor distance and angle of arrival are calculated, and the motion model between the target and the sensor is as follows: Figure 2 As shown, the specific process is as follows:
[0082] Step 2.1: Estimate the target initial state vector using a pseudo-linear estimation method and perform bias compensation.
[0083]
[0084]
[0085] in The target initial state vector estimated by the pseudolinear method. The target initial state vector is estimated by the deviation-compensated pseudolinear method. This is the deviation compensation item.
[0086] Step 2.2: Approximate the results of the bias-compensated pseudo-linear estimation method as the true parameters, and calculate the target-sensor distance and angle of arrival.
[0087]
[0088]
[0089]
[0090] in, and The target's x and y coordinates are estimated using the bias-compensated pseudolinear method. The target position vector is estimated using the deviation-compensated pseudolinear method.
[0091] Deviation term of pseudolinear method The estimated value using the pseudo-linear method approximates the true initial state of the target, with the deviation compensation term being...
[0092]
[0093] This uses The zero mean and its approximation
[0094]
[0095] .
[0096] Step 3: Based on the target-sensor distance and angle of arrival, construct the instrumental variable matrix and weight matrix, estimate the target initial state vector using the weighted instrumental variable method with selection strategy, and use it again as an approximation of the true parameters to recalculate the target-sensor distance and estimate the angle of arrival;
[0097] In practice, an instrumental variable matrix and a weight matrix can be constructed based on the distance and angle of arrival from the previous step. The initial state vector of the target can be estimated using the weighted instrumental variable method with a selection strategy. The result of the weighted instrumental variable method with a selection strategy can then be used as an approximation of the true parameters to recalculate the target-sensor distance and angle of arrival. The specific process is as follows:
[0098] Step 3.1: Construct the instrumental variable matrix and weight matrix based on the distance and angle of arrival from the previous step:
[0099] By choosing a strategy
[0100]
[0101] Based on the distance from the previous step and the angle of arrival Construct the instrumental variable matrix and weight matrix
[0102]
[0103]
[0104]
[0105] Step 3.2, using the weighted instrumental variable method with selection strategy.
[0106]
[0107] Estimate the target's initial state vector;
[0108] Step 3.3: The results of the weighted instrumental variable method with selection strategy are used again as an approximation of the true parameters to recalculate the target-sensor distance and angle of arrival.
[0109] Step 4: Reconstruct the instrumental variable matrix and weight matrix. Construct a penalty term from the target initial state vector estimated by the weighted instrumental variable method with selection strategy in the form of column-row multiplication. Then, estimate the target initial state vector using the weighted instrumental variable method with penalty term and perform bias compensation.
[0110] In practice, the instrumental variable matrix and weight matrix can be reconstructed. The target initial state vector estimated using the weighted instrumental variable method with selection strategy is used to construct a penalty term in the form of column-to-row multiplication. Then, the target initial state vector is estimated using the weighted instrumental variable method with penalty term, and bias compensation is performed. The specific process is as follows:
[0111] Step 4.1: Based on the target-sensor distance and angle of arrival recalculated in the previous step, construct the instrumental variable matrix. and weight matrix ;
[0112] Step 4.2, construct the penalty term matrix By introducing a penalty term into the general least squares problem, a pseudolinear method with a penalty term is obtained. Analogous to the relationship between the pseudolinear method and the weighted instrumental variable method with a choice strategy, [the following is discussed]. and Replace with and We obtain a weighted instrumental variable method with a penalty term and perform bias compensation.
[0113]
[0114]
[0115] in, It is a positive scalar penalty parameter. for The identity matrix. Construction form and penalty parameters The choice of [aspect name] will affect the performance of the estimator and needs to be optimized according to specific criteria.
[0116] Deviation compensation method:
[0117]
[0118] in, .according to Theorem for finite but sufficiently large Value, the right choice Ensure that it is consistent with the noise vector The lack of correlation will make the first term approximately zero, so only the second deviation term needs to be compensated. .
[0119] Furthermore, penalty parameters and The optimal selection criteria are as follows:
[0120] Will The decomposition into the part without angle measurement noise and the part with angle measurement noise are respectively represented as follows: and Its specific form is as follows:
[0121]
[0122] Here , .
[0123] definition , ,but
[0124]
[0125] in , .
[0126] Note The upper limit is and yes The lower bound, therefore Compared to and Minimization is used as the criterion for parameter selection.
[0127] Rewrite for:
[0128]
[0129] in, , , .
[0130] It can be known Therefore, it can be concluded that only when and Only then will Minimum at this time
[0131]
[0132] If observation noise There is non-uniformity; simply... Each element in the middle is multiplied by its corresponding ,but Will be included In this case, the following is adopted: and This can be achieved minimize. when Enough hours .
[0133] When taking the optimal hour,
[0134]
[0135]
[0136] Thus, optimal and Not only optimization criteria Minimize of ,and and of Broadly the same. Given ,
[0137]
[0138] This indicates It can also be minimize.
[0139] The bias-compensated weighted instrumental variable method for target motion analysis provided in this embodiment obtains a least squares estimate with a penalty term by introducing a penalty term into the least squares problem. It then introduces an instrumental variable matrix and a weighting matrix to obtain a weighted instrumental variable method with a penalty term, and further develops a bias-compensated weighted instrumental variable method by applying bias compensation. This method relies on the penalty term to implicitly improve the model's robustness through regularization, while bias compensation explicitly eliminates systematic errors. The two work synergistically to significantly improve the estimation accuracy and stability of target motion parameters.
[0140] The method of this disclosure will be further described below with reference to a specific embodiment, including the following steps:
[0141] Step 1: Establish a motion analysis model under pure azimuth measurement conditions, establish a pseudo-linear equation for target motion analysis under pure azimuth conditions, and calculate the matrix related to the measured angle of arrival;
[0142] The specific implementation process is as follows:
[0143] Step 1.1: Establish a motion analysis model under pure azimuth measurement conditions:
[0144] In this embodiment, the target initial state vector That is, the target is at its initial position and initial velocity Motion, Discrete Time Set to 30, a single sensor tracks a uniformly moving target in three segments. The kinematic parameters for the three segments are as follows: , , Each flight segment contains evenly distributed... ,Right now The second measurement, angle measurement, is... For a fixed period, the total observation duration is The observed noise is zero-mean Gaussian noise with a standard deviation of [value missing]. .
[0145] Within the total observation period, the first The time sensor's pure azimuth observation value of the target is Due to the presence of observation noise, In mathematical terms, it is represented as the sum of the true value and the noise disturbance.
[0146] Step 1.2: Establish the pseudo-linear equations for target motion analysis using pure azimuth angle, define unit orthogonal vectors, and construct the measurement matrix, observation vector, and observation noise matrix:
[0147] Use the observations obtained in step 1.1 Calculate the unit orthogonal vector Construct a measurement matrix , and observation noise matrix :
[0148]
[0149]
[0150]
[0151]
[0152] Step 2: Use a pseudo-linear estimation method to estimate the target's initial state vector and perform bias compensation. Use the result of the bias-compensated pseudo-linear estimation method as an approximation of the true parameters to calculate the target-sensor distance and angle of arrival.
[0153] The specific implementation process is as follows:
[0154] Step 2.1: Estimate the target initial state vector using a pseudo-linear estimation method and perform bias compensation.
[0155]
[0156]
[0157]
[0158] In this embodiment, , , .
[0159] Step 2.2: Approximate the results of the bias-compensated pseudo-linear estimation method as the true parameters, and calculate the target-sensor distance and angle of arrival.
[0160]
[0161]
[0162]
[0163] in, and The target's x and y coordinates are estimated using the bias-compensated pseudolinear method. The target position vector is estimated using the deviation-compensated pseudolinear method.
[0164] Step 3: Based on the distance and angle of arrival from the previous step, construct the instrumental variable matrix and weight matrix. Use the weighted instrumental variable method with selection strategy to estimate the target's initial state vector. Use the result of the weighted instrumental variable method with selection strategy as an approximation of the true parameters again, and recalculate the target-sensor distance and angle of arrival.
[0165] The specific implementation process is as follows:
[0166] Step 3.1: Construct the instrumental variable matrix and weight matrix based on the distance and angle of arrival from the previous step:
[0167] By choosing a strategy
[0168]
[0169] To select the policy threshold, it is generally in In this embodiment, the following is selected: .
[0170] Based on the distance from the previous step and the angle of arrival Construct the instrumental variable matrix and weight matrix
[0171]
[0172]
[0173]
[0174] Step 3.2: Estimate the target initial state vector using the weighted instrumental variable method with selection strategy.
[0175]
[0176] In this embodiment, .
[0177] Step 3.3: Use the results of the weighted instrumental variable method with selection strategy as an approximation of the true parameters again to recalculate the target-sensor distance and angle of arrival (the generation process is the same as step 2.2);
[0178] Step 4: Reconstruct the instrumental variable matrix and weight matrix. Use the weighted instrumental variable method with selection strategy to estimate the target initial state vector and construct a penalty term in the form of column-row multiplication. Then, use the weighted instrumental variable method with penalty term to estimate the target initial state vector and perform bias compensation.
[0179] The specific implementation process is as follows:
[0180] Step 4.1: Reconstruct the instrumental variable matrix based on the target-sensor distance and angle of arrival from the previous step. and weight matrix (Refer to step 3.1 for the generation process);
[0181] Step 4.2: Construct a penalty term, then use the weighted instrumental variable method with a penalty term to estimate the target initial state vector, and perform bias compensation:
[0182] Given the high computational demands of Target Motion Analysis (TMA), particularly in multi-target tracking scenarios where phased array radars need to locate all targets within a limited time, highly complex and computationally intensive algorithms are unacceptable. Therefore, we employ a weighted instrumental variable method with a selection strategy to estimate the target initial state vector, constructing a penalty term in the form of column-row multiplication.
[0183]
[0184] Then, the initial state vector of the target is estimated using the weighted instrumental variable method with a penalty term, and bias compensation is performed.
[0185]
[0186]
[0187]
[0188] In this embodiment, , , .
[0189] To reduce the impact of noise randomness and uncertainty on the experimental results, 10,000 Monte Carlo experiments were conducted at each noise level, and the mean values were taken. The mean values of the differences between the target initial state vector estimated by the Selective Angle Measurement-Weighted Instrumental Variable Estimator (SAM-WIVE) and the Bias Compensated Penalized Weighted Instrumental Variable Estimator (BCPWIVE) at different noise levels and the true target initial state are shown in Table 1.
[0190] Table 1
[0191] It should be understood that the various parts of this disclosure can be implemented in hardware, software, firmware, or a combination thereof.
[0192] The above description is merely a specific embodiment of this disclosure, but the scope of protection of this disclosure is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this disclosure should be included within the scope of protection of this disclosure. Therefore, the scope of protection of this disclosure should be determined by the scope of the claims.
Claims
1. A bias-compensated weighted instrumental variable method for target motion analysis, characterized in that, include: Step 1: Establish a motion analysis model under pure azimuth measurement conditions, and based on this, establish a pseudo-linear equation for the motion analysis of the target under pure azimuth and calculate the matrix related to the measured angle of arrival. Step 2: Use a pseudo-linear estimation method to estimate the initial state vector of the target and perform bias compensation. Calculate the target-sensor distance and angle of arrival based on the bias compensation results. Step 3: Based on the target-sensor distance and angle of arrival, construct the instrumental variable matrix and weight matrix, estimate the target initial state vector using the weighted instrumental variable method with selection strategy, and use it again as an approximation of the true parameters to recalculate the target-sensor distance and estimate the angle of arrival; Step 4: Reconstruct the instrumental variable matrix and weight matrix. Use the weighted instrumental variable method with selection strategy to estimate the target initial state vector and construct a penalty term in the form of column multiplication and row multiplication. Then, use the weighted instrumental variable method with penalty term to estimate the target initial state vector and perform bias compensation.
2. The method according to claim 1, characterized in that, Step 1 specifically includes: Step 1.1: Establish motion models for the target and sensors, and define the initial state vector of the target. And based on this, the pure azimuth angle observation value of the sensor for the target at each moment within the total observation time is obtained; Step 1.2: Establish pseudo-linear equations, calculate unit orthogonal vectors based on the observed values, and construct the measurement matrix accordingly. Observation vector and observation noise matrix .
3. The method according to claim 2, characterized in that, The pseudolinear equation is: ； in, , Let the target position vector be... This is the sensor position vector.
4. The method according to claim 3, characterized in that, Step 2 specifically includes: Step 2.1: Estimate the target initial state vector using a pseudo-linear estimation method and perform bias compensation. ； ； ； in, The target initial state vector estimated by the pseudolinear method. The target initial state vector is estimated by the pseudolinear method after bias compensation. This is the deviation compensation item. The target transition matrix; Step 2.2: Approximate the results of the bias-compensated pseudo-linear estimation method as the true parameters, and calculate the target-sensor distance and angle of arrival. ； ； ； in, and The target's x and y coordinates are estimated using the bias-compensated pseudolinear method. The target position vector is estimated using the deviation-compensated pseudolinear method. For the estimated target-sensor distance.
5. The method according to claim 4, characterized in that, Step 3 specifically includes: Step 3.1, based on target-sensor distance and angle of arrival Construct the instrumental variable matrix and weight matrix ； ； ； ； Step 3.2: Estimate the target initial state vector using the weighted instrumental variable method with selection strategy, wherein the expression for the weighted instrumental variable method with selection strategy is: ； Step 3.3: The results of the weighted instrumental variable method with selection strategy are used again as an approximation of the true parameters to recalculate the target-sensor distance and angle of arrival.
6. The method according to claim 5, characterized in that, Step 4 specifically includes: Step 4.1: Based on the recalculated target-sensor distance and angle of arrival, construct the instrumental variable matrix. and weight matrix ; Step 4.2, construct the penalty term matrix By introducing a penalty term into the general least squares problem, a pseudolinear method with a penalty term is obtained. Analogous to the relationship between the pseudolinear method and the weighted instrumental variable method with a choice strategy, [the following is discussed]. and Replace with and We obtain a weighted instrumental variable method with a penalty term and perform bias compensation. ； ； ； ； in, It is a positive scalar penalty parameter. for The identity matrix.
7. The method according to claim 6, characterized in that, The penalty term matrix The optimal selection criterion is The optimal selection criterion for the penalty parameter is as follows: .