TDOA positioning error correction method based on robust cascade optimization

Abstract

The invention provides a TDOA positioning error correction method based on robust cascade optimization, and relates to the technical field of wireless positioning and signal processing. The TDOA positioning error correction method based on robust cascade optimization comprises the following steps: S1, establishing a three-dimensional distance difference measurement model and a weight matrix; s2, based on the measurement model, a Chan two-step weighted least square method is adopted to obtain an initial value of a target position; s3, constructing a unified weighted residual cost function; s4, based on the cost function, adopting an improved RIME swarm intelligence algorithm to refine the target position; and S5, on the basis of an RIME refinement result, carrying out pull-back optimization by adopting a robust LM-IRLS method with priori constraint, and obtaining a final three-dimensional positioning result. By adopting a 'Chan + RIME + robust LM' cascade structure, positioning is transited from a closed fast initial value to swarm intelligence global refinement, and then high-noise pull-back is performed by robust local iteration with prior, so that positioning precision and stability are considered under different noise conditions, and divergence and failure probabilities are reduced.

Description

A robust cascaded optimization method for TDOA positioning error correction Technical Field

[0001] This invention relates to the field of wireless positioning and signal processing technology, specifically to a robust cascaded optimized TDOA positioning error correction method. Background Technology

[0002] The passive positioning technology based on TDOA measures the time difference of arrival of the same signal source by multiple spatially distributed base stations. The time difference can be converted into a distance difference, thereby establishing a set of nonlinear positioning equations.

[0003] In existing technologies, typical closed or near-closed solutions, such as the classic Chan-type two-step weighted least squares method, have advantages such as low computational cost, ease of engineering implementation, and rapid provision of initial position values. However, they are prone to significant performance degradation in the following situations: when measurement noise is high, linearization and error propagation lead to the accumulation of estimation bias, resulting in a significant increase in the output RMSE; when the base station geometry is poor or the target is located in a geometrically degraded region, the ill-conditioned matrix makes the solution highly sensitive to noise, and may even lead to numerical instability; when there are abnormal measurements, the traditional least squares objective is sensitive to outliers, which can easily cause the solution to be "biased". On the other hand, although directly using local iterative algorithms can refine nonlinear models, they are highly dependent on initial values: poor initial values ​​can easily lead to getting trapped in local minima, oscillations, or divergence. Swarm intelligence / random search algorithms have a certain global exploration capability, but under high noise or abnormal observation conditions, they may also encounter engineering problems such as search direction distortion and excessive step size leading to "runaway" behavior. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a robust cascaded optimization method for TDOA positioning error correction. This method solves the problems of typical closed or approximately closed-form solutions in existing technologies, such as the classic Chan-type two-step weighted least squares method. It offers advantages such as low computational cost, ease of engineering implementation, and rapid provision of initial position values. However, significant performance degradation can occur under the following conditions: when measurement noise is high, linearization and error propagation lead to the accumulation of estimation bias, resulting in a significant increase in the output RMSE.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a robust cascaded optimization method for TDOA positioning error correction, comprising the following steps:

[0006] S1, Establish a three-dimensional distance difference measurement model and weight matrix;

[0007] S2, Based on the measurement model, the Chan two-step weighted least squares method is used to obtain the initial value of the target position;

[0008] S3, construct a unified weighted residual cost function;

[0009] S4, Based on the cost function, the improved RIME swarm intelligence algorithm is used to refine the target position;

[0010] S5. Based on the RIME refinement results, the robust LM-IRLS method with prior constraints is used for pull-back optimization to obtain the final three-dimensional positioning results.

[0011] Preferably, in step S1, the array is arranged in three-dimensional space. There are 1 base station, and the coordinates of the base station are: The coordinates of the target to be estimated are: The first base station was selected as the reference station, and the second base station was selected as the third base station. The actual distance between each base station and the target is; Construct a distance difference measurement model: in It is Gaussian noise.

[0012] Preferably, the distance difference measurement vector is represented as follows; Its noise covariance matrix is: And construct the weight matrix from the covariance matrix; Used for weighted least squares and robust optimization in subsequent stages.

[0013] Preferably, in step S2, the Chan two-step weighted least squares method is used for initial value estimation, and the first step is constructed through linearization; And solve it; The second step is to introduce square constraints and construct... And solve it; Thus, the initial value estimate of Chan is obtained. .

[0014] Preferably, in step S3, a predicted distance difference vector is constructed based on the distance difference prediction model; And define the residual vector; Construct a unified weighted least squares cost function: .

[0015] Preferably, in step S4, the improved RIME swarm intelligence algorithm is used for position refinement, and the population initialization adopts a hybrid approach of local initialization and global initialization: And apply boundary projection constraints to all individuals.

[0016] Preferably, an adaptive exploration factor is set during the RIME algorithm iteration process; And define the soft update probability and the puncture probability: This allows for an adaptive transition in the search process from exploration to development.

[0017] Preferably, an improved soft update strategy is adopted in the RIME algorithm for the first... The iteration of the ... A number of particles are used to generate candidate solutions as follows: It combines a positive greedy selection mechanism with a periodic reset mechanism to avoid premature convergence.

[0018] Preferably, in step S5, a robust objective function with prior constraints is constructed: ,in Huber's loss function: .

[0019] Preferably, the robust objective function is solved iteratively using the LM–IRLS framework to construct the normal equation; And adaptively adjust the damping factor according to the descent of the objective function. The process continues until convergence, yielding the final localization result. .

[0020] This invention provides a robust cascaded optimized method for correcting TDOA positioning errors. It has the following beneficial effects:

[0021] This invention employs a cascaded structure of "Chan + RIME + Robust LM" to transition localization from closed-loop rapid initialization to swarm intelligence global refinement, followed by robust local iteration with prior knowledge for high-noise pullback. This balances positioning accuracy and stability under varying noise conditions, reducing the probability of divergence and failure. For the RIME refinement stage, this invention improves the population initialization and iterative update mechanism by using "local Gaussian initialization around the Chan initialization +..." A hybrid strategy of "global uniform initialization" improves early convergence efficiency while preserving global exploration capabilities; it introduces "soft update trigger probability and puncture probability" that adapt to iterations to achieve a smooth transition from early exploration to later development; it sets a lower limit for the contraction coefficient and a lower limit for the perturbation standard deviation in the update step size to avoid "locking up" or loss of contraction force in later searches; it also adaptively increases the puncture probability based on individual fitness and periodically resets the worst individual to effectively suppress premature convergence and degradation, and improve the stability and refinement sufficiency of the convergence curve; it achieves consistency between swarm intelligence search, local refinement, and evaluation metrics through a unified weighted residual cost function, facilitating parameter tuning, comparison, and engineering deployment; it proposes noise-adaptive prior weights and step size upper limits to significantly suppress iteration jumps and runaway caused by high noise / gross errors, improving the algorithm's controllability and robustness. Attached Figure Description

[0022] Figure 1 is a schematic diagram of the steps of the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] Example:

[0025] As shown in Figure 1, this embodiment of the invention provides a robust cascaded optimization method for TDOA positioning error correction, comprising the following steps:

[0026] S1, Establish a three-dimensional distance difference measurement model and weight matrix;

[0027] S2, Based on the measurement model, the Chan two-step weighted least squares method is used to obtain the initial value of the target position;

[0028] S3, construct a unified weighted residual cost function;

[0029] S4, Based on the cost function, the improved RIME swarm intelligence algorithm is used to refine the target position;

[0030] S5. Based on the RIME refinement results, the robust LM-IRLS method with prior constraints is used for pull-back optimization to obtain the final three-dimensional positioning results.

[0031] In step S1, the array is arranged in three-dimensional space. There are 1 base station, and the coordinates of the base station are: The coordinates of the target to be estimated are: The first base station was selected as the reference station, and the second base station was selected as the third base station. The actual distance between each base station and the target is; Construct a distance difference measurement model: in It is Gaussian noise.

[0032] The distance difference measurement vector is represented as: Its noise covariance matrix is: And construct the weight matrix from the covariance matrix; Used for weighted least squares and robust optimization in subsequent stages.

[0033] Multiple receiving base stations are pre-deployed in a three-dimensional space, the number of which is... The spatial coordinates of each base station are: The target node to be located is in an unknown location, and its spatial coordinates are represented as follows: Select one of the base stations as the reference base station (preferably the first base station), and the target reaches the first base station. The true geometric distance between base stations is defined as: By measuring the time difference of arrival of the target signal to each base station, a TDOA measurement model based on the distance difference is constructed. ,in, This represents the measured distance difference. To measure the noise, it is typically modeled as zero-mean Gaussian noise. All distance difference measurements are then combined into a measurement vector. The corresponding noise covariance matrix is ​​defined as: And a weighting matrix is ​​constructed by inverting the covariance matrix; The weight matrix is ​​used in all subsequent weighted least squares and robust optimization processes to fully consider the statistical correlation between different measurements.

[0034] In step S2, the Chan two-step weighted least squares method is used for initial value estimation. The first step is constructed through linearization. And solve it; The second step is to introduce square constraints and construct... And solve it; Thus, the initial value estimate of Chan is obtained. .

[0035] After obtaining the distance difference measurement model, the Chan two-step weighted least squares method is first used to perform an initial estimate of the target position to obtain a relatively reliable initial value. In the first step, the distance difference equation is linearized to construct the following linear model: And solve the parameter vector based on the weighted least squares criterion; In the second step, a square constraint relationship is introduced to further construct an approximate linear model; And then use weighted least squares to solve again; Through the above two steps of calculation, an initial estimate of the target location is obtained. The initial estimate has good accuracy and stability under low to medium noise conditions, providing a good starting point for subsequent cascade optimization.

[0036] In step S3, a predicted distance difference vector is constructed based on the distance difference prediction model; And define the residual vector; Construct a unified weighted least squares cost function: .

[0037] To ensure consistency across different optimization stages, a weighted residual cost function is constructed based on a unified distance difference prediction model. This is based on the estimated current target position. Construct the predicted distance difference vector; The difference between the measured value and the predicted value is defined as the residual vector; Based on this, a unified objective function in the sense of weighted least squares is constructed; This cost function serves as a common evaluation criterion for swarm intelligence optimization and robust local optimization, ensuring the continuity and consistency of the cascade optimization process.

[0038] In step S4, the improved RIME swarm intelligence algorithm is used for position refinement, and the population initialization adopts a hybrid approach of local and global initialization: And apply boundary projection constraints to all individuals.

[0039] During the RIME algorithm iteration process, an adaptive exploration factor is set; And define the soft update probability and the puncture probability: This allows for an adaptive transition in the search process from exploration to development.

[0040] An improved soft update strategy is adopted in the RIME algorithm for the th... The iteration of the ... A number of particles are used to generate candidate solutions as follows: It combines a positive greedy selection mechanism with a periodic reset mechanism to avoid premature convergence.

[0041] After obtaining the initial Chan estimation results, an improved RIME swarm optimization algorithm is further introduced to globally refine the target location, overcoming potential local extremum problems under nonlinear models. In the population initialization phase, a combination of local and global initialization is employed: In this process, some individuals are generated by perturbation around the initial value of Chan, while others are randomly generated within the search space, and boundary projection constraints are applied to all individuals.

[0042] An adaptive exploration factor is introduced during the algorithm iteration process; Based on this, the soft update probability and the puncture probability are defined; This allows the search strategy to gradually transition from global exploration to local development as the iteration process progresses. During the soft update phase, the... In the nth iteration The candidate solutions for each individual are generated in the following way; Furthermore, it combines a positive greedy selection mechanism and a periodic reset mechanism to improve the algorithm's global search capability and avoid premature convergence.

[0043] In step S5, a robust objective function with prior constraints is constructed: ,in Huber's loss function: .

[0044] The robust objective function is solved iteratively using the LM–IRLS framework to construct the normal equation; And adaptively adjust the damping factor according to the descent of the objective function. The process continues until convergence, yielding the final localization result. .

[0045] After completing the global refinement of swarm intelligence, in order to further improve the positioning accuracy and enhance the robustness to abnormal measurements, this embodiment introduces a robust LM-IRLS optimization process with prior constraints based on the RIME output results.

[0046] Construct the following robust objective function: ,in, The Huber loss function is defined as follows: By introducing the Chan initial value as a prior constraint, the optimization results are effectively pulled back, thus avoiding excessive deviation from the reasonable domain of solution. During the solution process, the LM–IRLS framework is used to construct the normal equations. And adaptively adjust the damping factor according to the descent of the objective function. The process continues until the preset convergence condition is met, ultimately obtaining the three-dimensional localization result of the target. .

[0047] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A robust cascaded optimization method for TDOA positioning error correction, characterized in that, Includes the following steps: S1. Establish a three-dimensional distance difference measurement model and weight matrix; S2. Based on the measurement model, use the Chan two-step weighted least squares method to obtain the initial value of the target position; S3. Construct a unified weighted residual cost function; S4. Based on the cost function, use an improved RIME swarm intelligence algorithm to refine the target position; S5. Based on the RIME refinement result, use a robust LM-IRLS method with prior constraints for pull-back optimization to obtain the final three-dimensional positioning result.

2. The robust cascaded optimization method for TDOA positioning error correction according to claim 1, characterized in that: In step S1, the array is arranged in three-dimensional space. There are 1 base station, and the coordinates of the base station are: The coordinates of the target to be estimated are: ； The first base station is selected as the reference station, and the second base station is selected as the third base station. The actual distance between each base station and the target is; Construct a distance difference measurement model: in It is Gaussian noise.

3. The robust cascaded optimization method for TDOA positioning error correction according to claim 2, characterized in that: The distance difference measurement vector is represented as: Its noise covariance matrix is: And construct the weight matrix from the covariance matrix; Used for weighted least squares and robust optimization in subsequent stages.

4. The robust cascaded optimization method for TDOA positioning error correction according to claim 1, characterized in that: In step S2, the Chan two-step weighted least squares method is used for initial value estimation. The first step is constructed through linearization. And solve it; The second step is to introduce square constraints and construct... And solve it; Thus, the initial value estimate of Chan is obtained. 。 5. The robust cascaded optimization method for TDOA positioning error correction according to claim 1, characterized in that: In step S3, a predicted distance difference vector is constructed based on the distance difference prediction model; And define the residual vector; Construct a unified weighted least squares cost function: 。 6. The robust cascaded optimization method for TDOA positioning error correction according to claim 1, characterized in that: In step S4, the improved RIME swarm intelligence algorithm is used for position refinement, and the population initialization adopts a hybrid approach of local and global initialization: And apply boundary projection constraints to all individuals.

7. The robust cascaded optimization method for TDOA positioning error correction according to claim 6, characterized in that: During the RIME algorithm iteration process, an adaptive exploration factor is set; And define the soft update probability and the puncture probability: This allows for an adaptive transition in the search process from exploration to development.

8. The robust cascaded optimization method for TDOA positioning error correction according to claim 6, characterized in that: An improved soft update strategy is adopted in the RIME algorithm for the th... The iteration of the ... A number of particles are used to generate candidate solutions as follows: It combines a positive greedy selection mechanism with a periodic reset mechanism to avoid premature convergence.

9. The robust cascaded optimization method for TDOA positioning error correction according to claim 1, characterized in that: In step S5, a robust objective function with prior constraints is constructed: ,in Huber's loss function: 。 10. A robust cascaded optimization method for TDOA positioning error correction according to claim 9, characterized in that: The robust objective function is solved iteratively using the LM–IRLS framework to construct the normal equation; And adaptively adjust the damping factor according to the descent of the objective function. The process continues until convergence, yielding the final localization result. 。

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