Double-radar track fusion method based on spatial deviation compensation under limited labels

Abstract

The invention discloses a double-radar track fusion method based on spatial deviation compensation under a limited label. The method comprises the following steps: randomly generating an initial sequence fusion factor for each radar; taking the initial sequence fusion factor as the input of a WFN network, and obtaining the fusion factor of each radar at the current moment; calculating a fusion matrix of the radar according to the fusion factor and the local estimation covariance of the corresponding radar; fusing the local state estimation of the radar based on the fusion matrix to obtain fusion state estimation; according to the method, the dimensionless fusion factor is selected as the input of the WFN network, so that the preprocessing and feature decoupling process of the multi-dimensional heterogeneous state information is avoided, the fusion of the high-dimensional state is directly driven, and the high-precision state estimation fusion under the limited label can be realized while the complexity is remarkably reduced.

Description

Technical Field

[0001] This invention belongs to the field of multi-sensor information fusion technology, and particularly relates to a dual radar track fusion method based on spatial deviation compensation under limited labels. Background Technology

[0002] Radar target tracking is the process of estimating the position, velocity, acceleration, and other motion characteristics of a target of interest online and forming a stable track through electromagnetic detection. It is widely used in various military and civilian fields, including long-range early warning, real-time monitoring, multi-aircraft cooperative positioning, and air traffic control. In practical applications, radar / sensor measurement data typically contains both random errors and systematic errors (i.e., biases). Without effective compensation for systematic biases, the accuracy and stability of target state estimation will be severely affected. Therefore, it is necessary to study radar target tracking bias registration techniques.

[0003] Classical spatial bias registration methods can be broadly classified into two categories: offline registration and online registration.

[0004] On the one hand, the core idea of ​​offline registration is to treat sensor bias as a fixed value that does not change or changes slowly over a period of time. It obtains a static bias estimate by batch processing measurement data, which is then used to calibrate all subsequent real-time data. The advantage of this method is that the computation is mainly completed offline, making it easy to implement. The basic method of offline registration is least squares estimation (LS), which finds a bias estimate that minimizes the sum of squared errors between the compensated data points and the true reference value. To handle noise issues in more realistic scenarios, generalized least squares (GLS) introduces noise covariance as a weight on top of LS, giving greater weight to data with higher accuracy, thus obtaining a more accurate estimate. Furthermore, maximum likelihood estimation (MLE), from a statistical probability perspective, finds the bias parameter most likely to generate the current observation data. When the noise is non-Gaussian distributed, it usually yields more robust estimation results compared to LS.

[0005] On the other hand, online registration methods assume that sensor bias is dynamically changing, requiring dynamic tracking and correction of bias while processing each frame of data. This approach can adapt to dynamic biases caused by changes in the sensor's environment or its own state. The mainstream techniques of this type of method are all based on the Kalman Filter (KF) framework, seamlessly integrating bias estimation into the recursive filtering process of the target state through strategies such as joint estimation or state augmentation. Commonly used methods include Augmented State Extended Kalman Filter (ASEKF), Augmented State Unscented Kalman Filter, and joint estimation filters based on maximum expectation. The Augmented State Extended Kalman Filter algorithm directly treats the unknown bias as part of the system state, forming a higher-dimensional "augmented state vector" together with the target's original state such as position and velocity. Subsequently, by establishing a dynamic model for the bias, the standard Kalman filter can recursively estimate the target state while simultaneously estimating and compensating for the sensor bias in real time, completing joint optimization.

[0006] In recent years, with the development of deep learning technology, spatial bias registration using neural networks has become a new research direction. Deep neural networks, with their powerful nonlinear fitting and feature extraction capabilities, such as convolutional neural networks and long short-term memory (LSTM) networks, can directly learn the complex mapping relationship between bias and measurement from sensor data, thereby achieving online bias registration of sensors.

[0007] However, these deep learning-based methods also have some limitations. They often rely on massive amounts of high-precision labels (such as the target's true trajectory or unbiased measurements) for supervised training, but in practical applications, obtaining such labels is extremely costly or even infeasible. Furthermore, they typically treat bias estimation and data fusion as two independent or separate tasks, lacking information feedback and collaborative optimization mechanisms between the two. This not only makes it difficult to effectively handle dynamically changing biases but also hinders the achievement of high-precision fusion estimation results. Summary of the Invention

[0008] The purpose of this invention is to provide a dual radar track fusion method based on spatial bias compensation under limited labels, so as to correct / compensate the bias of local state estimation, thereby improving the accuracy of fused state estimation.

[0009] This invention adopts the following technical solution: a dual-radar track fusion method based on spatial bias compensation under limited labels, comprising the following steps:

[0010] An initial sequence fusion factor is randomly generated for each radar; wherein, the initial sequence fusion factor is a combination of fusion factors based on time series.

[0011] Using the initial sequence fusion factor as input to the WFN network, the fusion factor for each radar at the current time is obtained;

[0012] The fusion matrix of the radar is calculated based on the fusion factor and the local estimated covariance of the corresponding radar.

[0013] The local state estimates of the radar are fused based on the fusion matrix to obtain the fused state estimate;

[0014] The loss functions used in training the WFN network include the mean squared error loss when the labels are known and the relative entropy loss for local state estimation and fusion state estimation when the labels are unknown.

[0015] The beneficial effects of this invention are: by selecting a dimensionless fusion factor as the input of the WFN network, this invention avoids the preprocessing and feature decoupling process of multidimensional heterogeneous state information, and directly drives the fusion of high-dimensional states, which significantly reduces complexity and enables high-precision state estimation fusion under limited labels. Attached Figure Description

[0016] Figure 1 This is an overall framework diagram of a dual radar track fusion method based on spatial deviation compensation under limited labels, according to an embodiment of the present invention.

[0017] Figure 2 This is a diagram of the weighted fusion network architecture in an embodiment of the present invention;

[0018] Figure 3 This is a comparison chart of target state position estimation accuracy in a 50% tag scenario in the verification embodiment of the present invention;

[0019] Figure 4 This is a comparison chart of sensor A deviation registration accuracy in a 50% tag scenario in the verification embodiment of the present invention;

[0020] Figure 5 This is a comparison chart of sensor B deviation registration accuracy in a 50% tag scenario in the verification embodiment of the present invention;

[0021] Figure 6 This is to verify the sensor A bias estimation results of a single Monte Carlo run in the 50% tag scenario of the present invention.

[0022] Figure 7 This is to verify the sensor B bias estimation results of a single Monte Carlo run in the 50% tag scenario of the present invention.

[0023] Figure 8 This is a comparison chart of the target state position estimation accuracy in ablation experiments of this invention under 50% tag scenario;

[0024] Figure 9This is a comparison chart of sensor A deviation registration accuracy in the ablation experiment of this invention under a 50% tag scenario;

[0025] Figure 10 This is a comparison chart of sensor B deviation registration accuracy in the ablation experiment of this invention under a 50% tag scenario. Detailed Implementation

[0026] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0027] Traditional radar target tracking methods, both offline and online, have their own technical drawbacks. Offline registration methods, such as generalized least squares or maximum likelihood estimation, obtain a static bias compensation value by batch processing all measurement data, but this cannot adapt to dynamic biases that change over time or in the environment.

[0028] On the other hand, online registration methods, such as augmented state extended Kalman filtering, can estimate bias online, but they incorporate bias into the state vector, requiring the establishment of an accurate dynamic model (such as a constant or random walk model). This is difficult to achieve when the bias characteristics are complex and variable. Moreover, as the number of sensors increases, the dimension of the augmented state expands rapidly, making it difficult to guarantee the observability of the system and easily leading to filter divergence.

[0029] In recent years, deep neural networks have been able to directly learn the complex mapping relationship between bias and measurement from sensor data, thereby achieving online bias registration of sensors. However, most existing solutions employ supervised learning, whose performance is highly dependent on massive amounts of high-precision labels, and their architectures generally lack collaborative optimization for bias estimation and data fusion. Therefore, how to effectively utilize limited sample labels to design a unified framework that can collaboratively optimize dynamic bias estimation and data fusion to achieve high-precision spatial bias registration and data fusion results is still in the exploratory stage, and there are no publicly available and mature methods yet.

[0030] Therefore, this invention proposes a dual-radar track fusion method based on spatial bias compensation under limited labels. This method, driven by data, aims to directly learn the nonlinear mapping relationship between the biased local estimates of the two radars and the high-precision fusion estimate. Its core is a Weighted Fusion Network (WFN), which adaptively learns and outputs the optimal fusion weights based on the input local estimates, thereby implicitly compensating for dynamic spatial biases during the fusion process. Simultaneously, this invention employs a self-feedback iterative mechanism during the offline training phase. This mechanism uses the bias estimation information obtained in the previous iteration to compensate for the original biased measurements, and then uses the compensated data for the next round of iterative training until the network model converges. This feedback iterative training method and the specially constructed semi-supervised loss function enable the finally trained network model to achieve high-precision bias estimation and data fusion results relying only on a limited number of sample labels.

[0031] This invention discloses a dual-radar track fusion method and apparatus based on spatial bias compensation under finite labeling, belonging to the field of multi-sensor information fusion technology. In multi-sensor target tracking systems, spatial bias registration is an important prerequisite for obtaining high-precision target state estimation. However, existing bias registration methods have inherent limitations: traditional offline registration methods, such as the least squares method, usually obtain a static bias compensation value through batch processing, which cannot adapt to changing dynamic spatial biases; while classic online registration methods, such as augmented state Kalman filtering, require the establishment of an accurate dynamic model for the bias (e.g., a constant or random walk model), which is difficult to achieve when the bias characteristics are complex and variable, and with the increase of sensors, the observability of the system is difficult to guarantee, easily leading to filter divergence. Considering that a certain amount of manually verified target real track sequence fragments can be accumulated in actual systems, deep learning methods are used to mine the structural features of historical data to characterize the statistical features of multi-platform radar data, providing a new possibility for high-precision dynamic bias estimation.

[0032] This invention discloses a dual-radar track fusion method based on spatial bias compensation under finite labels, comprising the following steps: randomly generating an initial sequence fusion factor for each radar; wherein, the initial sequence fusion factor is a combination of fusion factors based on time series; using the initial sequence fusion factor as input to the WFN network to obtain the fusion factor of each radar at the current time; calculating the fusion matrix of the radar based on the fusion factor and the local estimation covariance of the corresponding radar; fusing the local state estimates of the radar based on the fusion matrix to obtain the fused state estimate; wherein, the loss function used for training the WFN network includes the mean square error loss when the labels are known and the relative entropy loss of the local state estimate and the fused state estimate when the labels are unknown.

[0033] This invention avoids the preprocessing and feature decoupling process for multidimensional heterogeneous state information by selecting a dimensionless fusion factor as the input of the WFN network, and directly drives the fusion of high-dimensional states. This significantly reduces complexity while achieving high-precision state estimation fusion with limited labels.

[0034] This invention combines a weighted fusion network (WFN) and self-feedback iterative training to complete the task of spatial bias registration and estimation fusion between two radars. The technical solution includes: First, using an extended Kalman filter (EPF) to perform preliminary processing on the raw measurements from each radar to obtain a local estimate of the target state. Then, a sequence of weights with a fixed length, corresponding to the local estimates of the two radars, is defined as the input to the WFN. The core task of this WFN is to learn the nonlinear mapping relationship from the biased local estimate to the high-precision fusion estimate, and it can adaptively output the optimal fusion weights. Through this data-driven fusion process, the dynamic spatial bias of the sensors is implicitly learned and compensated by the network, thereby achieving dynamic bias registration.

[0035] Furthermore, this invention employs a self-feedback iterative mechanism during the offline training phase: the bias estimation information generated by the network in the initial iteration is used to compensate for the original biased measurements, and a new round of iterative training is performed until the network model meets the convergence condition and the iteration termination condition is reached. This mechanism enables the finally trained network to obtain more accurate dynamic bias estimation results. The overall process of this method in one iteration training is as follows: Figure 1 As shown, the specific implementation steps are as follows.

[0036] First, the radar i measures the original biased quantity in the m-dimensional dimension at time k. Or preliminary compensation measurement Perform extended Kalman filtering to obtain an n-dimensional local state estimate of the target of interest. Secondly, the local state estimates of radar sensor A and radar sensor B are fused using WFN. Next, an initial sequence fusion factor is set. As input to the WFN, it is averaged and initialized. The initial sequence fusion factor corresponds to a local estimate. k represents time. This represents the bias estimate of radar i at time k-1. Initial values ​​can be randomly generated at the beginning time. This represents the fusion factor of radar A at time k+1. This represents the fusion factor of radar B at time k+1. Let represent the local state estimate of radar A at time k+1. This represents the local state estimate of radar B at time k+1.

[0037] In existing technologies, local state estimates are typically fed into the network to generate new local state estimates. In the method of this invention, WFN does not require normalization of the input data. This reduces computational costs to some extent and is adaptable to data fusion in high-dimensional systems.

[0038] Compared to traditional deep learning fusion methods that directly use n-dimensional local state estimates with different physical meanings and dimensions as input, this invention selects dimensionless sequence fusion factors as input features, completely avoiding the cumbersome normalization preprocessing and feature decoupling processes for multi-dimensional heterogeneous data (data in local state estimates). This invention utilizes low-dimensional fusion factors to directly drive state fusion of high-dimensional states, and combines the constructed feedback mechanism with a semi-supervised loss function to significantly reduce model computational complexity while achieving high-precision state estimation fusion with limited labels.

[0039] Then, the output of WFN is the optimized sequence fusion factor. Nonnegativity constraints are then applied. The column fusion factors are convexly combined with the covariance of the local estimates (as shown in Equation 1) to obtain the fusion matrix (as shown in Equations 2 and 3). Finally, through fusion operations (as shown in Equation 4), the n-dimensional fusion estimate can be obtained. Deviation estimation of m dimensions and

[0040]

[0041]

[0042] In the formula, This indicates the covariance of the fusion estimate at time k. This represents the fusion factor of radar A at time k. This represents the local estimated covariance of radar A at time k. This represents the fusion factor of radar B at time k. This represents the local estimated covariance of radar B at time k. This represents the fusion matrix of radar A at time k. This represents the fusion state estimate at time k. This represents the local state estimate of radar A at time k. This represents the fusion matrix of radar B at time k. h represents the local state estimate of radar B at time k. i (·) is a transformation function that converts xyz values ​​in the Cartesian coordinate system to values ​​in the spherical coordinate system (radial distance r, pitch angle). (and azimuth angle θ), it can convert the target state in the spatial Cartesian coordinate system into information in the measurement space.

[0043] To ensure model performance with limited labels, this invention designs a refined iterative control strategy based on validation set loss monitoring during the training phase. During WFN network training, local state estimation or corrected local state estimation is used. The corrected local state estimation is determined by: correcting the biased measurement at the current time step based on the bias estimate from the previous time step to obtain the corrected measurement; and then filtering the corrected measurement using a radar filtering method to obtain the corrected local state estimate.

[0044] This strategy comprises two-stage loops: a network training loop based on validation set loss convergence, and a data feedback loop based on bias correction. The entire process is divided into a feedback-free initial training phase (τ = 0) and a feedback loop training phase (τ ≥ 1), as detailed below:

[0045] During the initial training phase without feedback (τ=0), the original biased measurements are... Input WFN for training. During training, monitor the current validation set loss (α) in real time. The network training is considered converged at the current stage when the current validation loss and the historical minimum validation loss satisfy the following relative convergence condition:

[0046]

[0047] In the formula, α represents the current number of training epochs of the network, and ε is a preset relative convergence accuracy threshold. Once this condition is met, the initial training phase ends, and the bias estimate from the network output is used. Initiate the subsequent feedback training phase.

[0048] During the feedback loop training phase (τ≥1), the original measurements are corrected using the bias estimate obtained from the previous iteration, resulting in compensated measurement data. Based on this compensated data, a new local estimate is generated and input into the WFN to start a new round of training. In each round of feedback training, the convergence condition in the above equation is followed to determine the termination of network parameter updates.

[0049] The above process is repeated cyclically. Once the current training round meets the convergence condition, the updated bias estimate is used to proceed to the next iteration. The entire training process terminates when the preset global maximum number of iterations is reached or overfitting occurs, thus continuously approximating the desired global optimal bias estimate through iterative correction. Furthermore, the learning rate of WFN is set to L. r Furthermore, a weight decay strategy is employed to prevent WFN overfitting, where the weight decay coefficient is d. w .

[0050] In actual testing, the method for determining the local state estimation is as follows: obtain the biased measurement of the radar at the current moment; generate the input of the radar filtering method based on the biased measurement and the deviation estimate of the previous moment; wherein, the deviation estimate is calculated based on the local state estimate and the fused state estimate of the previous moment.

[0051] In addition, biased measurements of the radar at the current moment can be obtained; these biased measurements can be directly used as inputs to the radar filtering method.

[0052] The WFN network designed in this invention consists of a single LSTM network and a fully connected neural network, such as... Figure 2 As shown. The LSTM network uses input gate i... k Forgotten Gate k Output gate h k A neural network combining the sigmoid function (σ) and the tanh function is used to optimize the weights of the input sequence. Where f k Decide which sequence information to discard and which to save; i k Filter the input information at the current moment and use candidate states. Determine the current cell unit C k state; h k The output of the LSTM layer is determined at the current moment and passed to the fully connected neural network to obtain the final optimized sequence weights.

[0053] The dimension of the input features of WFN is I. s The dimension of the hidden layer is H s The number of layers in a recurrent neural network is N. l The dimension of the output feature is O s To ensure training efficiency and real-time online data fusion, the time series length of WFN is set to 2, minimizing the number of network nodes. The parameter values ​​for the WFN network are shown in Table 1.

[0054] Table 1 WFN Network Parameter Settings

[0055] illustrate parameter Range of values Input feature dimensions <![CDATA[I s ]]> 4 Dimensions of Hidden Layers <![CDATA[H s ]]> 12 Number of layers in a recurrent neural network <![CDATA[N l ]]> 2 Output feature dimensions <![CDATA[O s ]]> 4 Convergence accuracy ε <![CDATA[1.0×10 -2 ]]> Learning rate <![CDATA[L r ]]> <![CDATA[1.0×10 -4 ]]> Weight decay coefficient <![CDATA[d w ]]> <![CDATA[1.0×10 -6 ]]>

[0056] To reduce WFN's reliance on a large number of labels (i.e., the real target state ξ), the following semi-supervised loss function is designed: When the labels are known, let δ = 1, where δ represents the identifier of the label, and calculate the fusion result. The mean squared error loss between ξ and δ; when the label is unknown, denote δ = 0, and calculate the local estimate. and The Kullback-Leibler divergence (relative entropy) between them. This loss function not only uses labeled data to calibrate the absolute accuracy of the fusion result, but also uses unlabeled data to maintain the inherent consistency of the fusion system at the probabilistic level. Based on this semi-supervised loss function L... F WFN can achieve high-precision data fusion and bias estimation with a limited number of labels.

[0057]

[0058] Where δ = 0 indicates that the label is unknown, D KL (p F ||p A ) represents p F and p A The Kullback-Leibler divergence between D KL (p F ||p B ) represents p F and p B Kullback-Leibler divergence between p F Let the probability density function of the fusion state estimate be denoted by the probability density function of the fusion state estimate, which follows the mean of the probability density function. Covariance is P F multivariate Gaussian distribution Similarly, p A Let p represent the probability density function for the local state estimation of radar A. B Let δ represent the probability density function for the local state estimation of radar B. Additionally, δ = 1 indicates that the tag is known. ξ represents the fusion state estimate, δ represents the true state of the target to be measured, and δ represents the identifier of the label.

[0059] In addition, L F The calculation result is the loss at a single sampling time step. Since the input and output of WFN are the sequence weights of two adjacent time steps, the fusion result... These are also two adjacent time points. Therefore, the loss of WFN is L. F The sum of the results at two adjacent time points.

[0060] Furthermore, this method utilizes the loss function L F The model measures the difference between the fused estimate and the label, and the relative entropy between the probability distributions of the fused estimate and the local estimate. It updates the weights, biases, and other parameters of the WFN through backpropagation and the ADAM optimizer, continuously performing forward and backward propagation until the model converges, thus establishing a mapping relationship between the local and fused estimates. The global state estimate for the current time step is obtained through weighted fusion of the WFN, achieving high-precision spatial bias registration between the two radars.

[0061] Verification Example:

[0062] Taking the cooperative tracking of a target by two three-coordinate radars, A and B, as an example, the two radars respectively acquire biased measurements of the tracked target's radial distance, azimuth angle, and elevation angle, with a sampling interval T = 1s, and a total of 400 samples are taken. The positions of radar platforms A and B are set as (50km, 0m, 0m) and (0m, 50km, 0m), respectively. The measurement noise of radars A and B is set to be independent of each other, both being Gaussian white noise, with a covariance of R. i (i = A, B), and generate training samples. Here:

[0063]

[0064] In the formula, the radial distance standard deviation of the i-th sensor The standard deviation of the azimuth angle of the i-th sensor The standard deviation of the pitch angle of the i-th sensor Assume the true state of the tracked target is At the initial time k=1, x1 and y1 are...

[0065] z1 is a randomly generated integer in the interval [20km, 40km], and v is a randomly generated integer in the interval [100m, 300m]. x,1 and v y,1 v is a randomly generated integer in the interval [-20m / s, 20m / s]. z,1 It is a randomly generated integer in the interval [-1m / s, 10m / s]. The actual state of the target is affected by process noise, which is Gaussian white noise with an intensity coefficient of 0.1.

[0066] To train the WFN network, training and test sets are generated under the condition that dynamic biases always exist between radars A and B, where the biases (i.e., system errors) are respectively... and This indicates the radial distance deviation of sensor A. This indicates the azimuth deviation of sensor A. This indicates the pitch angle deviation of sensor A, and similarly... Let represent the radial distance deviation, azimuth deviation, and elevation deviation of sensor B, respectively. Where i = A, B. The initial time is set. and The tracks are randomly generated from different numerical ranges, as shown in Table 2. Although the deviation of each track is a fixed value during the total sampling process, the deviations of different tracks in the sample set are different to make the algorithm adaptive. Based on the above parameter settings, a total of 3000 target tracks are generated, of which 2000 tracks are used as the training set and 1000 tracks are used as the test set.

[0067] Table 2 Sensor Dynamic Initial Deviation

[0068]

[0069] Test results and analysis:

[0070] This method (WFN) was compared with several bias registration algorithms, including Long Short-Term Memory Network (LSTM), Augmented State Extended Kalman Filter (ASEKF), Generalized Least Squares-Measurement Extended Dimension Filter (GLS-AMEKF), and Maximum Likelihood Estimation-Measurement Extended Dimension Filter (MLE-AMEKF), through simulations. The accuracy of the different algorithms was analyzed using the target state position and the root mean square error of sensor bias estimation. Here, after M Monte Carlo simulations, the root mean square error (RMSE) of the target state estimation at time k is defined as follows:

[0071]

[0072] In the formula, This is the target state estimate in the Mth Monte Carlo simulation at time k. These represent the positions of the target at time k along the three coordinate axes. These represent the target's velocities in the three coordinate axes at time k. The target is the true state, where the meaning of each symbol is the same as that of the symbols in the state estimation.

[0073] For scenarios where training is done using only 50% of the labels, Figure 3 The target state position estimation accuracy results of different methods are presented. Clearly, the RMSE of the position estimation by the method of this invention is lower than that of the other three comparative methods, exhibiting the highest estimation accuracy.

[0074] Furthermore, the comparison of the deviation registration accuracy of sensors A and B using different methods and the deviation estimation results of a single Monte Carlo simulation are as follows: Figures 4-7 As shown, in a scenario using only 50% of the labels, the method of this invention can simultaneously achieve high-precision dynamic bias estimation for sensors A and B. This demonstrates the superiority of this method in semi-supervised scenarios, achieving high-precision spatial bias registration between two radars.

[0075] Specifically, Figure 4 and Figure 5 The paper presents a comparison of the registration accuracy of various algorithms for sensor A and sensor B in a 50% labeling scenario, considering radial distance deviation, azimuth deviation, and pitch deviation. Experimental results show that the proposed method achieves the lowest RMSE curve and the smallest fluctuation amplitude in all deviation estimations for the two sensors. Multiple Monte Carlo simulations demonstrate that the proposed WFN exhibits good statistical accuracy and stability.

[0076] Figure 6 and Figure 7 The results of deviation estimation for sensor A and sensor B in a single Monte Carlo simulation experiment under the same scenario are presented, where the black line represents the true deviation value. The comparison shows that the estimation curve of the method of this invention can converge quickly and closely fit the dynamic change trend of the true deviation, intuitively reflecting that the algorithm has a good response speed when estimating the deviation and can provide high-precision deviation compensation information for subsequent track fusion.

[0077] In summary, even when using only 50% of the tags, the method of this invention can simultaneously achieve high-precision dynamic bias estimation for sensors A and B. This demonstrates the superiority of this method in semi-supervised scenarios and achieves high-precision spatial bias registration between two radars.

[0078] Ablation experiment results and analysis:

[0079] To further verify the effectiveness of the semi-supervised loss function in the method of this invention, an ablation experiment was provided. Under the same scenario using 50% labeled data, the performance of the semi-supervised loss function versus the supervised loss function alone in target state estimation and sensor bias registration was compared. Figures 8-10 As shown in the figure. Experimental results show that the RMSE of the target state estimation and dual-sensor bias estimation of the method of the present invention is lower than that of the method using only the supervised loss function, which proves the effectiveness of the method in semi-supervised scenarios.

[0080] Figure 8 This paper presents a comparison of the target state position estimation accuracy using different loss functions in a 50% labeled scenario. Experimental results show that, under the same finite label conditions, the method of this invention using a semi-supervised loss function has a significantly lower RMSE curve for position estimation than the method using only a supervised loss function, and also exhibits a smaller steady-state error after convergence. Figure 9 and Figure 10 A comparative ablation experiment is presented, showing the registration accuracy of sensor A and sensor B in a 50% labeled scenario, considering deviations in radial distance, azimuth angle, and pitch angle. The experimental curves demonstrate that the proposed method significantly outperforms the method using only supervised loss functions in terms of the RMSE of all deviation estimates for the two sensors.

[0081] In summary, Figures 8 to 10 Experimental results show that the RMSE of the proposed method in target state estimation and dual-sensor bias registration is lower than that of the method using only the supervised loss function. This strongly demonstrates that in a finite-label scenario, maintaining distribution consistency through a semi-supervised loss function and combining it with the designed feedback mechanism for continuous correction and refinement of bias can fully extract the implicit information in unlabeled measurements, ultimately significantly improving the overall fusion accuracy and bias registration capability of the system.

[0082] Therefore, this invention implicitly compensates for spatial bias by learning a mapping from biased local estimation to high-precision fusion estimation. In offline training, a self-feedback iterative training mechanism is constructed, which feeds back the bias estimation results obtained in the previous round to optimize the training data in the next round, thereby improving the model's estimation accuracy of dynamic bias during iteration.

[0083] In addition, this invention constructs a semi-supervised loss function suitable for estimation fusion. This loss function can not only use a small amount of labeled data for direct supervision in each round of training in the self-feedback iteration, but also discover and utilize the inherent constraints of the system contained in a large amount of unlabeled data. To a certain extent, this reduces the dependence of data-driven methods on a large number of ground truth labels and enhances the practicality and generalization ability of the method.

[0084] This invention employs a weighted fusion network to directly learn the complex nonlinear mapping from biased local estimation to high-precision fusion estimation. Simultaneously, based on a constructed self-feedback iterative training mechanism, spatial bias is implicitly and adaptively learned and compensated by the network, thereby improving the estimation accuracy of target state and spatial bias. Furthermore, combined with a specially designed semi-supervised loss function, this method can achieve high-precision spatial bias registration and target state estimation even with limited labels.

[0085] The present invention also discloses a dual radar track fusion device based on spatial deviation compensation under limited tags, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor implements the above-described method when executing the computer program.

[0086] The present invention also discloses an embodiment that provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps in the above-described method embodiments.

[0087] The present invention also provides a computer program product that, when run on a data storage device, enables the data storage device to implement the steps in the above-described method embodiments.

[0088] If the integrated unit module is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of the present invention can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying computer program code to a storage device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks.

[0089] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0090] Those skilled in the art will recognize that the algorithmic steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

Claims

1. A dual-radar track fusion method based on spatial bias compensation under finite labels, characterized in that, Includes the following steps: An initial sequence fusion factor is randomly generated for each radar; wherein, the initial sequence fusion factor is a combination of fusion factors based on time series. Using the initial sequence fusion factor as the input to the WFN network, the fusion factor for each radar at the current moment is obtained; The fusion matrix of the radar is calculated based on the fusion factor and the local estimated covariance of the corresponding radar. The local state estimates of the radar are fused based on the fusion matrix to obtain a fused state estimate; The loss function used in training the WFN network includes the mean squared error loss when the labels are known and the relative entropy loss for local state estimation and fusion state estimation when the labels are unknown.

2. The dual radar track fusion method based on spatial bias compensation under finite tags as described in claim 1, characterized in that, The relative entropy loss is D KL (p F ||p A )+D KL (p F ||p B ), δ=0; where δ=0 indicates that the label is unknown, D KL (p F ||p A ) represents p F and p A The Kullback-Leibler divergence between D KL (p F ||p B ) represents p F and p B Kullback-Leibler divergence between p F p represents the probability density function of the fusion state estimate. A Let p represent the probability density function for the local state estimation of radar A. B Let represent the probability density function for the local state estimation of radar B.

3. The dual radar track fusion method based on spatial bias compensation under finite tags as described in claim 2, characterized in that, The mean squared error loss is Where δ = 1 indicates that the label is known. ξ represents the fusion state estimate, δ represents the true state of the target to be measured, and δ represents the identifier of the label.

4. The dual radar track fusion method based on spatial bias compensation under finite tags as described in claim 3, characterized in that, The method for determining the local state estimate is as follows: Obtain the biased measurement of the radar at the current moment; The input to the radar filtering method is generated based on the biased measurement and the deviation estimate from the previous moment. The deviation estimate is calculated based on the local state estimate and the fusion state estimate of the previous time step.

5. The dual radar track fusion method based on spatial bias compensation under finite tags as described in claim 3, characterized in that, The method for determining the local state estimate is as follows: Obtain the biased measurement of the radar at the current moment; The biased measurement is used as the input to the radar filtering method.

6. A dual-radar track fusion method based on spatial bias compensation under finite tags as described in claim 4 or 5, characterized in that, During the training of the WFN network, the WFN network is trained using local state estimation or modified local state estimation. The method for determining the corrected local state estimate is as follows: The biased measurement at the current time is corrected based on the bias estimate of the previous time step to obtain the corrected measurement. The corrected measurement is filtered using radar filtering methods to obtain a corrected local state estimate.

7. The dual radar track fusion method based on spatial bias compensation under finite tags as described in claim 6, characterized in that, The fusion matrix of the radar is calculated based on the fusion factor and the local estimated covariance of the corresponding radar, including: in, This represents the fusion matrix of radar A at time k. This indicates the covariance of the fusion estimate at time k. This represents the fusion factor of radar A at time k. Let represent the local estimated covariance of radar A at time k.

8. The dual radar track fusion method based on spatial bias compensation under finite tags as described in claim 7, characterized in that, The method for calculating the fusion estimation covariance is as follows: in, This represents the fusion factor of radar B at time k. Let represent the local estimated covariance of radar B at time k.

9. The dual radar track fusion method based on spatial bias compensation under finite tags as described in claim 8, characterized in that, The fusion of the local state estimation of the radar based on the fusion matrix includes: in, This represents the fusion state estimate at time k. This represents the local state estimate of radar A at time k. This represents the fusion matrix of radar B at time k. This represents the local state estimate of radar B at time k.

10. A dual-radar track fusion device based on spatial bias compensation under limited tags, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1-9.

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