Neural network aided millimeter wave radar bayesian filtering method under dual-radar cooperation

Abstract

The application provides a neural network auxiliary millimeter wave radar Bayesian filtering method under dual radar cooperation, the NNABF algorithm provided by the application effectively fuses prior information of ground-based radar through a "Bayesian framework + neural network" hybrid architecture, and realizes stable tracking of a high-speed maneuvering target; the space-time features of a track are extracted through the introduction of a CNN, historical state memory coding is realized through a CAN cross attention network, and a gating unit of an EGBRNN is combined to dynamically correct model mismatch errors, so that continuous, stable and high-precision tracking of a target is maintained in a strong maneuvering and low observation frequency scene, the inherent limitations of a traditional single model method are overcome, a complex Bayesian filtering framework is simplified into a closed recursive structure through a Gaussian approximation strategy, the algorithm complexity is significantly reduced while the modeling expression capability is maintained, and the application has engineering feasibility; and can be applied to real-time tracking scenes of multiple types of maneuvering targets.

Description

Technical Field

[0002] This invention relates to the technical field of millimeter-wave radar signal processing and target tracking, specifically to a neural network-assisted Bayesian filtering method for millimeter-wave radar under dual-radar collaboration. Background Technology

[0004] The rapid development of modern air defense systems has led to increasingly complex aerial threats. These targets are characterized by high speed, strong maneuverability, and unpredictable movement patterns, posing a severe challenge to radar detection and tracking systems. Achieving high-precision and stable tracking of these targets is a core issue in point defense missions, directly affecting early warning capabilities and interception effectiveness.

[0005] In practical key area defense scenarios, airborne millimeter-wave radar undertakes the task of precise tracking of intruding targets. Millimeter-wave radar has a narrow beam and high angular resolution, possessing excellent angle and velocity measurement accuracy, making it suitable for closed-loop precision tracking. However, its beam coverage is limited, and it faces two prominent problems when performing tracking tasks independently. First, low data rate leads to tracking instability. Millimeter-wave radar has an extremely narrow beam, requiring scanning a large airspace when searching for or re-illuminating targets. Constrained by beam scanning and dwell time, the data rate is limited, resulting in sparse measurements and delayed updates. During the filtering process, state prediction lacks long-term information correction, leading to continuous error accumulation and a significant decrease in tracking accuracy and stability. Second, strong maneuvering causes model mismatch. Highly maneuverable targets often perform sudden maneuvers, causing severe mismatch in traditional filtering methods based on fixed motion models (such as uniform velocity CV or uniform acceleration CA models), resulting in a sharp decline in estimation accuracy.

[0006] Traditional classical filtering methods mainly include Kalman filtering (KF), extended Kalman filtering (EKF), and interactive multiple model (IMM) algorithms. KF is only applicable to linear systems, EKF achieves linearization through first-order Taylor expansion, while IMM addresses target maneuvers through weighted fusion of multiple models. However, all of these methods heavily rely on accurate system models and statistical assumptions about noise, and their performance is fundamentally limited when facing unknown maneuvers, complex environmental disturbances, and model mismatch.

[0007] In recent years, neural networks (NNs) have been gradually introduced into the field of target tracking due to their powerful nonlinear fitting capabilities, forming a new paradigm of hybrid filtering that combines data-driven and model-driven approaches. KalmanNet embeds recurrent neural networks into the KF framework to learn Kalman gain from data, compensating for model mismatch under partially unknown dynamic conditions. Long Short-Term Memory (LSTM) networks have also been used to directly model the nonlinear mapping relationship between target state and measurement to improve the performance of maneuvering target tracking. However, most existing methods are limited to single-sensor scenarios and have failed to fully explore the fusion potential of multi-source information, especially prior knowledge from heterogeneous sensors.

[0008] Therefore, there is currently a lack of a method in the technology that can effectively integrate prior information from ground-based radar, dynamically compensate for model mismatch errors, and achieve stable tracking of high-speed maneuvering targets under low data rate conditions. Summary of the Invention

[0010] To address the problems existing in the prior art, this invention provides a neural network-assisted Bayesian filtering method for millimeter-wave radar under dual-radar collaboration, in order to solve the technical problem of the lack of a method that can effectively fuse prior information from ground-based radar, dynamically compensate for model mismatch errors, and achieve stable tracking of high-speed maneuvering targets under low data rate conditions.

[0011] This invention provides a neural network-assisted Bayesian filtering method for millimeter-wave radar under dual-radar collaboration, comprising:

[0012] S1. Construct a joint state model of ground-based radar and airborne millimeter-wave radar based on a Bayesian framework. Introduce offline ground-based radar dataset and target historical flight track, establish a state-space model including joint state, memory and Bayesian filtering framework, and derive the state update expression.

[0013] S2. Based on the Gaussian approximation strategy, the Bayesian framework is simplified, and a recursive structure in the form of an extended Kalman filter is constructed to obtain a closed-loop analytical state prediction and update expression.

[0014] S3. Design a neural network-assisted Bayesian filter network, which includes a convolutional neural network feature extraction network, a cross-attention memory encoding network, and an interpretable gated Bayesian recurrent neural network.

[0015] S4. Train the neural network-assisted Bayesian filter network using measured data, deploy the trained neural network-assisted Bayesian filter network on the airborne millimeter-wave radar tracking system, integrate ground-based radar measurement priors, perform real-time state estimation on the input maneuvering target measurement sequence, and output continuous estimation results of target position and velocity.

[0016] Optionally, the construction of a joint state model for ground-based and airborne radar based on a Bayesian framework involves introducing offline ground-based radar datasets and historical flight track sequences, establishing a state-space model that includes joint state, memory, and a Bayesian filtering framework, and deriving a state update expression with a closed recursive form, including:

[0017] S101, the ground-based radar uses a wide beam to search for targets and continuously tracks and generates initial track information and target status guidance data after detecting a target;

[0018] S102. The airborne millimeter-wave radar receives the target status guidance data, points the beam at the predicted target position, performs narrow beam scanning, and measures the target status in real time.

[0019] S103. Combining the initial trajectory information of the ground-based radar and the target state data of the airborne millimeter-wave radar, a state prediction model is constructed.

[0020] S104. Introduce offline ground-based radar datasets and target historical tracks, establish a state-space model including joint state, memory, and Bayesian filtering framework, and derive the state update expression.

[0021] Optionally, steps S103 and S104 include:

[0022] S1031, The constructed state prediction model is expressed as follows:

[0023]

[0024] in, For the real-state prediction model function, This refers to the target's historical flight path for the ground-based radar. It is the number of samples in the target trajectory sequence. The noise distribution matrix is... To map process noise into the state space. For the first The target's motion status at all times;

[0025] S1032. Introduce the traditional state prediction model into equation (1), where the traditional state prediction model is expressed as:

[0026]

[0027] The prediction model and the measurement model are expressed as follows:

[0028]

[0029]

[0030] in, For the actual measurement model function, For traditional measurement model functions, For the error term of the prediction model, This refers to the error term in the measurement model.

[0031] S1033, and a two-level nested function structure is used to model the error term of the prediction model, expressed as:

[0032]

[0033] in, For memory encoding mapping, For memory vectors, For output mapping;

[0034] S1041, Introducing offline ground-based radar dataset The target's historical trajectory is represented as:

[0035]

[0036] in, The target's true state sequence obtained offline. For the corresponding ground-based radar measurement sequence, It is an offline accumulated track state sequence used to extract global information. The duration predicted by the system. It is the number of samples of the tracked target status in the offline ground-based radar dataset;

[0037] S1042, and the memory update process is represented as:

[0038]

[0039]

[0040]

[0041] in, For memory, a linear mapping function, and These correspond to the feature extraction module and the attention mechanism module, respectively.

[0042] S1043, Combining measurements at all times Offline ground-based radar dataset Historical flight path of the target The combined posterior density of the ground-based radar and airborne millimeter-wave radar at the previous moment Under these conditions, the joint state probability density prediction of ground-based radar and airborne millimeter-wave radar is expressed as:

[0043]

[0044] in,

[0045]

[0046]

[0047]

[0048] The update expression for the joint state probability density of ground-based radar and airborne millimeter-wave radar is as follows:

[0049] .

[0050] Optionally, the simplification of the Bayesian framework based on the Gaussian approximation strategy to construct a recursive structure of extended Kalman filter form, obtaining a closed-loop analytical state prediction and update expression, includes:

[0051] S201. Before implementing the Gaussian approximation strategy, the following assumptions are made: process noise and measurement noise follow a Gaussian distribution; the predicted probability density function of the measurement follows a Gaussian distribution; and the posterior probability density function of the state follows a Gaussian distribution. , , Follows a Gaussian distribution. Obtaining first and second moments respectively and The Gaussian distribution, and Obtaining first and second moments respectively and Gaussian distribution;

[0052] S202. Based on the assumptions of step S201, the state prediction and covariance are expressed as follows:

[0053]

[0054]

[0055] The predictions and covariance during the state update phase are expressed as follows:

[0056]

[0057]

[0058] Among them, the predicted measurement value The measurement covariance is defined by the following formula:

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] in, The process noise covariance matrix is... The measurement noise covariance matrix;

[0065] S203. The calculation is performed using a first-order Taylor expansion approximation. Let... and They are respectively and The Jacobian matrix, by referencing the linearization of Kalman filtering, allows equations (15), (16), and (19)-(23) to be replaced with:

[0066]

[0067]

[0068]

[0069]

[0070] .

[0071] Optionally, the convolutional neural network feature extraction network includes:

[0072] The information mean extraction module and the information covariance extraction module adopt the same structural module to estimate the mean vector and the information covariance matrix, respectively. The structural module of the convolutional neural network feature extraction network includes two convolutional layers, two average pooling layers, one linear layer and corresponding activation functions.

[0073] Optionally, the cross-attention memory encoding network includes:

[0074] The memory mean encoding module and the memory covariance encoding module use the same structural modules to estimate the memory mean and memory covariance matrix, respectively. The structural modules of the cross-attention memory encoding network include an embedding layer, a mapping layer, an attention calculation layer, and a linear output layer.

[0075] Optionally, the interpretable gated Bayesian recurrent neural network includes:

[0076] The memory update gate, state prediction gate, and state gate update gate all employ a structure consisting of two linear layers and a nonlinear activation function.

[0077] Compared with the prior art, the present invention:

[0078] 1. The proposed NNABF algorithm effectively integrates prior information from ground-based radar through a hybrid architecture of "Bayesian framework + neural network" to achieve stable tracking of high-speed maneuvering targets. In all test scenarios, the position RMSE of NNABF is 2-5m lower than that of the traditional KF algorithm, and the terminal convergence tracking error is less than 0.3m.

[0079] 2. By introducing CNN to extract the spatiotemporal features of the trajectory, using CAN cross-attention network to realize historical state memory encoding, and combining EGBRNN gating unit to dynamically correct model mismatch error, continuous, stable and high-precision tracking of the target is maintained in scenarios with strong maneuverability and low observation frequency, overcoming the inherent limitations of traditional single model methods.

[0080] 3. By using a Gaussian approximation strategy, the complex Bayesian filtering framework is simplified into a closed recursive structure, which significantly reduces the algorithm complexity while maintaining the modeling expressiveness and has engineering feasibility; it can be applied to real-time tracking scenarios of various types of maneuvering targets. Attached Figure Description

[0082] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0083] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0084] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0085] Figure 2 This is a schematic diagram of the network structure of the method of the present invention;

[0086] Figure 3 This is the RMSE diagram of the track test set in the X direction in the method of the present invention;

[0087] Figure 4 This is a schematic diagram illustrating the relationship between the velocity RMSE of the track test set and time in the method of the present invention;

[0088] Figure 5 This is a schematic diagram illustrating the variation of training and validation losses for the track test set with each round in the method of this invention. Detailed Implementation

[0090] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other implementation cases obtained by those skilled in the art without creative effort are within the scope of protection of this application. Functional units with the same reference numerals in the examples of this invention have the same and similar structures and functions.

[0091] See Figure 1 This invention provides a neural network-assisted Bayesian filtering method for millimeter-wave radar under dual-radar collaboration, comprising:

[0092] S1. Construct a joint state model of ground-based radar and airborne millimeter-wave radar based on a Bayesian framework. Introduce offline ground-based radar dataset and target historical flight track, establish a state-space model including joint state, memory and Bayesian filtering framework, and derive the state update expression.

[0093] S2. Based on the Gaussian approximation strategy, the Bayesian framework is simplified, and a recursive structure in the form of an extended Kalman filter is constructed to obtain a closed-loop analytical state prediction and update expression.

[0094] S3. Design a neural network-assisted Bayesian filter network, which includes a convolutional neural network feature extraction network, a cross-attention memory encoding network, and an interpretable gated Bayesian recurrent neural network.

[0095] S4. Train the neural network-assisted Bayesian filter network using measured data, deploy the trained neural network-assisted Bayesian filter network on the airborne millimeter-wave radar tracking system, integrate ground-based radar measurement priors, perform real-time state estimation on the input maneuvering target measurement sequence, and output continuous estimation results of target position and velocity.

[0096] In this embodiment, the following abbreviations will be explained first: Neural Network Assisted Bayesian Filter (NNABF); Neural Network (NN); Kalman Filter (KF); Extended Kalman Filter (EKF); Interactive Multiple Model (IMM) algorithm; Cross-Attention Network (CAN); Convolutional Neural Network (CNN).

[0097] S1. Construct a joint state model of ground-based radar and airborne millimeter-wave radar based on a Bayesian framework. Introduce offline ground-based radar datasets and target historical tracks, establish a state-space model that includes joint state, memory, and Bayesian filtering framework, and derive the state update expression.

[0098] The S101 ground-based radar uses a wide beam to search for targets and continuously tracks and generates initial track information and target status guidance data after detecting a target.

[0099] Ground-based radar acquires prior information and generates initial tracks. Employing a wide-beam search mode, the ground-based radar continuously tracks and generates initial track information upon initial target detection. Target status guidance data is reported to the airborne millimeter-wave radar processing unit via a communication link.

[0100] S102. The airborne millimeter-wave radar receives the target status guidance data, points the beam at the predicted target position, performs narrow beam scanning, and measures the target status in real time.

[0101] Airborne millimeter-wave radar acquisition and closed-loop tracking: The airborne millimeter-wave radar receives guidance data from the ground-based radar, points its beam at the predicted target location, and performs narrow-beam scanning to achieve target acquisition. It then enters closed-loop precision tracking mode to measure the target's status in real time.

[0102] S103. Combining the initial trajectory information of the ground-based radar and the target state data of the airborne millimeter-wave radar, a state prediction model is constructed.

[0103] Finally, a joint filtering framework was constructed. During the closed-loop tracking process, the ground-based radar continuously outputs low-precision wide-area observation data. The two measurement data streams undergo joint Bayesian filtering in the airborne processor, and state estimation is completed through a neural network-assisted Bayesian filter (NNABF).

[0104] Therefore, in the joint modeling process, considering the prior information provided by ground-based radar and the non-Markov state prediction process, the following state prediction model was constructed:

[0105]

[0106] Among them, the true state prediction model function It incorporates the influence of previous states and takes into account the target's historical flight path accumulated from multiple offline frames by ground-based radar. Used to extract global information. The number of samples in the target trajectory sequence; noise distribution matrix. process noise Mapped to the state space, this represents the respective influence on the state components; the... The target's motion state at any given time is .

[0107] First, the traditional state prediction model is introduced into the equation, which is expressed as:

[0108]

[0109] This transforms the original state evolution process, which possessed non-Markovian characteristics, into an equivalent problem introducing modeling errors within the standard first-order Markov framework. Therefore, the system's prediction and measurement models can be expressed as:

[0110]

[0111]

[0112] in, For the actual measurement model function, For traditional measurement model functions; error terms for prediction and measurement models. and and The multiple historical states prior to the given time are related, which clearly exhibits non-Markovian properties, making it impossible for the model in the equation to directly support recursive calculations.

[0113] Therefore, a two-level nested function structure is used to analyze the error term. Modeling:

[0114]

[0115] Among them, the function It is a memory-encoded mapping used to encode historical state sequences and ground-based radar prior information into memory vectors. And functions This serves as the output mapping, extracting key regular features from memory and converting them into modeling errors. In the equation, the memory vector... It incorporates high-dimensional historical state information and possesses non-Markovian properties, therefore it cannot be directly used for recursive filtering. Furthermore, the cumulative track sequence... It will greatly increase the function The computational complexity is low, and the influence of the sequence on the state prediction at each time step varies, exhibiting a dynamic driving characteristic related to the current state. This invention introduces a neural network (NN) to learn the mapping relationship between global information and state prediction. This mapping serves as a form of memory. It can be directly applied to the error terms in the state prediction and measurement processes. and This helps to achieve more accurate target tracking filtering.

[0116] S104. Introduce offline ground-based radar datasets and target historical tracks, establish a state-space model including joint state, memory, and Bayesian filtering framework, and derive the state update expression.

[0117] Consider the following offline data:

[0118]

[0119] in, It is a sequence of the target's true state obtained offline. These are the corresponding ground-based radar measurement sequences. It is an offline accumulated track state sequence used to extract global information. For ease of training, it will... All flight paths were cut into frame; This is the duration predicted by the system; This represents the number of samples of the tracked target's state in the dataset. This offline dataset can be obtained by collecting sensor measurement data, calibrating ground truth data, and executing tracking algorithms.

[0120] Inspired by the memory iteration mechanism, this step constructs the following memory update process:

[0121]

[0122]

[0123]

[0124] in, For memory, a linear mapping function, and These correspond to the feature extraction module and the attention mechanism module, respectively, both of which need to be obtained through NN training.

[0125] For this system model, combining measurements at all times... Offline ground-based radar dataset Historical flight path of the target The combined posterior density of the ground-based radar and airborne millimeter-wave radar at the previous moment Under these conditions, the joint state probability density prediction of ground-based radar and airborne millimeter-wave radar is expressed as:

[0126]

[0127] in,

[0128]

[0129]

[0130]

[0131] The update expression for the joint state probability density of ground-based radar and airborne millimeter-wave radar is as follows:

[0132] .

[0133] S2. The Bayesian framework is simplified based on the Gaussian approximation strategy to construct a recursive structure in the form of an extended Kalman filter, thereby obtaining a closed-loop analytical state prediction and update expression.

[0134] After constructing the joint state model of the ground-based radar and airborne millimeter-wave radar in step S1, it is necessary to simplify the complex posterior density function distribution to ensure the deployability of the proposed BF framework in practical applications. To this end, this invention introduces a Gaussian approximation strategy to construct a recursive structure of EKF form, thereby obtaining closed-form analytical prediction and update expressions, achieving efficient estimation of state, memory variables, and error terms.

[0135] S201. Before implementing the Gaussian approximation strategy, the following assumptions are made:

[0136] Assumption 1. Process noise and measurement noise follow a Gaussian distribution;

[0137] Assumption 2. The predicted probability density function of the measurement follows a Gaussian distribution;

[0138] Assumption 3. The posterior probability density function of the state follows a Gaussian distribution;

[0139] Assumption 4. , , It follows a Gaussian distribution;

[0140] Assumption 5 Obtaining first and second moments respectively and The Gaussian distribution, and Obtaining first and second moments respectively and Gaussian distribution;

[0141] S202. Based on assumptions 1-5 in step S201, the state prediction and covariance are expressed as follows:

[0142]

[0143]

[0144] The predictions and covariance during the state update phase are expressed as follows:

[0145]

[0146]

[0147] Among them, the predicted measurement value The measurement covariance is defined by the following formula:

[0148]

[0149]

[0150]

[0151]

[0152]

[0153] in, The process noise covariance matrix is... The measurement noise covariance matrix;

[0154] S203. To improve filtering efficiency, this invention employs a first-order Taylor expansion approximation in Gaussian approximation filtering. Let... and They are respectively and The Jacobian matrix, by referencing the linearization of Kalman filtering, allows equations (15), (16), and (19)-(23) to be replaced with:

[0155]

[0156]

[0157]

[0158]

[0159]

[0160] By introducing the aforementioned Gaussian approximation strategy, this invention successfully simplifies the joint state probability modeling problem of ground-based radar and airborne radar in BF into a closed recursive structure without sacrificing modeling expressive power.

[0161] S3. Design a neural network-assisted Bayesian filter network, which includes a convolutional neural network feature extraction network, a cross-attention memory encoding network, and an interpretable gated Bayesian recurrent neural network.

[0162] See Figure 2After completing the Gaussian approximation, in order to effectively express the ground-based radar information and dynamically correct the error term in the state modeling, it is necessary to design a matching network structure. To this end, this step focuses on feature extraction, constructs a functionally defined network module, and achieves high-precision target tracking through end-to-end training.

[0163] 1. Convolutional Neural Network (CNN) for Feature Extraction:

[0164] For feature extraction mapping, a conventional form of CNN can be used for construction. Borrowing the structure of the Interpretable Gated Bayesian Recurrent Neural Network (EGBRNN), two structurally identical modules—an information mean extraction module and an information covariance extraction module—are used to estimate the mean vector. Information covariance matrix Each CNN module mainly consists of two convolutional layers, two average pooling layers, one linear layer, and corresponding activation functions. The internal construction process is as follows.

[0165] (1) Input:

[0166] CNN is used to estimate the mean vector. Covariance Matrix Based on conditional probability density function Its input is a sequence of flight paths. The shape is adjusted to suit the network input through a normalization operation, i.e.:

[0167]

[0168] in, , , The corresponding input convolutional layer's channel number, height, and width satisfy the following conditions: , , ; For sequence The state dimension.

[0169] (2) Convolutional layer:

[0170] Convolutional layers extract local features from the input data through local receptivity, reducing the spatial dimensionality of the data while preserving key structural information. To extract more discriminative deep features, two-dimensional convolutional layers are used, and an activation function is introduced for non-linear mapping. Its calculation expression is:

[0171]

[0172] in, Represents the index of a certain convolutional network layer; The weight matrix of the convolution kernel; For convolution bias, These are the height and width of the convolution kernel, respectively; It is a commonly used activation function that helps models learn more complex nonlinear features and increases the nonlinear capabilities of the network. It is defined as:

[0173]

[0174] For a given number of output channels of a convolutional layer Its output height and width are respectively , The calculation method is as follows:

[0175]

[0176]

[0177] in, The stride of the convolution kernel movement. This is padding for the convolution; the output of the convolutional layer is... .

[0178] (3) Pooling layer:

[0179] Typically, a pooling layer is connected after each convolutional layer, mainly to reduce the spatial resolution of the feature map, reduce computational overhead, and enhance the model's robustness to local perturbations (such as translation and rotation). Pooling operations can effectively extract key features and improve the model's generalization ability. Common pooling methods include average pooling and max pooling. The pooling layer in this invention uses average pooling. Its calculation expression is as follows:

[0180]

[0181] in, , These represent the height and width of the pooling kernel, and the output of the pooling layer. ,satisfy: The height and width of each layer's output are calculated using the following formula:

[0182]

[0183]

[0184] (4) Linear layer:

[0185] Linear layers are used to map the local features extracted by convolution to a new representation space, facilitating further high-level abstraction. This layer uses a weight matrix... and bias terms A linear transformation is achieved, represented as follows:

[0186]

[0187] in, The output of the linear layer is This represents the hidden state dimension of the CNN; the first dimension, 1, represents a global feature.

[0188] (5) Output:

[0189] Through the aforementioned CNN encoding process, the final result is the target trajectory sequence. Feature representation in To adapt to Gaussian filter modeling, the CNN module converts the output feature vector into a mean vector through different branch structures. Covariance Matrix This allows us to construct a constrained representation of ground-based radar information within the filter. To match the batch size during network training, the first dimension of the linear layer's output is copied, ultimately yielding the features extracted by the CNN.

[0190]

[0191] in, This refers to the batch size.

[0192] 2. Cross-Attention Memory Encoding Network (CNN):

[0193] After obtaining the mean and covariance matrices of the features through CNN encoding, the memory for the current time step is generated. The goal is to be able to record the historical memory of the target's motion state. Features of the current frame To achieve this organic integration, a state-driven attention network (CAN) is introduced. This network is based on a learnable dynamic weight mechanism that can effectively adjust the contribution of static features to the target's current state. In this attention mechanism, the target's historical state memory is utilized. Considered as query vector Q, features It is then decomposed into key K and value V. The memory vector generated by the attention structure can express the degree of attention the current state pays to static features, thereby accurately identifying and utilizing static information to adapt to dynamic environments. Similarly, two structurally identical modules, the memory mean encoding module and the memory covariance encoding module, are used here to estimate the mean of the memory. Covariance Its structure mainly includes an embedded layer. It consists of four parts: a mapping layer, an attention computation layer, and a linear output layer.

[0194] (1) Input:

[0195] CAN is used for estimation , Therefore, based on the conditional probability density function The mean of the features Covariance and the mean of historical memory Covariance As input, This represents the hidden state dimension of the EGBRNN network. All inputs need to be aligned along this dimension, uniformly mapped to a suitable input format, i.e.:

[0196]

[0197]

[0198] in, The sequence length corresponding to the embedding layer and the hidden state dimension of CAN, respectively, satisfy: .

[0199] (2) Embedding layer:

[0200] The input vector is projected onto a unified embedding dimension space through two linear mapping layers, ensuring that inputs from different sources have the same feature dimension for subsequent weighted fusion. The mapping process is as follows:

[0201]

[0202]

[0203] in, , , , The weight matrix and bias terms are used; the output is... , , This represents the hidden state dimension of CAN.

[0204] (3) Mapping layer:

[0205] This module uses three sets of linear mappings to map the input layer output to queries, keys, and values, respectively. , , Variables. The target's historical memory. Corresponding embedding layer output Mapped to Static features Corresponding embedding layer output Decompose into a group , Yes. Its mapping is written as:

[0206]

[0207]

[0208]

[0209] in, , The weight matrix and bias terms are learnable. When encoding current information, the network may overemphasize its own position while neglecting other positions. Therefore, this invention employs a multi-head attention mechanism as a solution. It is divided into multiple headers, and each header has a separate query, key, and value mapping function; The dimensions of each head are , Representing the The index of the size can be divided into a total of Size, and meets .

[0210] (4) Attention computation layer:

[0211] By analyzing each head The dot product is scaled and then normalized using the softmax function to obtain the attention weights for each head. :

[0212]

[0213] The enhanced attention value is obtained by weighting and summing these weights. :

[0214]

[0215] By concatenating the attention values ​​of each head, we can obtain the output of the attention computation layer. :

[0216]

[0217] (5) Linear layer:

[0218] After obtaining the attention output, it is output through a linear layer:

[0219]

[0220] in, , These are the learnable weight matrix and bias terms.

[0221] (6) Output:

[0222] The two modules of the network output the memorized mean. Covariance Two parts:

[0223]

[0224] 3. Interpretable Gated Bayesian Recurrent Neural Network (EGBRNN):

[0225] This section's network structure is still based on the three types of gated units in the original EGBRNN architecture: Memory Update Gate (MUG), State Prediction Gate (SPG), and State Update Gate (SUG). These three types of gated units, together with the NN module, form the core filtering structure, used to estimate the mean and covariance of the model mismatch error during filtering. The above structure incorporates ground-based radar information and offline data through the NN to assist in learning the error term distribution. Its overall design strictly follows the Black-Frank theory, and all modules adopt a unified two-layer linear NN structure (two linear layers + a nonlinear activation function). Therefore, the designed gated module does not require a complex structure to complete nonlinear modeling and learnable mapping. A general gated network mapping function is defined. for:

[0226]

[0227] in, These are all learnable weights and bias vectors of the gating unit, and their shapes are determined by the specific gating unit.

[0228] (1) Memory Update Gate (MUG):

[0229] Based on conditional probability density function MUG is used for estimation , Unlike the original EGBRNN, the MUG designed in this invention not only needs to incorporate historical memory. It also needs to be combined with memory. and current status information Therefore, the input vector should be expanded to include a combination of multi-source state information, as follows:

[0230]

[0231] Among them, the linear layer .

[0232] (2) State Prediction Gate (SPG):

[0233] Based on conditional probability density function SPG is used for estimation , Its input vector It can be written as:

[0234]

[0235] Among them, the linear layer , .

[0236] (3) State gate update gate (SUG):

[0237] Based on conditional probability density function SUG is used for estimation , Its input vector It can be written as:

[0238]

[0239] Among them, the linear layer , .

[0240] Based on the learnable weights and biases in the network described above, a set of learnable parameters for each module is constructed, namely:

[0241]

[0242] in, It is a set of learnable parameters.

[0243] Based on the above network structure and input, each component of the network has a specific function, and the error caused by model mismatch can be compensated in a targeted manner.

[0244] Based on the Minimum Mean Square Error (MMSE) criterion commonly used in BF (Browser-Based Function), this step employs a regularized Mean Square Error (MSE) loss function to train the NNABF. Considering an offline dataset, the loss function can be written as:

[0245]

[0246] in, This is the coefficient of the regularization term. The MSE loss term directly measures the difference between the model's predicted values ​​and the true values, while the regularization term suppresses overfitting and enhances the model's generalization ability by controlling the parameter size. To improve training efficiency, this step uses the mini-batch stochastic gradient descent algorithm. Specifically, the dataset is divided into several mini-batches, and the size of each batch is represented as... In the In this iteration, let the randomly selected sample number be denoted as... The loss function corresponding to this mini-batch is:

[0247]

[0248] Given the differentiability of the constructed network structure, the Backpropagation Through Time (BPTT) algorithm is used for parameter updates during the training phase.

[0249] S4. Train the neural network-assisted Bayesian filter network using measured data, deploy the trained neural network-assisted Bayesian filter network on the airborne millimeter-wave radar tracking system, integrate ground-based radar measurement priors, perform real-time state estimation on the input maneuvering target measurement sequence, and output continuous estimation results of target position and velocity.

[0250] The results were validated and analyzed using experimental data, which consisted of 1000 target tracks under different flight conditions, including climbs, dives, uniform acceleration, and turns. The data was divided into training, validation, and test sets in a 3:1:1 ratio.

[0251] The simulation parameters are set as shown in the table below:

[0252] Table 1 Simulation Parameter Settings

[0253] Frame period 0.01 Second Process noise accuracy 0.01 - Distance measurement noise 0.1 - Speed ​​measurement noise 0.5 - Initial covariance value 10 - Sample size 1000 indivual Learning rate 0.005 - Training rounds 50 wheel

[0254] The root mean square error (RMSE) is used as the evaluation metric, and the RMSE for position and velocity are calculated separately. In all scenarios, the proposed NNABF algorithm outperforms the traditional KF algorithm in both tracking accuracy and stability.

[0255] (1) Location RMSE: such as Figure 3 As shown, in the track test set, the position RMSE of NNABF was lower than that of KF throughout the entire time range. Especially after 1.3s during the target maneuver phase, the RMSE of NNABF in the X direction stabilized within 3m, while that of KF rose to more than 8m.

[0256] (2) Speed ​​RMSE: such as Figure 4 As shown, the velocity estimation performance of NNABF also remains at a low level, significantly lower than that of KF. The velocity changes significantly around 2.8s, causing the velocity tracking accuracy to deteriorate around 2.8s, but it is still lower than that of KF.

[0257] (3) Training loss: such as Figure 5As shown, the training and validation set losses of the trajectory both decrease steadily with each training round and eventually converge to a low level, without overfitting, thus verifying the model's generalization ability.

[0258] In summary, the NNABF algorithm outperforms the KF algorithm in overall tracking performance across various scenarios, verifying that the proposed NNABF algorithm, through a hybrid architecture of "Bayesian framework + neural network," effectively integrates prior information from ground-based radar to achieve stable tracking of high-speed maneuvering targets. In all test scenarios, the NNABF position RMSE is 2-5m lower than that of the traditional KF algorithm, and the terminal convergence tracking error is less than 0.3m. Furthermore, by introducing CNN to extract spatiotemporal features of the trajectory, implementing historical state memory encoding through a CAN cross-attention network, and combining the gating unit of EGBRNN to dynamically correct model mismatch errors, it maintains continuous, stable, and high-precision tracking of targets in scenarios with high maneuverability and low observation frequency, overcoming the inherent limitations of traditional single-model methods. At the same time, by using a Gaussian approximation strategy to simplify the complex Bayesian filtering framework into a closed recursive structure, it significantly reduces the algorithm complexity while maintaining modeling expressiveness, demonstrating engineering feasibility. It can be applied to real-time tracking scenarios of various types of maneuvering targets.

[0259] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0260] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A neural network-assisted Bayesian filtering method for millimeter-wave radar under dual-radar collaboration, characterized in that, include: S1. Construct a joint state model of ground-based radar and airborne millimeter-wave radar based on a Bayesian framework. Introduce offline ground-based radar dataset and target historical flight track, establish a state-space model including joint state, memory and Bayesian filtering framework, and derive the state update expression. S2. Based on the Gaussian approximation strategy, the Bayesian framework is simplified, and a recursive structure in the form of an extended Kalman filter is constructed to obtain a closed-loop analytical state prediction and update expression. S3. Design a neural network-assisted Bayesian filter network, which includes a convolutional neural network feature extraction network, a cross-attention memory encoding network, and an interpretable gated Bayesian recurrent neural network. S4. Train the neural network-assisted Bayesian filter network using measured data, deploy the trained neural network-assisted Bayesian filter network on the airborne millimeter-wave radar tracking system, integrate ground-based radar measurement priors, perform real-time state estimation on the input maneuvering target measurement sequence, and output continuous estimation results of target position and velocity.

2. The millimeter-wave radar Bayesian filtering method with neural network assistance under dual radar collaboration as described in claim 1, characterized in that, The construction of a joint state model for ground-based and airborne radar based on a Bayesian framework involves incorporating offline ground-based radar datasets and historical flight track sequences. A state-space model is established, including joint state, memory, and a Bayesian filtering framework. A state update expression with a closed recursive form is derived, including: S101, the ground-based radar uses a wide beam to search for targets and continuously tracks and generates initial track information and target status guidance data after detecting a target; S102. The airborne millimeter-wave radar receives the target status guidance data, points the beam at the predicted target position, performs narrow beam scanning, and measures the target status in real time. S103. Combining the initial trajectory information of the ground-based radar and the target state data of the airborne millimeter-wave radar, a state prediction model is constructed. S104. Introduce offline ground-based radar datasets and target historical tracks, establish a state-space model including joint state, memory, and Bayesian filtering framework, and derive the state update expression.

3. The millimeter-wave radar Bayesian filtering method with neural network assistance under dual radar collaboration as described in claim 2, characterized in that, Steps S103 and S104 include: S1031, The constructed state prediction model is expressed as follows: in, For the real-state prediction model function, This refers to the target's historical flight path for the ground-based radar. It is the number of samples in the target trajectory sequence. The noise distribution matrix is... To map process noise into the state space. For the first The target's motion status at all times; S1032. Introduce the traditional state prediction model into equation (1), where the traditional state prediction model is expressed as: The prediction model and the measurement model are expressed as follows: in, For the actual measurement model function, For traditional measurement model functions, For the error term of the prediction model, This refers to the error term in the measurement model. S1033, and a two-level nested function structure is used to model the error term of the prediction model, expressed as: in, For memory encoding mapping, For memory vectors, For output mapping; S1041, Introducing offline ground-based radar dataset The target's historical trajectory is represented as: in, The target's true state sequence obtained offline. For the corresponding ground-based radar measurement sequence, It is an offline accumulated track state sequence used to extract global information. The duration predicted by the system. It is the number of samples of the tracked target status in the offline ground-based radar dataset; S1042, and the memory update process is represented as: in, For memory, a linear mapping function, and These correspond to the feature extraction module and the attention mechanism module, respectively. S1043, Combining measurements at all times Offline ground-based radar dataset Historical flight path of the target The combined posterior density of the ground-based radar and airborne millimeter-wave radar at the previous moment Under these conditions, the joint state probability density prediction of ground-based radar and airborne millimeter-wave radar is expressed as: in, The update expression for the joint state probability density of ground-based radar and airborne millimeter-wave radar is as follows: 。 4. The millimeter-wave radar Bayesian filtering method with neural network assistance under dual radar collaboration as described in claim 2, characterized in that, The Gaussian approximation strategy simplifies the Bayesian framework, constructs a recursive structure in the form of an extended Kalman filter, and obtains a closed-loop analytical state prediction and update expression, including: S201. Before implementing the Gaussian approximation strategy, the following assumptions are made: process noise and measurement noise follow a Gaussian distribution; the predicted probability density function of the measurement follows a Gaussian distribution; and the posterior probability density function of the state follows a Gaussian distribution. , , Follows a Gaussian distribution. Obtaining first and second moments respectively and The Gaussian distribution, and Obtaining first and second moments respectively and Gaussian distribution; S202. Based on the assumptions of step S201, the state prediction and covariance are expressed as follows: The predictions and covariance during the state update phase are expressed as follows: Among them, the predicted measurement value The measurement covariance is defined by the following formula: in, The process noise covariance matrix is... The measurement noise covariance matrix; S203. The calculation is performed using a first-order Taylor expansion approximation. Let... and They are respectively and The Jacobian matrix, by referencing the linearization of Kalman filtering, allows equations (15), (16), and (19)-(23) to be replaced with: 。 5. The millimeter-wave radar Bayesian filtering method with neural network assistance under dual radar collaboration as described in claim 1, characterized in that, The convolutional neural network feature extraction network includes: The information mean extraction module and the information covariance extraction module adopt the same structural module to estimate the mean vector and the information covariance matrix, respectively. The structural module of the convolutional neural network feature extraction network includes two convolutional layers, two average pooling layers, one linear layer and corresponding activation functions.

6. The millimeter-wave radar Bayesian filtering method with neural network assistance under dual radar collaboration as described in claim 5, characterized in that, The cross-attention memory encoding network includes: The memory mean encoding module and the memory covariance encoding module use the same structural modules to estimate the memory mean and memory covariance matrix, respectively. The structural modules of the cross-attention memory encoding network include an embedding layer, a mapping layer, an attention calculation layer, and a linear output layer.

7. The millimeter-wave radar Bayesian filtering method with neural network assistance under dual radar collaboration as described in claim 6, characterized in that, The interpretable gated Bayesian recurrent neural network includes: The memory update gate, state prediction gate, and state gate update gate all employ a structure consisting of two linear layers and a nonlinear activation function.

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