Multi-radar fusion method and system based on interactive model self-feedback learning

Abstract

The invention provides a multi-radar fusion method and system based on interactive model self-feedback learning, and the method mainly comprises the steps: constructing an interactive multi-model Kalman filter according to the flight characteristics of a guided projectile and radar performance constraints, and obtaining the fusion state estimation of each radar under different motion trajectories of the guided projectile; solving the strong correlation between the guided projectile and the multiple radars by adopting an approximate ideal solution sorting method based on the trajectory prediction information, obtaining the fusion weight of state estimation of each radar, and fusing the fusion state estimation of all radars; and feeding back a fusion result to the interactive multi-model Kalman filter, carrying out adaptive learning, and optimizing state estimation of the Kalman filter. The method is suitable for measuring the motion parameters of the guided projectile based on multiple radars in a high-dynamic environment.

Description

Technical Field

[0001] The present invention belongs to the field of guided projectile trajectory measurement in a high dynamic environment, and relates to a multi-radar fusion method and system based on interactive model self-feedback learning. Background Art

[0002] The core of guided artillery shells lies in the deep integration of efficient guidance technology with conventional ammunition. Accurately obtaining their high-precision flight parameters is a prerequisite and core cornerstone for achieving precision strikes. Unlike conventional carriers, guided artillery shells are in a highly dynamic environment, characterized by high muzzle velocity (≥1000m / s), high rotation (≥20r / s), and high overload (≥10,000g). Accurately measuring their flight parameters is extremely difficult, therefore, research into precise measurement technology for guided artillery shells is urgently needed.

[0003] The core of guided projectile measurement is to accurately and comprehensively acquire the projectile's motion parameters from launch, flight, to impact. Measurement methods are primarily categorized as onboard and external. Onboard measurement utilizes an inertial measurement unit (IMU) and a global navigation satellite system (GNSS) integrated within the projectile to acquire motion parameters during flight. IMUs offer advantages such as high autonomy, high measurement frequency, and compact design, enabling autonomous measurement. However, due to the dead reckoning principle, errors accumulate rapidly, making long-term, independent, high-precision measurement difficult. GNSS offers advantages such as all-weather operation, high measurement accuracy, and long-term stability, but satellite signals are susceptible to environmental and weather interference. IMUs and GNSS complement each other, and their combined measurement approach enables long-term, stable measurement. External measurement relies on ground-based measurement systems for non-contact observation of the projectile, primarily including Doppler radar, electro-optical tracking systems, and high-speed photography. Doppler radar utilizes the Doppler effect of electromagnetic waves to transmit continuous or pulsed waves and receive the echoes reflected from the projectile, measuring its radial velocity changes and inferring the velocity, trajectory, and some ballistic parameters of the guided projectile. Compared to photoelectric measurement, it offers superior measurement stability and high accuracy even in complex environments, making it a core method for measuring the external trajectory of guided projectiles.

[0004] With the advancement of radar technology, multi-radar systems have emerged to overcome the weak anti-interference performance of single radars in low signal-to-noise ratio environments. These systems can measure guided projectiles at different angles, offer strong tracking capabilities, and offer high measurement accuracy, making them an effective solution for high-precision trajectory measurement in complex environments. The multi-radar data fusion problem can be viewed as a time series data fusion problem. Traditional adaptive weighted fusion methods, which aim for minimum mean square error (MSE), assign weights to each sensor based on covariance. However, due to the lack of a mechanism to reject anomalous data, they are susceptible to noise interference. While the Kalman filter can leverage the statistical properties of the system model to obtain state estimates through recursive operations, it places strict demands on the system model, requiring the establishment of precise state equations, observation equations, and prior statistical properties of noise. This often leads to significant limitations in complex or uncertain environments. Summary of the Invention

[0005] The purpose of the present invention is to provide a multi-radar fusion method and system based on interactive model self-feedback learning, to improve the fusion accuracy based on multi-radar measurement in a high dynamic environment, and to achieve high-precision measurement of the flight state of guided projectiles.

[0006] The technical solutions for achieving the purpose of the present invention are:

[0007] A multi-radar fusion method based on interactive model self-feedback learning, comprising:

[0008] Based on the flight characteristics of the guided projectile and the radar performance constraints, an interactive multi-model Kalman filter is constructed to obtain the fusion state estimation of each radar under different motion trajectories of the guided projectile;

[0009] Based on the trajectory prediction information, the close-to-ideal solution sorting method is used to solve the strong correlation between the guided projectile and multiple radars, obtain the fusion weight of each radar state estimate, and then fuse the fused state estimates of all radars;

[0010] The fusion results are fed back to the interactive multi-model Kalman filter for adaptive learning and optimization of the Kalman filter's state estimation.

[0011] Furthermore, the state equation and observation equation of the interactive multi-model Kalman filter are:

[0012]

[0013] Where, represent the position, velocity, and acceleration of the projectile on the x-axis, y-axis, and z-axis at time k, respectively. Φ(k) is the state transfer matrix, ω(k) is the process noise, Z(k) = (x, y, z) is the observation vector of the radar at time k, H(k) is the observation matrix, and υ(k) is the observation noise.

[0014] Furthermore, the fusion state of each radar under different motion trajectories of the guided projectile is estimated as follows:

[0015]

[0016] Where, is the fusion state estimation value of the sth sensor under different motion trajectories of the guided projectile at time k, n is the number of motion trajectories of the guided projectile, j represents the jth motion trajectory, μ j,s (k) represents the fusion probability between models, represents the fused state estimate of model j.

[0017] Furthermore, based on the trajectory prediction information, the near-ideal solution sorting method is used to solve the strong correlation between the guided projectile and multiple radars, and the fusion weight of each radar state estimation is obtained, including:

[0018] Based on the radar observation in the Kalman filter, the residual vector is constructed, the residual matrix is ​​obtained, and the residual matrix is ​​dimensionless.

[0019] Determine the positive ideal solution r + and negative ideal solution r - , r represents the size of the standardized difference between the local estimated value and the global target value of different feature data of different radars;

[0020] Calculate the Euclidean distance of each radar to the positive and negative ideal solutions;

[0021] The relative closeness between each radar and the positive ideal solution is calculated, and the relative closeness is normalized to obtain the fusion weight of each radar state estimation.

[0022] Furthermore, the residual matrix is:

[0023]

[0024] in, is the residual vector of the sth sensor at time k, the Z s (k) is the observation vector of the sth sensor at time k, H s (k) is the measurement matrix of the sth sensor at time k.

[0025] Furthermore, the positive ideal solution r + and negative ideal solution r - They are:

[0026]

[0027] Where, m is the characteristic number, including the three-axis position, velocity, and acceleration of the projectile, and S is the total number of sensors.

[0028] Furthermore, the fusion weight of each radar state estimation is:

[0029]

[0030] Among them, C s is the relative closeness between the sth radar and the positive ideal solution, ω s is the fusion weight of the s-th radar state estimate.

[0031] Furthermore, the fusion state estimation of all radars is fused as follows:

[0032]

[0033] in, is the estimated value of the fusion state of the guided projectile under different motion trajectories by the sth sensor at time k.

[0034] Furthermore, the state estimation of the optimized Kalman filter is:

[0035]

[0036] Where, is the multi-radar fusion result at time k, is the filtering result of the sth radar at time k.

[0037] A multi-radar fusion system based on interactive model self-feedback learning, comprising:

[0038] The first fusion state estimation unit constructs an interactive multi-model Kalman filter based on the flight characteristics of the guided projectile and the radar performance constraints to obtain the fusion state estimation of each radar under different motion trajectories of the guided projectile;

[0039] The second fusion state estimation unit uses the approximate ideal solution sorting method based on the trajectory prediction information to solve the strong correlation between the guided projectile and multiple radars, obtains the fusion weight of each radar state estimate, and then fuses the fusion state estimate of each radar;

[0040] The self-feedback learning unit feeds the fusion results back to the interactive multi-model Kalman filter for adaptive learning and optimization of the state estimation of the Kalman filter.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows: on the one hand, the present invention realizes real-time data fusion through adaptive weights; on the other hand, the optimized fusion result at the current moment is injected into the prediction process at the next moment through self-feedback, forming a closed loop of "fusion, evaluation, feedback, and optimization". Through the closed-loop optimization mechanism, when the guided projectile maneuvers rapidly, the self-feedback mechanism can quickly adapt and dynamically feed back the fusion result at the current moment to the prediction process at the next moment, and use the global consistency of the fusion result to compensate for the local measurement deviation, thereby accelerating the filter convergence and suppressing the influence of abnormal noise; when some radars fail, the system automatically enhances the weight of the self-feedback item, and uses the high-confidence fusion result of the previous moment to correct the current estimate, maintain stable tracking and avoid filter divergence; based on the new information of trajectory prediction, the present invention adopts the approximate ideal solution sorting method to solve the strong correlation between the ballistic physical model and multiple radars, completes the fusion of multi-radar measurement data, has a more stable state estimation in complex scenarios, and significantly improves the accuracy and robustness of multi-radar fusion filtering. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 Flowchart of a multi-radar fusion method with self-feedback learning based on an interactive model.

[0043] Figure 2 It is a framework for interactive model self-feedback learning multi-radar fusion method.

[0044] Figure 3 Flowchart of multi-radar fusion self-feedback learning for interactive model.

[0045] Figure 4 Schematic diagram of multi-radar self-feedback learning. DETAILED DESCRIPTION

[0046] Next, the implementation of the present invention will be described in detail with reference to the accompanying drawings.

[0047] In order to overcome the shortcomings of the existing technology, the present invention proposes a multi-radar fusion method based on interactive model self-feedback learning, which mainly includes three parts: multi-physical state model interaction, data feature strong correlation analysis and trajectory prediction error fusion self-feedback learning. Figure 1-Figure 4 , specifically including:

[0048] Step 1: Construct an interactive multi-model Kalman filter to obtain the fusion state estimation of each radar under different motion trajectories of the guided projectile.

[0049] The multi-radar guided projectile motion parameter measurement combined with the filter tracking algorithm and the fusion algorithm to estimate the guided projectile motion state value and the current multi-radar fusion estimation value is an adaptive estimation process that is resistant to noise interference. Establishing an accurate guided projectile motion state model is the basis for the optimal estimation of the filtering algorithm. According to the high-dynamic motion constraints of the guided projectile, within the effective measurement range of the radar, the flight process of the guided projectile can be approximately regarded as a combination of uniform motion and uniformly accelerated motion. Therefore, the motion model of the projectile is established as uniform motion and uniformly accelerated motion. In order to avoid the difficulty of a single, fixed model in describing the motion of the projectile, this application adopts an interactive multiple model Kalman filter (IMMKF) with adaptive switching of multiple motion modes to adapt to the different motion states of the guided projectile. Based on the three-dimensional rectangular coordinate system, the state equation and the observation equation are established as:

[0050]

[0051] Where, where Φ(k) represents the position, velocity, and acceleration of the projectile on the x-, y-, and z-axes, respectively. Φ(k) is the state transition matrix, ω(k) is the process noise, Z(k) = (x, y, z) is the radar observation vector at time k, H(k) is the observation matrix, and υ(k) is the observation noise.

[0052] IMMKF includes four parts: input interaction, filter update, model probability update, and output interaction. IMMKF is a conventional technology in this field, and the process will not be described in detail here.

[0053] The model transition probability M represents the possibility of transition between different motion models and is a Markov matrix, as shown in formula (2), p ij represents the model state transition probability from the i-th model to the j-th model.

[0054]

[0055] If the number of models is 2, M can be initialized as:

[0056] according to Figure 1 , using the probability of the model, the filter estimation results of different radars are fused between models to obtain the fused state estimation between different models and covariance estimate p s (k|k).

[0057]

[0058] Where j = 1, 2...n represents the number of ballistic physical models, s represents the sth radar, μj,s (k) represents the fusion probability between models, represents the fused state estimate of model j.

[0059] If the number of models is 2, μ j,s The initialization value of (k) can be [0.5 0.5].

[0060] Step 2: Based on the trajectory prediction information, the approximate ideal solution sorting method is used to solve the strong correlation between the trajectory physical model and multiple radars, and complete the multi-radar measurement data fusion.

[0061] Since multiple radars are used to measure guided projectiles, n groups of multi-model interactive fusion results will be obtained. According to formula (5), the approach to ideal solution sorting method is used based on the trajectory prediction information to solve the strong correlation between the trajectory physical model and multiple radars.

[0062] Using radar observation Z s (k) and H(k)X j,s (k|k) is used to construct the residual vector and obtain the residual matrix of all radars And perform dimensionless processing.

[0063]

[0064] Determine the positive ideal solution r + and negative ideal solution r - , r represents the size of the standardized difference between the local estimated value of different feature data of different radars and the global target value. The positive and negative solutions can be expressed as:

[0065]

[0066] Where, m is the number of data features, including the three-axis position, velocity, and acceleration of the projectile, s = 1, 2...S, and S is the total number of sensors.

[0067] Calculate the Euclidean distance of each radar to the positive and negative ideal solutions, the optimal Euclidean distance Worst Euclidean distance

[0068]

[0069] Where i=1,2,...m represents the number of data features.

[0070] Formula (11) is used to calculate the relative closeness of each radar to the positive ideal solution, C s The larger the value of , the greater the weight value when participating in fusion. Finally, use formula (12) to calculate C s Perform standardization to obtain the fusion weight ω of each radars .

[0071]

[0072] According to formula (13), multi-radar measurement data fusion is completed.

[0073]

[0074] Step 3: Use the fusion results for self-feedback learning to update the multi-radar filter states. This fusion method is suitable for multi-radar guided projectile motion parameter measurement in highly dynamic environments, improving projectile measurement accuracy.

[0075] Traditional multi-sensor fusion adopts open-loop mode, which only performs weighted fusion on the independent estimation of each radar. In the actual fusion process, the fusion results of multi-radar measurement data are The measurement accuracy will be higher than that of a single radar. Therefore, this application introduces a self-feedback learning term into the interactive multi-model filter fusion algorithm, and different radars have different fusion results. Perform adaptive learning and provide feedback to the state at the next moment to improve filtering accuracy and system robustness.

[0076]

[0077] Where, is the multi-radar fusion result at time k, is the filtering result of sensor s at time k, C s It is the radar strong correlation analysis ratio.

[0078] This embodiment further provides a multi-radar fusion system based on interactive model self-feedback learning, including:

[0079] The first fusion state estimation unit constructs an interactive multi-model Kalman filter based on the flight characteristics of the guided projectile and the radar performance constraints to obtain the fusion state estimation of each radar under different motion trajectories of the guided projectile;

[0080] The second fusion state estimation unit uses the approximate ideal solution sorting method based on the trajectory prediction information to solve the strong correlation between the guided projectile and multiple radars, obtains the fusion weight of each radar state estimate, and then fuses the fusion state estimate of each radar;

[0081] The self-feedback learning unit feeds the fusion results back to the interactive multi-model Kalman filter for adaptive learning and optimization of the state estimation of the Kalman filter.

[0082] This method uses self-feedback learning from the multi-radar fusion results of an interactive model to update the multi-radar filter states, forming a closed loop of "fusion, evaluation (strong correlation analysis), feedback, and optimization." This self-feedback mechanism enables rapid self-adaptation, dynamically feeding the current fusion result back into the prediction process for the next moment. The global consistency of the fusion result compensates for local measurement deviations, enabling multi-radar guided projectile motion parameter measurement. This method is suitable for multi-radar guided projectile motion parameter measurement in highly dynamic environments.

Claims

1. A multi-radar fusion method based on interactive model self-feedback learning, characterized in that: include: Based on the flight characteristics of the guided projectile and the radar performance constraints, an interactive multi-model Kalman filter is constructed to obtain the fusion state estimation of each radar under different motion trajectories of the guided projectile; Based on the trajectory prediction information, the close-to-ideal solution sorting method is used to solve the strong correlation between the guided projectile and multiple radars, obtain the fusion weight of each radar state estimate, and then fuse the fused state estimates of all radars; The fusion results are fed back to the interactive multi-model Kalman filter for adaptive learning and optimization of the Kalman filter's state estimation.

2. The multi-radar fusion method based on interactive model self-feedback learning according to claim 1 is characterized in that: The state equation and observation equation of the interactive multi-model Kalman filter are: Where, represent the position, velocity, and acceleration of the projectile on the x-axis, y-axis, and z-axis at time k, respectively. Φ(k) is the state transfer matrix, ω(k) is the process noise, Z(k) = (x, y, z) is the observation vector of the radar at time k, H(k) is the observation matrix, and υ(k) is the observation noise.

3. The multi-radar fusion method based on interactive model self-feedback learning according to claim 1, characterized in that: The fusion state of each radar under different motion trajectories of the guided projectile is estimated as follows: Where, is the fusion state estimation value of the sth sensor under different motion trajectories of the guided projectile at time k, n is the number of motion trajectories of the guided projectile, j represents the jth motion trajectory, μ j,s (k) represents the fusion probability between models, represents the fused state estimate of model j.

4. The multi-radar fusion method based on interactive model self-feedback learning according to claim 1, characterized in that: Based on the trajectory prediction information, the approach to ideal solution sorting method is used to solve the strong correlation between the guided projectile and multiple radars, and the fusion weight of each radar state estimation is obtained. Specifically, the following steps are performed: Based on the radar observation in the Kalman filter, the residual vector is constructed, the residual matrix is ​​obtained, and the residual matrix is ​​dimensionless. Determine the positive ideal solution r + and negative ideal solution r - , r represents the size of the standardized difference between the local estimated value and the global target value of different feature data of different radars; Calculate the Euclidean distance of each radar to the positive and negative ideal solutions; The relative closeness between each radar and the positive ideal solution is calculated, and the relative closeness is normalized to obtain the fusion weight of each radar state estimation.

5. The multi-radar fusion method based on interactive model self-feedback learning according to claim 4 or claim 1, characterized in that: The residual matrix is: in, is the residual vector of the sth sensor at time k, the Z s (k) is the observation vector of the sth sensor at time k, H s (k) is the measurement matrix of the sth sensor at time k.

6. The multi-radar fusion method based on interactive model self-feedback learning according to claim 5 or claim 1, characterized in that: Positive ideal solution r + and negative ideal solution r - They are: Where, i=1,2...m, where m is the characteristic number, including the three-axis position, velocity, and acceleration of the projectile, and S is the total number of sensors.

7. The multi-radar fusion method based on interactive model self-feedback learning according to claim 6 or claim 1, characterized in that: The fusion weight of each radar state estimation is: Among them, C s is the relative closeness between the sth radar and the positive ideal solution, ω s is the fusion weight of the s-th radar state estimate.

8. The multi-radar fusion method based on interactive model self-feedback learning according to claim 7 or claim 1, characterized in that: The fusion state of all radars is estimated and fused as follows: in, is the estimated value of the fusion state of the guided projectile under different motion trajectories by the sth sensor at time k.

9. The multi-radar fusion method based on interactive model self-feedback learning according to claim 8 or claim 1, characterized in that: The state estimate of the optimized Kalman filter is: Where, is the multi-radar fusion result at time k, is the filtering result of the sth radar at time k.

10. A multi-radar fusion system based on interactive model self-feedback learning that implements the method according to any one of claims 1 to 9, characterized in that: include: The first fusion state estimation unit constructs an interactive multi-model Kalman filter based on the flight characteristics of the guided projectile and the radar performance constraints to obtain the fusion state estimation of each radar under different motion trajectories of the guided projectile; The second fusion state estimation unit uses the approximate ideal solution sorting method based on the trajectory prediction information to solve the strong correlation between the guided projectile and multiple radars, obtains the fusion weight of each radar state estimate, and then fuses the fusion state estimate of each radar; The self-feedback learning unit feeds the fusion results back to the interactive multi-model Kalman filter for adaptive learning and optimization of the state estimation of the Kalman filter.

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