Track Disconnect Repair Method Based on Adaptive Kalman Prediction

Abstract

This invention discloses a track break repair method based on adaptive Kalman prediction. The implementation steps are as follows: preprocessing the ship track dataset to establish a CV model of the target ship's uniform linear motion; tracking the target ship's points and updating the covariance matrix; using the tracking covariance matrix to update the target state equation, thus predicting the target point; employing a nearest neighbor association (NN) algorithm, through a rectangular gate, detecting new points appearing after the predicted points, and associating these new points with track batch numbers to achieve adaptive track prediction. This invention predicts ship points in real time at track breaks using an adaptive Kalman prediction algorithm, repairing missing points in existing track technologies, reducing algorithm complexity, improving track continuity, enhancing the quality and speed of predicted points, and expanding its practicality and applicability.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and more specifically relates to a track disruption repair method based on adaptive Kalman prediction in the field of target tracking technology. This invention can be used for real-time track disruption repair of target vessels monitored by shore-based maritime radar. Background Art

[0002] Currently, ship tracks are primarily monitored by sensors such as radar and AIS. Different monitoring methods differ in their monitoring range and update frequency. For example, satellite monitoring has a wide range but lacks real-time accuracy, while radar can continuously monitor targets but has a limited range. In maritime radar surveillance scenarios, terrain, clutter, and interference can cause target ships to lose their echoes when passing under bridges or in offshore wind farm areas, resulting in track breaks. In such cases, numerous broken tracks create data redundancy in the tracking system, reducing track continuity. Track management and maintenance consume significant computational resources, impacting tracking performance. Furthermore, tracks originating from the same target being identified as different targets can lead to incorrect estimates of target status and quantity, negatively affecting situational awareness and assessment, resource coordination and allocation, and information exchange and fusion within the tracking system.

[0003] Harbin Institute of Technology disclosed a method for tracking maneuvering targets on a non-stationary platform in its patent application "A method for tracking maneuvering targets on a non-stationary platform" (application number CN 202311521216.8, publication number CN 117233745 A). The implementation steps of this method are as follows: (1) collecting state measurements of the maneuvering target at different time points; (2) performing track filtering based on target features, scoring and pruning the track hypothesis tree according to the target features, and using an interactive multi-model to register the complex motion state of the target in real time; (3) using a point-filling method to maintain the track in order to protect long tracks. In order to address the problem of track loss, a track segment association method is used to train and learn the data before and after the track interruption, and predict the interrupted track based on the trained model to achieve track continuation. However, this method still has the following three shortcomings: First, training and learning from data before and after the track interruption will lead to inaccurate actual predictions; second, the algorithm is only applicable to cases where the track is interrupted once, and is not applicable to cases where the track is interrupted multiple times; third, the algorithm used in this method repairs between new and old tracks, and cannot repair the interrupted track in real time after the track is interrupted.

[0004] The 20th Research Institute of China Electronics Technology Group Corporation disclosed a multi-radar measurement lag disorder filtering method in its patent application document "A Multi-Radar Measurement Lag Disorder Filtering Method" (application number CN 202210559004.8, publication number CN 114895299 A). The implementation steps of the method are as follows: (1) The real-time processing center in multi-radar fusion receives the measurement data of the aggregated points. If there is no measurement data at the current time, it is considered that the measurement data is missing, and a point filling operation is performed, that is, prediction is made according to the track information to obtain the predicted measurement data, and the predicted measurement data is considered as the measurement data at this time; if there is measurement data at the current time, the timestamp of the measurement data is compared with the time value of the current time. If they are the same, the measurement data is processed by data association to obtain the measurement data after the track association of the same target; if there is measurement data at the current time, the timestamp of the measurement data is compared with the time value of the current time. If they are the same, the measurement data is processed by data association to obtain the measurement data after the track association of the same target; if there is measurement data at the current time, the measurement data is processed by data association to obtain the measurement data after the track association of the same target. If the timestamp of the measurement data is less than the current time, it is considered that there is a delay in the measurement data, that is, there is a problem of measurement lag and disorder. The delayed measurement data is also processed by data association to obtain the delayed measurement data after the same target track is associated. The delayed measurement data replaces the original measurement data that was supplemented at this time. (2) The target state at the current time is re-filtered. The specific steps of the filtering process are as follows: (2a) Initial filtering: that is, least squares filtering, using the current measurement and the measurement at the previous time for coarse filtering; (2b) Using the Kalman filtering method for fine filtering. (2c) Second filtering update stage: finally estimate the covariance matrix of the state, the filtered value at time t and the overall covariance, and then process the next time, iteratively update, until the tracking is completed. Since the least squares filtering method can use the measurement at the current time and the measurement at the previous time for fitting filtering, the delayed measurement can directly replace the supplemented measurement data in the filtering process, which can effectively solve the problem of delayed and disordered measurement, make full use of the effective measurement data that arrives late, improve the filtering accuracy and make the track smoother. However, this method still has the following three shortcomings: First, prediction based on track information may result in inaccurate and unreliable predictions; second, timestamps are generally in milliseconds, and using timestamp differences as the criterion for patching is too stringent; third, the algorithm used in this method is too cumbersome, and frequent single-step predictions lead to low program efficiency, making it difficult to guarantee real-time performance in situations where track interruptions are long and there are many track points that need to be patched. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the existing technology by proposing a track break repair method based on adaptive Kalman prediction, which aims to solve the problems of difficulty in real-time prediction of ship tracks and inaccurate prediction.

[0006] The technical approach to achieving the objective of this invention is as follows: First, if three consecutive radar target states (not equal to 1) appear on a certain flight path (radar target state 1 indicates tracking, 2 indicates extrapolation, and 3 indicates loss), prediction begins. The number of prediction steps depends on the next newly appearing radar target state (not equal to 1) or a prediction threshold. During prediction, the first 10 radar target state (not equal to 1) points are selected, a CV model is established, and updated using a Kalman filter algorithm to calculate the covariance matrix. The covariance matrix is ​​then used to update the target state equation to achieve prediction. For each prediction step, the algorithm calculates a point and establishes a rectangular gate 300 meters away from that point. If a newly appearing point is detected in the rectangular gate (this point must satisfy the radar target state of 1), prediction stops, and a nearest neighbor (NN) association is performed with the newly appearing point. The core idea of ​​Neural Networks (NNs) is: if only one measurement falls within the relevant gate, that measurement can be directly used for track updates; however, if more than one measurement falls within the target's relevant gate, the candidate measurement with the smallest statistical distance should be used for track updates. When terminating prediction, one scenario is that a rectangular gate detects newly appearing points. Another scenario is that no new points are detected, in which case a prediction threshold is set, and the prediction stops when the threshold is reached. Long Short-Term Memory (LSTM) networks exhibit high accuracy in single-dimensional time-series predictions (such as stock price predictions) and also demonstrate strong predictive capabilities in multi-input, multi-output scenarios. For example, in ship track prediction, many researchers use the ship's longitude, latitude, speed, and heading as inputs to an LSTM network model. After passing through LSTM network layers and fully connected layers, the output is the ship's longitude and latitude information. Results show that LSTM can effectively learn and identify the feature values ​​of ship trajectories, such as longitude, latitude, speed, and heading, and then accurately predict the ship's future position. However, this only learns the features of a single, complete ship track, making predictions at the end of the track. If the track breaks off somewhere in the middle, the LSTM will not be able to accurately predict the track at the break point, leading to model divergence. Furthermore, the LSTM network model is unsuitable for scenarios with multiple different ship tracks, i.e., multi-task, multi-input, multi-output scenarios. First, accurate prediction of a single track can be achieved by training the model on that track alone. However, if multiple tracks exist, distinguishing between them becomes impossible, causing the LSTM network model to fail to differentiate them, resulting in model divergence and inaccurate predictions. While using track batch numbers as features allows the network to differentiate between tracks, these batch numbers are only unique to a specific ship, resulting in a lack of universality.

[0007] The steps of this invention include the following:

[0008] Step 1, enter the flight track data;

[0009] Step 2: Read the track points of each ship at each time point that have not yet been read;

[0010] Step 3: Determine whether there are 3 consecutive track points with radar tracking target status not equal to 1 at the time of reading. If so, it is considered that there is an interruption in the track and proceed to step 4. Otherwise, proceed to step 2.

[0011] Step 4: Using the CV model, model the target ship with interrupted track to obtain the target state equation and the observation equation of the radar system.

[0012] Step 5: Starting from the point where the track with the interruption phenomenon is interrupted, backtrack 10 radar target status points with a state of 1 to perform Kalman tracking and update the covariance matrix.

[0013] Step 6: Update the target state equation using the updated covariance matrix to achieve single-step point prediction;

[0014] Step 7: Determine if the number of steps for single-step point prediction is less than or equal to 120 steps. If so, proceed to step 8.

[0015] Otherwise, delete the predicted points and proceed to step 2;

[0016] Step 8: Detect whether the newly appearing point at the single-step predicted point falls within the rectangular gate. If so, proceed to step 9; otherwise, proceed to step 6.

[0017] Step 9: Associate the predicted points with the newly emerged points using nearest neighbor (NN) data, update the track batch number, and perform track repair while performing adaptive track prediction.

[0018] Compared with the prior art, the present invention has the following advantages:

[0019] First, this invention establishes a target motion model by tracing back the points at the break point, overcoming the limitation of the traditional Track Segment Association (TSA) post-processing algorithm, which is only applicable to scenarios where the target breaks once, thus improving the practicality of the algorithm.

[0020] Secondly, this invention, by modeling each track individually, is applicable to multiple tracks with interruptions. During target tracking, the covariance rectangle is updated; in target prediction, the covariance matrix updated in the final step is used to update the target state equation, achieving single-step prediction of ship tracks with better track quality than LSTM. This overcomes the bottleneck of real-time ship track prediction caused by the existing LSTM algorithm, avoids high hardware requirements, and results in low computational complexity, thus effectively improving practicality and applicability.

[0021] Third, because the present invention uses an adaptive Kalman prediction algorithm to predict ship points in real time at the point where the track is broken, it repairs the missing points in the existing track and associates the predicted points with the newly appearing points with the nearest neighbor, thus improving the continuity of the track. Attached Figure Description

[0022] Figure 1 This is a flowchart of an embodiment of the present invention;

[0023] Figure 2 This is a schematic diagram of the interrupted flight paths 1 and 2 according to an embodiment of the present invention;

[0024] Figure 3 The image shows the repair results of trajectory 1 and trajectory 2 predicted by adaptive Kalman in the simulation experiment of this invention.

[0025] Figure 4 This is a flight path diagram showing no interruptions in the simulation experiment of this invention;

[0026] Figure 5 This is a training loss curve of the existing LSTM trajectory prediction method in the simulation experiment of this invention;

[0027] Figure 6 This is a prediction image of the existing LSTM track prediction method at the track break point in the simulation experiment of this invention;

[0028] Figure 7 This is a test image of the existing LSTM trajectory prediction method in the simulation experiment of this invention on the entire dataset of interrupted trajectories. Detailed Implementation

[0029] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0030] Reference Figure 1 The implementation steps of the embodiments of the present invention will be further described below.

[0031] Step 1: Enter flight track data.

[0032] The data of each ship's track received by the radar display and control equipment at every moment is entered into a hash table.

[0033] The track data includes track batch number, tracking sequence number, timestamp, longitude, latitude, speed, heading, angle, and radar tracking target status.

[0034] In this embodiment of the invention, track 1 and track 2 are used as measured track data.

[0035] Reference Figure 2 The following is a further description of the schematic diagrams of the interrupted flight paths 1 and 2 of this invention.

[0036] Figure 2 The horizontal axis represents longitude, and the vertical axis represents latitude. Red dots represent ship markers, and the background image uses the Satellite plot included in MATLAB 2022b. Figure 2 (a) is a schematic diagram of the interrupted track 1. Figure 2 (b) is a schematic diagram of the interrupted track 2. Track 1 track number = 200108921, tracking number = 2, timestamp = 193190464, longitude = 120.87564087°, latitude = 27.19651604°, speed = 0.583153 knots, heading = 302.637°, angle = 211.31°, radar target tracking status = 1. Track 2 track number = 200125341, tracking number = 9, timestamp = 335852736, longitude = 120.78741455°, latitude = 27.44536209°, speed = 11.0799 knots, heading = 147.67°, angle = 264.09°, radar target tracking status = 1.

[0037] Step 2: Read the track points of each ship at each moment that have not yet been read.

[0038] Step 3: Determine whether there are 3 consecutive track points with radar tracking target status not equal to 1 at the time of reading. If so, it is considered that there is an interruption in the track and proceed to step 4. Otherwise, proceed to step 2.

[0039] Step 4: Using the CV model, model the target ship with interrupted track to obtain the target state equation and the observation equation of the radar system.

[0040] The CV model is as follows:

[0041] X(k)=[x(k)v x (k)y(k)v y (k)] T

[0042]

[0043] Where X(k) represents the radar tracking target state vector at the k-th radar sampling time, x(k), v x (k),y(k),v y (k) represents the radar's k-th sampling time, the radar tracking target's x-axis position and velocity, and y-axis position and velocity, respectively. The superscript T indicates the transpose operation, and T represents the radar's sampling time. x(k-1), v x (k-1),y(k-1),v y (k-1) represents the position and velocity of the target along the x-axis and y-axis at the (k-1)th radar sampling time, respectively. 2×1 (k) represents the zero mean and variance at the k-th radar sampling time. White noise, diag(·) denotes a diagonal matrix, J = [0.5, 1, 0.5, 1].

[0044] The steps for modeling target ships with interrupted flight paths are as follows:

[0045] The first step is to construct the target state vector for radar observation according to the following formula:

[0046] y(k)=s(k)+v noise (k)

[0047] Where y(k) represents the target state vector observed by the radar at the k-th radar sampling time, s(k) represents the true state vector of the radar-tracked target at the k-th radar sampling time, and v noise (k) represents the radar positioning error at the k-th radar sampling time, which has zero mean and variance. White noise, sqrtm(·) represents the matrix square root operation.

[0048] The second step is to calculate the true state vector of the radar-tracked target and the velocity of the radar-tracked target according to the following formula:

[0049]

[0050] v(k+1)=v(k)+T0a(k)a(k)=u(k)+w(k)

[0051] Where s(k+1) represents the true state vector of the radar-tracked target at the (k+1)th radar sampling time, v(k) represents the velocity of the radar-tracked target at the kth radar sampling time, T0 = 5s, a(k) represents the acceleration of the radar-tracked target at the kth radar sampling time, v(k+1) represents the velocity of the radar-tracked target at the (k+1)th radar sampling time, u(k) represents the control signal of the ship's propulsion system, which is the known output maneuver signal, and w(k) represents the random acceleration caused by sea wind and waves, which has zero mean and variance. independence from v noise (k) white noise,

[0052] The third step involves the radar tracking target state vector as follows:

[0053] x(k+1)=Φx(k)+Bu(k)+Γw(k)

[0054] y(k)=Hx(k)+v noise (k)

[0055] Where x(k+1) represents the radar tracking target state vector at the (k+1)th radar sampling time, and Φ represents the state transition matrix. x(k) represents the radar tracking target state vector at the k-th radar sampling time, and B and Γ represent the noise driving matrices. H represents the observation matrix, H =

[10] .

[0056] Step 5: Starting from the point where the track with the interruption phenomenon is interrupted, backtrack 10 radar target status points with a state of 1 to perform Kalman tracking and update the covariance matrix.

[0057] The steps of the Kalman tracing are as follows:

[0058] The first step is to initialize the initial conditions of the given filter: P0, Q0, R0, where... Let P0 represent the initial target state estimate, Q0 represent the initial covariance matrix, and R0 represent the initial target process noise matrix.

[0059] The second step is to predict the state estimate and the estimation error covariance according to the following formula:

[0060]

[0061] in, Indicates the estimated value The prediction F represents the radar target state estimate at the (k-1)th radar sampling time. k-1P represents the radar target tracking state transition matrix at the (k-1)th radar sampling time. kk-1 P represents k-1 The predicted value, P k-1 Let Q represent the covariance matrix at the (k-1)th radar sampling time. k-1 This represents the process noise variance matrix at the (k-1)th radar sampling time.

[0062] The third step is to calculate the measurement prediction, the information covariance matrix, and the Kalman gain according to the following formula:

[0063]

[0064] in, Indicates the estimated value The prediction H represents the estimated observed state of the target. k S represents the observation matrix at the k-th radar sampling time. k H represents the information covariance matrix at the k-th radar sampling time. k-1 R represents the observation matrix at the (k-1)th radar sampling time. k Let K represent the observation noise matrix at the k-th radar sampling time. k This represents the Kalman gain at the k-th radar sampling time.

[0065] Fourth step, calculate the state estimate and the covariance of the estimation error according to the following formula:

[0066]

[0067] P k =P kk-1 -K k H k P kk-1 .

[0068] in, Let z represent the radar target state estimate at the k-th radar sampling time. k This represents the observed state value of the target.

[0069] Step 6: Update the target state equation using the updated covariance matrix to achieve single-step point prediction.

[0070] The single-step point prediction is obtained by the following formula:

[0071] x k+1 =F k x k +P

[0072] Where, x k+1 F represents the radar tracking target state value at the (k+1)th radar sampling time.k Let P represent the radar tracking target state transition matrix at the k-th radar sampling time, and let P represent the covariance matrix updated last during the tracking filtering process.

[0073] Step 7: Determine if the number of prediction steps for a single point is less than or equal to 120. If yes, proceed to step 8; otherwise, delete the predicted points and proceed to step 2.

[0074] Step 8: Detect whether the newly appearing point at the single-step predicted point falls within the rectangular wave gate. If so, proceed to step 9; otherwise, proceed to step 6.

[0075] The rectangular wave gate is obtained by the following formula:

[0076]

[0077] Among them, v k,i Let z represent the i-th component of the residual, |·| denotes the absolute value operation, and z k,i Let z represent the i-th component being measured. kk-1,i K represents the i-th component of the measurement prediction value. G K represents the gate constant. G ≥3.5, i=1,2,...,n z n z Indicates the number of measurements.

[0078] Step 9: Associate the predicted points with the newly emerged points using nearest neighbor (NN) data, update the track batch number, and perform track repair while performing adaptive track prediction.

[0079] The Nearest Neighbor NN data association refers to using the Nearest Neighbor NN algorithm, based on the discrimination criteria, to select the measurement that falls within the gate and is statistically closest to the target prediction position as the candidate measurement.

[0080] The discrimination criterion refers to any one of the following conditions:

[0081] Condition 1: If there is only one measurement in the gate of a target, then the target is associated with this measurement.

[0082] Condition 2: If a measurement has fallen into the gate of a target, then the measurement is associated with the target.

[0083] Condition 3: When a target's gate contains multiple measurements, the target is associated with the most recent measurement.

[0084] Condition 4: When a measurement falls within the gates of multiple targets, the measurement is associated with the nearest target.

[0085] The technical effects of the present invention will be further described below in conjunction with simulation experiments.

[0086] 1. Simulation experimental conditions:

[0087] The hardware platform for the simulation experiment of this invention is: an Intel(R) Core(TM) i7-12800HX CPU with a main frequency of 2.00GHz, 32GB of memory, and an RTX3070 Ti graphics card.

[0088] The software platform for the simulation experiments of this invention is: Windows 11 operating system, MATLAB 2022b and PyCharm 2024.

[0089] The input data used in the simulation experiment of this invention is Figure 2 The two flight paths.

[0090] 2. Simulation content and result analysis:

[0091] The simulation experiment of this invention uses both the present invention and existing technology (Long Short-Term Memory gate network LSTM) to repair the input track data, and the results are as follows. Figure 3 As shown.

[0092] In simulation experiments, one existing technology used is:

[0093] The existing Long Short-Term Memory (LSTM) gate network method refers to the LSTM ship trajectory prediction method proposed by Li Yong et al. in their paper "LSTM Ship Track Prediction Model" (Computer Technology and Development vol.39, no.9, pp.149–154, 2021), which is abbreviated as LSTM trajectory prediction method.

[0094] The following is combined Figure 3 The simulation diagrams further illustrate the effects of the present invention.

[0095] Figure 3 The image shows the repair results of track 1 and track 2 based on the adaptive Kalman prediction of this invention. Figure 3 (a) shows the repair result of track 1. Figure 3 (b) is a diagram showing the repair results of track 2. Figure 3 The horizontal axis represents longitude, and the vertical axis represents latitude. Figure 3 The red dots represent radar target status 1, which is the true value; the black dots represent radar target status 2, which is the abnormal value; the orange dots represent radar target status 3, which indicates the termination of the track; and the green dots represent repaired tracks.

[0096] Figure 3 There are enlarged views of two locations, A and B. Figure 3(a) At point A on track 1, the algorithm adaptively predicts the target track and successfully detects the newly appearing point. Figure 3 (a) At point B of track 1, the track is interrupted at a long interval, and there is only one radar target with a status of 1 near the end of point B, which is challenging. However, the algorithm can accurately detect this target, further verifying the accuracy of the algorithm prediction in this invention. Figure 3 (b) At point A of track 2, there is also a long track interruption interval. The algorithm predicts that it will not exceed 10 minutes and there will be approximately 116 points. Figure 3 (b) At point B of track 2, due to the short interval between interruptions, the algorithm can adaptively predict and correctly correlate with subsequent tracks. Figure 3 It can be seen that the Kalman prediction algorithm of the present invention can effectively repair broken tracks, proving the effectiveness of the algorithm of the present invention.

[0097] Figure 4 This is a flight path diagram showing that there is no interruption in the present invention. Figure 4 The horizontal axis represents longitude, and the vertical axis represents latitude. Figure 4 The red dots represent ship markers, which serve as the raw data. These ship markers are generated by... Figure 3 (b) Track 2 is a complete track generated by manual completion at points A and B, without any track interruptions. Furthermore, existing LSTM track prediction methods can only learn the features of complete tracks, not those with interrupted tracks. The first 80% of the data was used to form the training set, and the last 20% was used to form the test set. The data in both sets were normalized to ensure they were within the same range.

[0098] A multiple-input multiple-output (MIMO) LSTM model is built using the Keras library. This model consists of one input layer, one LSTM layer, two fully connected layers, and two output layers. The output layers predict lat and lon, respectively. The model is compiled, specifying the mean squared error (MSE) as the loss function and Adam as the optimizer. The structure and parameters of the LSTM network are shown in Table 1, with a total of 80034 trainable parameters.

[0099] Table 1 LSTM Network Layer Structure and Parameters

[0100] Layer Output Shape Param InputLayer (None, 10, 7) 0 LSTM (None, 128) 69632 Dense (None, 64) 8256 Dense (None, 32) 2080 lat(Dense) (None, 1) 33 lon(Dense) (None, 1) 33

[0101] The model is trained using the `fit()` method, with training and test sets passed in, and epochs = 100 and batch_size = 512. In the simulation experiment of this invention, approximately 10 ship track features can be selected as input, i.e., the input layer step size is 10 steps, predicting one from 10 historical points. Different step sizes will have varying degrees of impact on the network's accuracy, the number of hidden layer neurons, and the experimental precision.

[0102] Figure 5 The training loss curve for the existing LSTM trajectory prediction method is shown. Figure 5 The horizontal axis represents the number of training epochs, and the vertical axis represents the loss value. The blue line represents the loss on the training set, and the green line represents the loss on the test set. Save the model after training.

[0103] Load the trained model, define a single-step prediction function, iterate the model prediction results, and examine the performance of the LSTM algorithm in predicting ship tracks.

[0104] Figure 6 This is a prediction graph of the existing LSTM track prediction method at the point of track break. Figure 6 The horizontal axis represents longitude, and the vertical axis represents latitude. Blue dots represent actual points, and red dots represent predicted points. At the point where the track breaks, LSTM prediction can predict points relatively well, but the distance between the predicted end and the adjacent actual points is relatively large. Figure 6 It simply shows the best result out of many training and prediction experiments.

[0105] Figure 7 This is a test graph for the existing LSTM trajectory prediction method on the entire dataset with interrupted trajectories. Figure 7 The horizontal axis represents longitude, and the vertical axis represents latitude. In most cases, the predicted points by the LSTM network will have a large interval. Figure 7 The model is trained using the complete dataset of the flight path, eliminating any gaps in the flight path. After training, the model is loaded into the dataset containing interrupted flight paths. Figure 7 In the diagram, blue represents the actual points, and tan represents the predicted points. At the point where the track breaks, the predicted tan points are spaced further apart. This phenomenon is caused by the model not having sufficiently learned the features such as ship speed.

[0106] against Figure 3(a) For track 1, similarly, the interrupted points need to be manually filled in to create a dataset, which is then input into the LSTM network for subsequent training and prediction. This makes the training process very cumbersome and is not conducive to engineering implementation. On the other hand, the LSTM prediction network model has more than 80,000 parameters, further increasing the model training time and requiring certain computer equipment, which is not conducive to the real-time performance of track prediction. Compared with the algorithm proposed in this invention, the algorithm proposed in this invention can predict the points at the break points better, and the interval of the predicted points is uniform, and the speed is faster than the LSTM network.

Claims

1. A track break repair method based on adaptive Kalman prediction, characterized in that, A model of the target ship's uniform linear motion is established. The updated covariance matrix is ​​used to update the target state equation to predict the target point trajectory. The nearest neighbor association (NN) algorithm is used to achieve adaptive trajectory prediction. The steps of this repair method are as follows: Step 1, enter the flight track data; Step 2: Read the track points of each ship at each time point that have not yet been read; Step 3: Determine whether there are 3 consecutive track points with radar tracking target status not equal to 1 at the time of reading. If so, it is considered that there is an interruption in the track and proceed to step 4; otherwise, proceed to step 2. Step 4: Using the CV model, model the target ship with interrupted track to obtain the target state equation and the observation equation of the radar system. Step 5: Starting from the point where the track with the interruption phenomenon is interrupted, backtrack 10 radar target status points with a state of 1 to perform Kalman tracking and update the covariance matrix. Step 6: Update the target state equation using the updated covariance matrix to achieve single-step point prediction; Step 7: Determine if the number of prediction steps for a single point is less than or equal to 120. If yes, proceed to step 8; otherwise, delete the predicted points and proceed to step 2. Step 8: Detect whether the newly appearing point at the single-step predicted point falls within the rectangular gate. If so, proceed to step 9; otherwise, proceed to step 6. Step 9: Associate the predicted points with the newly emerged points using nearest neighbor (NN) data, update the track batch number, and perform track repair while performing adaptive track prediction.

2. The track break repair method based on adaptive Kalman prediction according to claim 1, characterized in that, The data entry mentioned in step 1 refers to entering the point data of each ship track received by the radar display and control equipment at each moment into a hash table; the point data includes track batch number, tracking sequence number, timestamp, longitude, latitude, speed, heading, angle, and radar tracking target status.

3. The track break repair method based on adaptive Kalman prediction according to claim 1, characterized in that, The CV model described in step 4 is as follows: X(k)=[x(k) v x (k) y(k) v y (k)] T Where X(k) represents the radar tracking target state vector at the k-th radar sampling time, x(k), v x (k),y(k),v y (k) represents the radar's k-th sampling time, the radar tracking target's x-axis position and velocity, and y-axis position and velocity, respectively. The superscript T indicates the transpose operation, and T represents the radar's sampling time. x(k-1), v x (k-1),y(k-1),v y (k-1) represents the position and velocity of the target along the x-axis and y-axis at the (k-1)th radar sampling time, respectively. 2×1 (k) represents the zero mean and variance at the k-th radar sampling time. White noise, diag(·) denotes a diagonal matrix, J = [0.5, 1, 0.5, 1].

4. The track break repair method based on adaptive Kalman prediction according to claim 1, characterized in that, The steps for modeling the target vessel with interrupted tracks described in step 4 are as follows: The first step is to construct the target state vector for radar observation according to the following formula: y(k)=s(k)+v noise (k) Where y(k) represents the target state vector observed by the radar at the k-th radar sampling time, s(k) represents the true state vector of the radar-tracked target at the k-th radar sampling time, and v noise (k) represents the radar positioning error at the k-th radar sampling time, which has zero mean and variance. White noise, sqrtm(·) represents the matrix square root operation. The second step is to calculate the true state vector of the radar-tracked target and the velocity of the radar-tracked target according to the following formula: v(k+1)=v(k)+T0a(k) a(k)=u(k)+w(k) Where s(k+1) represents the true state vector of the radar-tracked target at the (k+1)th radar sampling time, v(k) represents the velocity of the radar-tracked target at the kth radar sampling time, T0 = 5s, a(k) represents the acceleration of the radar-tracked target at the kth radar sampling time, v(k+1) represents the velocity of the radar-tracked target at the (k+1)th radar sampling time, u(k) represents the control signal of the ship's propulsion system, which is the known output maneuver signal, and w(k) represents the random acceleration caused by sea wind and waves, which has zero mean and variance. independence from v noise (k) white noise, The third step involves the radar tracking target state vector as follows: x(k+1)=Φx(k)+Bu(k)+Γw(k) y(k)=Hx(k)+v noise (k) Where x(k+1) represents the radar tracking target state vector at the (k+1)th radar sampling time, and Φ represents the state transition matrix. x(k) represents the radar tracking target state vector at the k-th radar sampling time, and B and Γ represent the noise driving matrices. H represents the observation matrix, H = [1 0].

5. The track break repair method based on adaptive Kalman prediction according to claim 1, characterized in that, The Kalman tracking steps described in step 5 are as follows: The first step is to initialize the initial conditions of the given filter: P0, Q0, R0, where... Let P0 represent the initial target state estimate, Q0 represent the initial covariance matrix, and R0 represent the initial target process noise matrix. The second step is to predict the state estimate and the estimation error covariance according to the following formula: in, Indicates the estimated value The prediction F represents the radar target state estimate at the (k-1)th radar sampling time. k-1 P represents the radar target tracking state transition matrix at the (k-1)th radar sampling time. k|k-1 P represents k-1 The predicted value, P k-1 Let Q be the covariance matrix at the (k-1)th radar sampling time. k-1 Let be the process noise variance matrix at the (k-1)th radar sampling time. The third step is to calculate the measurement prediction, the information covariance matrix, and the Kalman gain according to the following formula: in, Indicates the estimated value The prediction H represents the estimated observed state of the target. k S represents the observation matrix at the k-th radar sampling time. k H represents the information covariance matrix at the k-th radar sampling time. k-1 R represents the observation matrix at the (k-1)th radar sampling time. k Let K represent the observation noise matrix at the k-th radar sampling time. k This represents the Kalman gain at the k-th radar sampling time. Fourth step, calculate the state estimate and the covariance of the estimation error according to the following formula: P k =P k|k-1 -K k H k P k|k-1 in, Let z represent the radar target state estimate at the k-th radar sampling time. k This represents the observed state value of the target.

6. The track break repair method based on adaptive Kalman prediction according to claim 1, characterized in that, The single-step spot prediction described in step 6 is obtained by the following formula: x k+1 =F k x k +P Where, x k+1 F represents the radar tracking target state value at the (k+1)th radar sampling time. k Let P represent the radar tracking target state transition matrix at the k-th radar sampling time, and let P represent the covariance matrix updated last during the tracking filtering process.

7. The track break repair method based on adaptive Kalman prediction according to claim 1, characterized in that, The rectangular gate described in step 8 is obtained by the following formula: Among them, v k,i Let z represent the i-th component of the residual, |·| denotes the absolute value operation, and z k,i Let z represent the i-th component being measured. k|k-1,i K represents the i-th component of the measurement prediction value. G K represents the gate constant. G ≥3.5, i=1,2,...,n z n z Indicates the number of measurements.

8. The track break repair method based on adaptive Kalman prediction according to claim 1, characterized in that, The nearest neighbor NN data association mentioned in step 8 refers to using the nearest neighbor NN algorithm to select, according to the discrimination criteria, the measurement that falls within the gate and is statistically closest to the target prediction position as the candidate measurement.

9. The track break repair method based on adaptive Kalman prediction according to claim 8, characterized in that, The discrimination criterion refers to any one of the following conditions: Condition 1: If there is only one measurement in the gate of a target, then the target is associated with this measurement. Condition 2: If a measurement has fallen into the gate of a target, then the measurement is associated with the target. Condition 3: When a target's gate contains multiple measurements, the target is associated with the most recent measurement. Condition 4: When a measurement falls within the gates of multiple targets, the measurement is associated with the nearest target.

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