A sky wave over-the-horizon radar particle filtering detection before track method

Abstract

This invention relates to radar target detection and tracking technology. To address the limitations of traditional particle filtering over long-term accumulation, it provides a pre-detection tracking method for skywave over-the-horizon radar. This method divides virtual frames and velocity intervals using motion constraints to obtain multiple parallel processing channels, thereby narrowing the coherent pulse number estimation interval and performing coherent processing. Simultaneously, before particle filtering, the constant false alarm rate (CA-CFAR) method ensures that particles are randomly generated only in range-Doppler cells exceeding a threshold, further reducing the particle number. This invention reduces computational load while improving the detection and tracking capabilities of OTH radar for weak targets. This invention combines echo data preprocessing with coherent and non-coherent processing techniques, improving the detection and tracking performance of weak targets in skywave over-the-horizon radar while reducing computational complexity through multi-channel and low-threshold methods.

Description

Technical Field

[0001] This invention pertains to radar target detection and tracking technology, and specifically relates to a tracking method before detection by particle filtering in skywave over-the-horizon radar. Background Technology

[0002] With the rapid development of new aerospace threats, stealth aircraft, small, slow-moving targets, and cruise missiles—typically weak targets—are increasingly used on the modern battlefield. These targets typically have small radar cross-sections (RCS), complex trajectories, low flight altitudes, and compact platform dimensions, resulting in echo signal strength at the radar receiver that is far lower than the background clutter or system noise levels. This means their signal-to-noise ratio (SNR) and signal-to-clutter ratio (SCR) are both low, making them easily submerged in environmental noise or clutter. Traditional threshold-based detect-before-track (DBT) strategies are ineffective in such low SNR environments. Therefore, efficient detection and continuous tracking of weak targets has become a significant technical challenge for radar systems. To address this issue, track-before-detect (TBD) methods have attracted widespread attention in recent years. Unlike traditional radar processing methods that set fixed thresholds for observation data, the TBD method directly estimates the target state in the undecided raw signal domain. It fully utilizes the accumulation effect of multi-dimensional information such as time and space to achieve target detection and tracking. This processing mechanism is particularly suitable for unfavorable conditions such as low SNR, low SCR, and the inability to perform coherent accumulation of the target, significantly improving the detection performance and tracking stability of weak targets.

[0003] Based on the multi-stage decision optimization problem, the TBD algorithm based on dynamic programming (DP) has been proposed and applied to airborne radar and radar systems with dual high pulse repetition frequency (PRF). To further improve the performance of moving target detection and tracking, dynamic programming-based TBD methods such as a method for modeling the target motion equation based on fuzzy numbers and DP-TBD combined with Kalman filtering (KF) and Interacting Multiple Model (IMM) have been proposed. However, dynamic programming-based TBD methods all focus on target detection performance and are less feasible in terms of continuous target tracking, and the algorithms have a large computational load.

[0004] Particle filtering (PF), as a powerful nonlinear, non-Gaussian Bayesian state estimation method, has become a core algorithm for implementing TBD (Target Detection and Tracking). Particle filtering overcomes the limitations of Kalman filtering in nonlinear systems by approximating the posterior probability density function of the target state using a set of weighted particles as samples. It is particularly suitable for target tracking problems where nonlinear state transition models coexist with non-Gaussian observation noise. The TBD algorithm based on particle filtering constructs a probability distribution model of target presence or absence using the observation sequence without setting an observation threshold. It recursively estimates the target's state at each time step, such as range and Doppler, thereby achieving target detection and tracking, including steps such as state prediction, importance sampling, weight update, and resampling. However, in the context of skywave over-the-horizon radar, the large amount of non-Gaussian noise, broadband clutter, and non-uniform background introduced by the ionospheric reflection mechanism significantly reduces the efficiency of traditional detection methods, resulting in low range and azimuth accuracy. Therefore, the classical DBT method has a low probability of successfully detecting the target and cannot achieve target tracking. With a large amount of echo data and a large number of particles, the computational load of the traditional PF-TBD algorithm becomes extremely high.

[0005] In other words, over-the-horizon (OTH) radar requires a long observation time and a large measurement space when conducting simultaneous air and sea detection. Traditional particle filtering methods have the following limitations:

[0006] 1) The demand for particles has surged.

[0007] The accuracy of particle filtering depends on the size of the particle set. More data measurement space requires more particles to effectively cover the state space; otherwise, particles will not be able to randomly move around the target location, resulting in the target not being detected. At the same time, there is particle degeneracy, where a few particles occupy all the weights, and the estimation accuracy drops sharply.

[0008] 2) The contradiction between computing resources and real-time performance

[0009] The computational complexity of particle filtering is linearly related to the number of particles. However, large-scale particle assemblies significantly extend the time for a single filtering iteration. During detection and tracking, computational delays may cause the system to fail to respond to dynamic changes in a timely manner, or even lead to control failure. Summary of the Invention

[0010] The technical problem to be solved by this invention is to provide a tracking method for particle filtering detection in skywave over-the-horizon radar, in order to overcome the limitations of traditional particle filtering under long-term accumulation.

[0011] The technical solution adopted by this invention to solve the above-mentioned technical problems is a tracking method before particle filter detection in skywave over-the-horizon radar, comprising the following steps:

[0012] Based on the target maximum speed v max Speed ​​range Divided into several channels;

[0013] Within each channel, based on the number of coherent pulses M p The echo data with a total number of pulses M is divided into K virtual frames;

[0014] Perform moving target detection processing on each virtual frame and extract Doppler region data corresponding to the current velocity range;

[0015] Each extracted virtual frame data is binarized using the constant false alarm rate (CA-CFAR) method to generate a binary flag matrix. In the binary matrix, 1 indicates that the target exists and 0 indicates that the target does not exist. New particles are randomly generated at the positions marked as 1 in the binary flag matrix.

[0016] The target existence is determined and its state is estimated based on the particle filter-based pre-detection tracking method.

[0017] This invention provides a preprocessing method to reduce particle count and measurement space. Multiple parallel processing channels are obtained by dividing virtual frames and velocity ranges through motion constraints, thereby narrowing the coherent pulse number estimation range and performing coherent processing. Simultaneously, before particle filtering, the constant false alarm rate (CA-CFAR) method ensures that particles are randomly generated only in range-Doppler cells exceeding a threshold, further reducing the particle count. This invention reduces computational load while improving the OTH radar's detection and tracking capabilities for weak targets.

[0018] The beneficial effect of this invention is that it combines echo data preprocessing with coherent and non-coherent processing techniques, and improves the detection and tracking performance of weak targets under skywave over-the-horizon radar by means of multi-channel and low threshold, while reducing computational complexity. The method is applicable to the detection and tracking of weak targets with low signal-to-noise ratio and low signal-to-clutter ratio by skywave over-the-horizon radar. Attached Figure Description

[0019] Figure 1 A comparison chart of particle existence probabilities using different algorithms in Scene 1;

[0020] Figure 2 This is a comparison chart of the RMSE of distance units for different algorithms in Scene 1;

[0021] Figure 3 Comparison of RMSE of Doppler cells using different algorithms in Scene 1;

[0022] Figure 4This is a comparison chart of particle existence probabilities for different algorithms in Scene 2;

[0023] Figure 5 This is a comparison chart of the RMSE of distance units for different algorithms in scenario two.

[0024] Figure 6 Comparison of RMSE of Doppler units for different algorithms in scenario 2;

[0025] Figure 7 A comparison chart of particle existence probabilities using different algorithms in Scene 3;

[0026] Figure 8 This is a comparison chart of the RMSE of distance units for different algorithms in scenario three;

[0027] Figure 9 Comparison of RMSE of Doppler units for different algorithms in scenario 3;

[0028] Figure 10 This is a comparison chart of the running times of different algorithms in scenario one. Detailed Implementation

[0029] The above invention, a multi-channel, low-threshold skywave over-the-horizon radar particle filter detection-pre-tracking method, is referred to as MCC-PF-TBD.

[0030] The total number of particles is known to be , The components of time particles are One "surviving" particle and A "dead" particle. The state of existence of surviving particles at any given time is marked as The existence state of dead particles is marked as . At time t, the posterior probability density function of the particle is expressed by the particle set. To represent. Among them... for Time of the first The motion state of each particle, including distance And Doppler information , Represents the normalized weights of the particles. T This represents the transpose. Assume the object detection threshold is... Then MCC-PF-TBD from arrive The specific steps of one iteration at time point are as follows:

[0031] 1) Particles exhibit state transitions:

[0032] according to The set of existence states of particles at any given moment and probability transition matrix predict The set of existence variables of the particle set at time .

[0033] 2) Particle motion state prediction:

[0034] based on The existence state of a particle at any given time is used to update its motion state. An existing particle should be defined for any... All Motion state prediction mainly includes the following parts:

[0035] (1) For The state exists at all times. and A state exists at all times The particle that is formed is called a newborn particle. Motion state at any moment Similar to the initial motion state of the particles, based on the particle's newborn probability distribution... Obtained by sampling;

[0036] (2) For The state exists at all times. and A state exists at all times The particle, called the continuation particle, has... Motion state at any moment From the state transition matrix, we have:

[0037] ;

[0038] in, for The state transition matrix at each time step is determined based on the model. This is process noise.

[0039] 3) Particle weight update:

[0040] based on Calculate the particle's weight based on its position at each time step. If the particle dies, its weight is set to 1; if the particle exists, its weight needs to be calculated based on the posterior probability density function. Calculate particle weights :

[0041] ;

[0042] express Motion state at any moment Doppler measurement space , express Motion state at any moment Distance dimension of measurement space , express Time measurement signal in Doppler - Distance dimension amplitude, and The index value of the average measurement space;

[0043] 4) Particle weight normalization:

[0044] Particle weight Normalization process yields normalized weights. :

[0045] ;

[0046] 5) Resampling:

[0047] Based on the normalized weights of the particles Resampling is performed. The particle weights after resampling are all changed. .

[0048] 6) Target existence probability estimation:

[0049] Based on the number of surviving particles after resampling, The probability of the existence of the target at any given time Make an estimate:

[0050] ;

[0051] in, represent The total number of particles with a target variable of 1 at any given time. Based on the known detection threshold... Determine the existence status of the target. If If, then the target is determined to exist; if If the target does not exist, then it is determined that the target does not exist.

[0052] 7) Target motion state estimation:

[0053] .

[0054] for The estimated state of the target's motion at any given time, assuming the target's maximum velocity. It is known that the total pulse can be divided into multiple virtual frames based on motion constraints, with coherent processing within each virtual frame and non-coherent processing between virtual frames. Furthermore, multi-channel range-Doppler (MC) data can be formed by partitioning the velocity spectrum, allowing parallel processing of the echo data within each channel, thereby further reducing the range-Doppler spectrum range and computational load. The specific steps are as follows:

[0055] Step 1: Echo data segmentation and virtual frame formation

[0056] target speed range Divided into The speed range satisfies:

[0057] ;

[0058] Indicates the target speed. This represents the minimum value in the p-th velocity interval. This represents the maximum value in the (p-1)th velocity interval. ;

[0059] Let the estimated number of coherent pulses within a velocity range be denoted as . The target can be obtained at The maximum number of distance units traversed within the passage :

[0060] ;

[0061] in For radar range resolution unit, Indicates the pulse product time.

[0062] Because the target is in the coherent accumulation time No distance travel will occur within the area. This indicates pulse coherence, so we get :

[0063] ;

[0064] Thus, the minimum coherent pulse number is obtained. :

[0065] ;

[0066] in This indicates rounding down. This represents the pulse repetition time, so The values ​​of satisfy:

[0067] ;

[0068] in This indicates the total number of pulses.

[0069] Choose one Value, the echo data matrix Divided into Submatrix:

[0070] ;

[0071] Each submatrix is ​​artificially divided and can also be referred to as a channel, with a size of [missing information]. , The echo distance dimension is used; the submatrix is ​​called virtual frame data, and the k-th... The submatrix is ​​represented as:

[0072] ;

[0073] in:

[0074] ;

[0075] ;

[0076] Where k takes the value of an integer from 1 to K. Indicates rounding up. This represents the number of pulses contained in the k-th channel. (Previous) Each channel contains [number] channels. Each channel corresponds to a complete velocity range coherent processing unit; the Kth group (the last group) has the following pulse count: total pulse count M minus the previous pulse count. Pulse used in the channel This ensures that the sum of the pulse counts for all channels equals the total pulse count M. It can be seen that, as... The increase, This will decrease, meaning the number of virtual frames for subsequent noncoherent processing will decrease, while the gain from noncoherent accumulation will increase with the increase in the number of accumulated frames. To ensure the robustness of the algorithm, the final number of coherent pulses is selected as follows: :

[0077] .

[0078] Step 2: Moving Target Detection MTD Processing

[0079] when Values At that time, the random phase of the airborne target echo signal remains unchanged within each virtual frame, and no range travel effect occurs. Therefore, coherent processing of the echo data can be performed within the virtual frame. By using the MTD method to coherently accumulate the data of each virtual frame, we can obtain...

[0080] ;

[0081] The coherent accumulation of each virtual frame data is obtained through Discrete Fourier Transform (DFT):

[0082] ;

[0083] Step 3: Extract partial MTD processing results

[0084] because and Given that, it is only necessary to consider the speed range. Subsequent pre-detection tracking TBD processing is performed on the corresponding Doppler region. The extracted MTD results are then processed. Represented as:

[0085] ;

[0086] in The size is Indicates from the first MTD results of virtual frames The extracted data The final determined measurement space, i.e. Depend on indivual composition, The value range is 1 to , The value range is 1 to .

[0087] Steps 2 and 3 complete the moving target detection processing for each virtual frame and extract the Doppler interval data corresponding to the current velocity interval.

[0088] Step 4: Low Threshold Preprocessing Steps

[0089] To further reduce computational load, a low-threshold preprocessing technique can be added to each channel of each virtual frame, ensuring that particles are randomly generated only at distances exceeding the threshold – specifically within Doppler units. This invention employs the CA-CFAR method, with the specific steps as follows:

[0090] Specify a distance-Doppler cell as the detection cell and set a threshold. Let the reference window contain a total of Reference units, when the detection value at the nth detection unit Greater than the preset power threshold If the time condition is met, it is judged as having a goal; otherwise, it is judged as having no goal.

[0091] ;

[0092] If a target is identified, the element value of the corresponding range-Doppler cell in the binary flag matrix is ​​set to 1; if noise is identified, the element value of the corresponding range-Doppler cell in the binary flag matrix is ​​set to 0.

[0093] A protection unit is placed around the detection unit to eliminate excess signal energy around the detection unit, and a reference unit is then selected around the protection unit. The signal power is respectively... The average power of all cells within the reference window is calculated as an estimate of the background noise power. :

[0094] ;

[0095] Based on the preset false alarm probability Through the standardization factor Adjust threshold :

[0096] ;

[0097] in and The relationship depends on the noise distribution assumptions; for Gaussian white noise, Calculation as follows

[0098] ;

[0099] To ensure that the CFAR starting point begins from the first point in the range-Doppler spectrum, its size needs to be expanded to provide sufficient reference and guard cells at the edge points of the range-Doppler spectrum, preventing target loss due to undetectable points in the edge regions. This invention employs edge zero-padding to increase the required number of guard and reference cells.

[0100] Step 5: TBD processing before detection

[0101] Airborne targets can only undergo noncoherent accumulation between virtual frames, which is achieved through the following detection and estimation framework:

[0102] ;

[0103] in Indicates the first The measurement space of the velocity range, H1 indicates the presence of the target, and H0 indicates the absence of the target; The value function is represented in the particle filter algorithm. and The likelihood function is used to estimate The degree of confidence; For the first The motion states of each particle in channels 1p to Kp of the velocity range; For the first Target estimation results for channels 1p to Kp in the velocity range.

[0104] The first line of expression is used for target existence detection, and the second line of expression is used for target parameter estimation. Measurement space of velocity range In the process, we search for observations that can make the values... With parameters correlation Largest parameter As an estimation result If this maximum correlation exceeds the threshold If the objective is found to exist (H1), then the objective is found to exist (H0); otherwise, the objective is found to not exist (H0).

[0105] MCC-PF-TBD first needs to pass... Divide the channel into possible speed ranges for the target. Average score Number of speed channels in the segment. It depends on the required accuracy of the speed estimate. Each search speed... This reflects the direction of the target's movement. Furthermore, through the above... The calculation formula yields the coherent pulse number for each channel. However, when... When the value approaches 0, the number of coherent pulses approaches infinity. To limit this situation, the maximum number of coherent pulses is set to not exceed the maximum speed. Definite 2 times, that is

[0106] ;

[0107] Then, moving target detection (MTD) processing is performed on the divided virtual frames in each channel. and Given that, it is only necessary to consider the speed range. Subsequent processing is performed on the corresponding Doppler interval, which reduces the measurement space size.

[0108] Before PF-TBD processing, the MTD results of each partially extracted frame are processed by CA-CFAR to generate a binary flag matrix. Positions exceeding the threshold are assigned a distance-Doppler cell position of 1, while positions within the threshold are assigned a position of 0. Therefore, newly generated particles only... The positions are randomly generated. This step significantly reduces the number of particles, further reducing the computational load.

[0109] Assume the initial position of the target is ,by The process moves radially at a constant velocity. The process noise is modeled as variance. Zero-mean Gaussian process, false alarm probability The parameters of the OTH radar are shown in Table 1. The simulation experiment includes the following three different scenarios, as shown in Table 2.

[0110] Table 1 Radar Setting Parameters

[0111] parameter value 100s 10000 600 5000m

[0112] Table 2 Simulation Scene Parameter Settings

[0113] Scene Accumulated pulse count (CPI) Target maximum speed ( ) Scene 1 10000 408 Scene 2 5000 408 Scene 3 10000 500

[0114] The main metrics used in this invention are the average probability of the target's existence, the root mean square error of the target's state, and the average running time.

[0115] No. Average probability of target presence per frame for:

[0116] ;

[0117] in, Indicates the number of Monte Carlo simulations. Indicates the first The Monte Carlo simulation experiment The probability of the target existing at frame time.

[0118] No. Frame target distance RMSE ( ) and Doppler RMSE ( )for:

[0119] ;

[0120] in, and For the first In the Monte Carlo experiment True and estimated values ​​of the target's true distance cell in the frame. and The true and estimated values ​​of the target true Doppler cells can also be given. The statistical results of the Monte Carlo simulations were used to compare the simulation time consumption.

[0121] This simulation uses MATLAB R2024b to verify the tracking performance of the algorithm on an Intel(R) Core(TM) i7-10700 processor and 16.0 GB of memory.

[0122] Assuming a threshold Through 500 Monte Carlo experiments were conducted in different scenarios to obtain... Figures 1-10 Results. Overall, the MCC-PF-TBD algorithm performs best in all three scenarios, and the three algorithms show similar trends across various evaluation metrics. , In the scenario, from Figure 1 As can be seen, a total of 16 frames of data were generated. MCC-PF-TBD exceeded the threshold in the 4th frame, indicating that the target was detected, while the other two comparison algorithms only detected the target in the 5th and 6th frames, respectively. Therefore, MCC-PF-TBD outperforms the other two comparison algorithms in detection performance at lower SNR. Meanwhile, from... Figure 2 and Figure 3 The distance unit RMSE (RMSE) can be seen D ) and Doppler unit RMSE (RMSE R The MCC-PF-TBD algorithm consistently achieves the lowest convergence speed, and its convergence to a lower level is faster than the other two algorithms compared. This is because the multi-channel partitioning and CFAR's low-threshold preprocessing significantly reduce the number of new particles, allowing more particles to fall within effective cells, thus improving computational efficiency. Figure 4 It can be seen that, , In scenario (Scenario 2), the frame rate is reduced to 8 frames. If the accumulated frame rate is further reduced, there may be cases where the target cannot be detected. Therefore, the accumulated pulse count has a significant impact on detection performance. Figure 5 and Figure 6 It can be seen that the distance unit RMSE (RMSE) D ), Doppler unit RMSE (RMSE) R All of these are lowest in MCC-PF-TBD. And... , In scenario (Scenario 3), from Figure 7 As can be seen, MCC-PF-TBD only detected the target in the 6th frame. The reason for the reduced detection performance compared to Scene 1 is that, according to the above, Scene 3... The number of coherent pulses obtained from the calculation formula The change increases the number of non-coherent pulses within the virtual frame. Performing MTD processing will result in a loss of coherent performance. Figure 8 and Figure 9 It can be seen that the distance unit RMSE (RMSE) D ), Doppler unit RMSE (RMSE) R All of them have the lowest MCC-PF-TBD. Figure 10The results reflect the running time and number of particles required for each algorithm. It can be seen that MCC-PF-TBD requires the fewest new particles and its running time is significantly reduced compared to the other two algorithms.

[0123] In summary, the multi-channel, low-threshold skywave over-the-horizon radar particle filter pre-detection tracking algorithm proposed in this invention improves detection and tracking performance and significantly reduces computational load compared to existing particle filter pre-detection tracking algorithms, making it an effective pre-detection tracking method.

Claims

1. A tracking method before particle filter detection in skywave over-the-horizon radar, characterized in that, Includes the following steps: Based on the target maximum speed v max Speed ​​range Divided into several channels; Within each channel, based on the number of coherent pulses M p The echo data with a total number of pulses M is divided into K virtual frames; Perform moving target detection processing on each virtual frame and extract Doppler region data corresponding to the current velocity range; Each extracted virtual frame data is binarized using the constant false alarm rate (CA-CFAR) method to generate a binary flag matrix. In the binary matrix, 1 indicates that the target exists and 0 indicates that the target does not exist. New particles are randomly generated at the positions marked as 1 in the binary flag matrix. The target existence is determined and its state is estimated based on the particle filter-based pre-detection tracking method.

2. The method as described in claim 1, characterized in that, The number of coherent pulses M p The selection satisfies: This represents the minimum value in the p-th velocity interval. This represents the maximum value in the p-th velocity range. N c Δr is the number of channels; Δr is the distance resolution; PRT is the pulse repetition time; min is the minimum value.

3. The method as described in claim 1, characterized in that, The virtual frames are divided as follows: the first K-1 virtual frames each contain M... p The Kth virtual frame contains M−(K−1)M pulses; p One pulse; in, , This indicates rounding up to the nearest integer.

4. The method as described in claim 1, characterized in that, The moving target detection process employs discrete Fourier transform to perform coherent accumulation on each virtual frame.

5. The method as described in claim 1, characterized in that, The binarization process using the Cell Average Constant False Alarm Rate (CA-CFAR) method is as follows: Specify a distance-Doppler unit as the detection unit, set up a protection unit around the detection unit, and then select a reference unit around the protection unit; Calculate the average signal power within the reference cell as a background noise estimate. ; Based on the preset false alarm probability Calculate the detection threshold T. , for Number of reference units; The signal power of each range-Doppler cell is binary-valued to generate a binary flag matrix; the elements of the binary flag matrix corresponding to the range-Doppler cell with signal power greater than the detection threshold T are set to 1, otherwise they are set to 0.

6. The method as described in claim 1, characterized in that, The particle filtering detection-pre-tracking method includes: particle presence state transition, particle motion state prediction, particle weight update and normalization, resampling, target presence probability estimation, and target motion state estimation.

7. The method as described in claim 6, characterized in that, Target Existence Probability The estimate is: ； in, represent The target number of particles with a variable of 1 at any given time is: , for The state of the i-th particle at time i. Indicates a dead particle. Indicates surviving particles; Based on known detection thresholds Determine the existence state of the target, if If, then the target is determined to exist; if If the target does not exist, then it is determined that the target does not exist.

8. The method according to claim 7, characterized in that, The target motion state is estimated as follows: ； in, for The estimated value of the target's motion state at any given time. for The motion state of the i-th particle at time i.

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