Pre-Tracking Method for Radar Weakly Fluctuating Target Detection Based on Multi-Bernoulli Filtering

Abstract

The present invention discloses a pre - tracking method for radar weak - fluctuation targets based on multi - Bernoulli filtering. In the MB - TBD of the present invention, in addition to considering amplitude information, phase marginalization is also performed to improve the distinguishability between targets and noise. Three types of Swerling - type complex likelihood ratios (CLR) are used to replace the squared - modulus likelihood ratio (SLR). To adapt to the situation where the prior information of the appearance of fluctuating targets is unknown, an idea of successive division of targets is borrowed to propose a TBD (LABer - STC - TBD) with an adaptive birth distribution of the multi - Bernoulli filter based on the measurement likelihood ratio. Compared with the existing MB - TBD adaptive birth algorithms, the new algorithm overcomes the detection difficulty when weak and strong targets appear simultaneously during target fluctuations, and after the MB - TBD update is completed, an algorithm based on distance and particle weights (DPM) is proposed to merge the Bernoulli components of the same target. Finally, the estimation and detection performances in different situations studied are compared, and the advantages of the LABer - STC - TBD algorithm under target amplitude fluctuations are shown.

Description

Technical Field

[0001] The present invention relates to the technical field of radar detection and tracking of weak fluctuating multi-targets, and particularly to a method for tracking before detection of weak fluctuating targets by radar based on multi-Bernoulli filtering. Background Art

[0002] Traditional radar multi-target tracking (MTT) algorithms process the preprocessed data by compressing the single-frame data scanned by the radar antenna into a finite point set through image processing. However, for targets in a low signal-to-noise ratio environment, the echoes of the targets are usually lower than the threshold of the preprocessing, which may lead to target loss and missed detection; if the threshold is lowered, a large number of false alarms will be generated, making it impossible to maintain the target track.

[0003] To solve the above problems, the tracking before detection (TBD) algorithm is adopted. Without setting a threshold for the measurement signal, based on the continuity of the target movement in space and the time correlation of the target echo data in several consecutive frames, multiple frames of data are jointly processed, and target detection and tracking are achieved through multi-frame energy accumulation. Most of the TBD implementation technologies are based on batch processing, such as tracking before detection based on dynamic programming and tracking before detection based on Hough transform. However, since batch processing requires discretization of the target state and waiting for multiple frames of measurement data to be processed, the real-time performance of batch processing implementation is very poor.

[0004] The particle filter in the Bayesian framework can also be used to implement the TBD algorithm (PF-TBD). The main tasks of multi-target detection and tracking are to estimate the time-varying number of targets and their states through measurement values. In practical applications, the number of targets is generally unknown, and with the increase in the number of targets, the dimension of the target posterior probability will increase, making it more difficult to estimate the multi-target posterior probability. Therefore, the PF-TBD filter has certain limitations for MTT with an unknown number of targets.

[0005] Therefore, the existing technologies cannot effectively solve the problem of detecting and tracking weak fluctuating multi-targets. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for tracking before detection of weak fluctuating targets by radar based on multi-Bernoulli filtering, aiming to solve the technical problem that the existing technologies cannot effectively solve the problem of detecting and tracking weak fluctuating multi-targets.

[0007] To achieve the above purpose, a method for tracking before detection of weak fluctuating targets by radar based on multi-Bernoulli filtering adopted by the present invention includes the following steps:

[0008] S1: Initialize the system parameters and read the original measurement data at the (k - 1)-th and k-th moments in the radar receiver;

[0009] S2: Use the LABer-STC-TBD algorithm to adaptively generate new targets for the original measurement data at time k-1;

[0010] S3: Obtain the complex measurement and squared measurement data at time k, calculate the complex likelihood ratio and squared modulus likelihood ratio for three types of amplitude fluctuations respectively, and give the SMC implementation of MB-TBD filtering under amplitude fluctuations;

[0011] S4: Delete the Bernoulli components with probabilities lower than the threshold, and merge the Bernoulli components using the DPM algorithm;

[0012] S5: Extract the target states with probabilities greater than 0.5. The number of Bernoulli components with probabilities greater than 0.5 is the number of estimated targets at time k;

[0013] S6: Judge whether k+1 is greater than the total target movement time. If it is greater, the algorithm ends; otherwise, return to S2.

[0014] The system parameters include:

[0015] Sampling interval T, current time k, total target movement time K, the scanning area of the radar in polar coordinates [r min , r max ×[θ min , θ max , the measurement data Z k and Z k-1 , a range and azimuth surveillance radar covering the defined area in polar coordinates. For the range, assume that the transmitted pulse is a linear frequency modulation signal with bandwidth B and duration T ε , the speed of light c, the range resolution cell For the angle, consider a linear phased array with N a antennas at the radar receiving end, with an interval of where λ is the wavelength of the carrier frequency, and the angle resolution is

[0016] In the steps of using the LABer-STC-TBD algorithm to adaptively generate new targets for the original measurement data at time k-1:

[0017] Given the false alarm rate P fa of the resolution cell, the threshold γ can be calculated, and a threshold γ more suitable for the target fluctuation situation is corrected:

[0018]

[0019] The LABer-STC-TBD algorithm first selects the measurements from the previous time to adaptively generate new targets, that is:

[0020]

[0021] The adaptive birth distribution can be expressed as:

[0022]

[0023]

[0024] Eliminate the Bernoulli components with a probability of existence lower than 0.5, and use the detected Bernoulli components to correct the existing measurements to eliminate the influence of this component on the remaining detected targets. When the detected target has an effect on the resolution cell (l, m), the measurement of the resolution cell (l, m) after eliminating the effect of this target from the measurement equation is:

[0025]

[0026] At this time, the sensor obtains the corrected measurement set in the entire N r ×N θ scene as:

[0027]

[0028] Then return to the above steps and increase the false alarm rate until the existence probabilities of all Bernoulli components are lower than 0.5.

[0029] In the steps of calculating the complex likelihood ratio and the squared modulus likelihood ratio for three types of amplitude fluctuations respectively:

[0030] Calculate the squared modulus likelihood ratios for amplitude fluctuation types Swerling 0, 1, and 3 respectively;

[0031] Calculate the complex likelihood ratios for amplitude fluctuation types Swerling 0, 1, and 3 respectively.

[0032] In the steps of deleting the Bernoulli components with a probability of existence lower than the threshold and merging the Bernoulli components using the DPM algorithm:

[0033] The DPM algorithm first deletes the Bernoulli components with a probability of existence lower than the threshold, then classifies the Bernoulli components according to the distance, and then retains the Bernoulli component with the highest probability of existence for the same target. After selection, there is only one component for the same target; if the probabilities of existence of two components are the same, that is and the distance of the Bernoulli components is within the threshold, then merge these two components and re - define the new component, specifically depending on and

[0034] In the steps of taking the Bernoulli components and estimating the number of targets:

[0035] After the DPM algorithm ends, Bernoulli components with an existence probability greater than 0.5 are extracted, and the number of Bernoulli components with an existence probability greater than 0.5 is the number of estimated targets.

[0036] The beneficial effects of the present invention are as follows: First, MB-TBD usually only performs marginal integration on amplitude information without considering the fact that the measurement is complex. In the present invention, in addition to considering amplitude information, phase marginalization is also performed in MB-TBD to improve the distinguishability between targets and noise. More precisely, three types of Swerling complex likelihood ratios (CLR) are used instead of the squared modulus likelihood ratio (SLR). In addition, to adapt to the situation where the prior information of the appearance of fluctuating targets is unknown, an idea of successive division of targets is borrowed to propose a TBD (LABer-STC-TBD) for adaptive birth distribution of the multi-Bernoulli filter based on measurement likelihood ratio. Compared with the existing MB-TBD adaptive birth algorithms, the new algorithm overcomes the detection difficulty when weak and strong targets appear simultaneously during target fluctuations, and after the MB-TBD update ends, an algorithm based on distance and particle weights (DPM) is proposed to merge the Bernoulli components of the same target. Finally, the estimation and detection performances in different situations studied are compared, and the advantages of the LABer-STC-TBD algorithm under target amplitude fluctuations are shown, and for the three fluctuation models, the CLR method is superior to the SLR method in both detection and estimation. Brief Description of the Drawings

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0038] Figure 1 It is a flowchart of the steps of the method for pre-tracking the detection of weak fluctuating radar targets based on multi-Bernoulli filtering of the present invention.

[0039] Figure 2 It is a schematic flowchart of the method for pre-tracking the detection of weak fluctuating radar targets based on multi-Bernoulli filtering of the present invention.

[0040] Figure 3 It is the true trajectory of the target movement in Simulation Scenario 1 of the present invention.

[0041] Figure 4 It is the OSPA of the LABer-STC-TBD algorithm and the KpBer-TBD algorithm under Swerling 0 of the present invention.

[0042] Figure 5It is a comparison graph of target potential estimation between the Swerling 0 LABer-STC-TBD algorithm and the KpBer-TBD algorithm of the present invention.

[0043] Figure 6 It is the OSPA of the Swerling 1 LABer-STC-TBD algorithm and the KpBer-TBD algorithm of the present invention.

[0044] Figure 7 It is a comparison graph of target potential estimation between the Swerling 1 LABer-STC-TBD algorithm and the KpBer-TBD algorithm of the present invention.

[0045] Figure 8 It is the OSPA of the Swerling 3 LABer-STC-TBD algorithm and the KpBer-TBD algorithm of the present invention.

[0046] Figure 9 It is a comparison graph of target potential estimation between the Swerling 3 LABer-STC-TBD algorithm and the KpBer-TBD algorithm of the present invention.

[0047] Figure 10 It is the true trajectory of target movement in simulation scenario 2 of the present invention.

[0048] Figure 11 It is the OSPA of the complex likelihood ratio and the squared modulus likelihood ratio with different signal-to-noise ratios under Swerling 0 of the present invention.

[0049] Figure 12 It is the target potential estimation of the complex likelihood ratio and the squared modulus likelihood ratio with different signal-to-noise ratios under Swerling 0 of the present invention.

[0050] Figure 13 It is the OSPA of the complex likelihood ratio and the squared modulus likelihood ratio with different signal-to-noise ratios under Swerling 1 of the present invention.

[0051] Figure 14 It is the target potential estimation of the complex likelihood ratio and the squared modulus likelihood ratio with different signal-to-noise ratios under Swerling 1 of the present invention.

[0052] Figure 15 It is the OSPA of the complex likelihood ratio and the squared modulus likelihood ratio with different signal-to-noise ratios under Swerling 3 of the present invention.

[0053] Figure 16 It is the target potential estimation of the complex likelihood ratio and the squared modulus likelihood ratio with different signal-to-noise ratios under Swerling 3 of the present invention. Detailed implementation manners

[0054] Embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, and should not be construed as a limitation of the present invention.

[0055] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. In addition, in the description of the present invention, the meaning of "a plurality" is two or more unless otherwise specifically defined.

[0056] Please refer to Figure 1 , the present invention provides a pre-tracking method for detecting weak fluctuating radar targets based on multi-Bernoulli filtering, including the following steps:

[0057] S1: Initialize the system parameters and read the raw measurement data at the (k - 1)-th and k-th moments in the radar receiver;

[0058] S2: Use the LABer-STC-TBD algorithm to adaptively generate new targets for the raw measurement data at the (k - 1)-th moment;

[0059] S3: Obtain the complex measurement and squared measurement data at the k-th moment, calculate the complex likelihood ratio and squared modulus likelihood ratio for three types of amplitude fluctuations respectively, and give the SMC implementation of the MB-TBD filter under amplitude fluctuations;

[0060] S4: Delete the Bernoulli components with probabilities lower than the threshold, and merge the Bernoulli components using the DPM algorithm;

[0061] S5: Extract the Bernoulli components and estimate the number of targets;

[0062] S6: Determine whether k + 1 is greater than the total target movement time. If it is greater, the algorithm ends; otherwise, return to S2.

[0063] Specifically, the system parameters include:

[0064] The system parameters include the sampling interval T, the current moment k, the total target movement time K, and the radar scanning area [r min , r max × [θ min , θ max, the measurement data Z in the radar receiving and tracking scenario k and Z k-1 , a range and azimuth surveillance radar covering a defined area in polar coordinates. For range, assume the transmitted pulse is a linear frequency modulated signal with bandwidth B and duration T ε , the speed of light c, and the range resolution cell For angle, consider a linear phased array of N a antennas at the radar receiving end, with an interval of where λ is the wavelength of the carrier frequency, and the angle resolution is

[0065] Initialize k = 2. In the TBD algorithm, the measurements consist of the range and azimuth received by the radar array antennas. The sensor provides a two-dimensional image of the surveillance area at an interval of time T. The detection area scenario considered in this paper is as Figure 3 shown. Each image consists of N c = N r ×N θ resolution cells, and each cell has a definite range resolution Δ r and angle resolution Δ θ . Define the center of each cell (l, m) as (lΔ r , mΔ θ ), where l = 1, 2, … N r , m = 1, 2, … N θ .

[0066] The measurement intensity in the (l, m) resolution cell is:

[0067]

[0068] is complex Gaussian noise, which is defined as: and are independent zero-mean Gaussian white noises with covariance ;

[0069] is an unknown phase assumed to be uniformly distributed on [0, 2π) at time k;

[0070] h (l,m) (x k.i ) represents the contribution from the target cell (l, m), which depends on the point spread function h and the target position x k.i ; for simplicity, h (l,m) (x k.i ) is denoted as

[0071] ρ k,iis the amplitude of the target, described by the Swerling model, i.e.:

[0072] Under the Swerling 0 model, the amplitude ρ of each target k,i is equal to the unknown parameter ρ i .

[0073] For the Swerling 1 model, it is assumed that the amplitude ρ of the target k,i follows a Rayleigh distribution, and its probability density function (PDF) is:[[]]

[0074]

[0075] and σ ρ,i is a parameter of the Rayleigh distribution,

[0076] When the amplitude fluctuation type is Swerling 3, ρ k,i follows a chi-square distribution with four degrees of freedom, then the PDF of ρ k,i is as follows:[[]]

[0077]

[0078] and is an unknown parameter,

[0079] H1 and H0 are respectively assumed to have N k targets and no targets.[[]]

[0080] The complete measurement set received from a given sensor can be expressed as

[0081]

[0082] And the historical measurement set up to time k is:[[]]

[0083] Z 1:k ={z i , i = 1, 2…k}[[]]

[0084] At time k, the radar measurement has two forms of expression: one is the complex measurement z k for coherent integration, and the other is the squared measurement |z k | 2 .

[0085] For |z k | 2 Although N k targets exist and provide different independent random phases However, by changing the parameters, it can be proved that the density actually only depends on N k-1 phase variable, since variable can be defined at any phase as follows:

[0086]

[0087] where is still an independent symmetric complex Gaussian noise sample, and the phase is uniformly distributed on [0, 2π); depends only on N k -1 phase variables.

[0088] For the ambiguity function of range matched filtering, we have:

[0089]

[0090] where,,

[0091] The azimuth ambiguity function of adaptive beamforming is:

[0092]

[0093] where,, and

[0094] The overall ambiguity function in the range-azimuth cell (l, m):

[0095]

[0096] The size of h(x k ) is N c = N r × N θ , that is:

[0097]

[0098] An important RFS distribution is the Bernoulli RFS X. The probability that the set is empty is 1 - r; the probability that it contains only one element is r, and its spatial distribution follows the probability density p. The probability density of the Bernoulli RFS is:

[0099]

[0100] The multi-Bernoulli RFS X is represented by the union of M independent Bernoulli RFS Xs to represent a fixed number M of targets. Therefore, the set represents the multi-Bernoulli RFS, where r (i) and p (i)respectively represent the existence probability and the spatial probability density of the \(i\)-th Bernoulli component. The multi-Bernoulli RFS probability density \(\pi(X)\) is as follows:

[0101]

[0102] Multi-Bernoulli prediction: Given the posterior multi-Bernoulli parameters at time \(k - 1\) then the predicted multi-Bernoulli parameters are:

[0103]

[0104] where:

[0105]

[0106] Multi-Bernoulli update: Given the predicted multi-Bernoulli parameters then the updated multi-Bernoulli parameters are:

[0107]

[0108] where:

[0109]

[0110] Furthermore, TBD uses the original measurement values of the given sensor. On the one hand, TBD performs threshold-free processing on all measurement information, and at this time the detection probability of the target is 1, that is, \(p\) D,k (X k ) \(\equiv 1\); on the other hand, for a given scene which is a set of \(N\) r × \(N\) θ pixels, it is called an image; the measurement is an image composed of thousands or even millions of pixels. However, the target does not affect all pixels, but only occupies a small part of the image area. This means that if \(p(Z\) k |X k ) is directly used, it will lead to very low computational efficiency. Define the likelihood ratio as the ratio of the target presence likelihood \(p(Z\) k |X k ) to the target absence likelihood \(p_0(Z\) k ).

[0111]

[0112] The calculation of the likelihood ratio is restricted to the area around the target, which maximally improves the calculation efficiency. Each pixel unit received by the radar sensor is a complex random variable containing amplitude information and phase information. The existing MB-TBD algorithm is for target tracking under the condition of no target fluctuation, and only amplitude information is considered while ignoring the phase information during the implementation process. The present invention considers two implementations under the condition of target amplitude fluctuation in MB-TBD. One is the squared modulus likelihood ratio under the square of the radar measurement, denoted as L S ; the other is the complex likelihood ratio considering the phase information, denoted as L C .

[0113] Specifically, in the step of using LABer-STC-TBD to adaptively generate new targets for the original measurement data at time k - 1:

[0114] The traditional MB-TBD assumes that the newly generated RFS is known a priori, and uses the prior knowledge to initialize the multi-Bernoulli filter (KpBer-TBD). However, in the case where the prior knowledge cannot be realized and the low signal-to-noise ratio, the multi-Bernoulli components may fail due to continuous misdetections, resulting in the inability of the traditional multi-Bernoulli filter to initialize the target. For the low signal-to-noise ratio environment, missed detection is a common phenomenon. If the newly generated target appears in the state area not covered by the target generation intensity, it is difficult for KpBer-TBD to detect the target, even if a large number of newly generated targets cover the entire space. The usual strategy is to let the newly generated distribution cover the entire scene. However, this requires a large number of particles to represent the newly generated model. Although this method can solve the problem, the efficiency is very low.

[0115] The LABer-STC-TBD algorithm first selects the measurements from the previous moment to adaptively generate new targets. Not all measurement information is used to drive the newly generated distribution, that is:

[0116]

[0117] Given the false alarm rate P of the resolution cell fa the threshold γ can be calculated. The threshold γ is to avoid information redundancy and discard the measurements that may come from noise or clutter. The present invention corrects a threshold γ that is more suitable for the target fluctuation situation:

[0118]

[0119] Since each Bernoulli component represents a target, and this paper considers target detection and tracking under the condition of non-overlapping targets, after selecting the measurements, partitioning is performed so that the particles in each cluster are generated by the measurements around the target diffusion position. This not only avoids the chaos of the particles in the assumed components but also minimizes the overlapping assumed components as much as possible. The adaptive newly generated distribution can be expressed as:

[0120]

[0121] After calculating the existence probability of each cluster, the hypothetical components with an existence probability lower than 0.5 are removed, and the existing measurements are corrected using the detected Bernoulli components to eliminate the influence of this component on the detection of the remaining targets. When the detected target has an effect on the resolution cell (l, m), the measurement of the resolution cell (l, m) after eliminating the effect of this target from the measurement equation is:

[0122]

[0123] At this time, the sensor is in the entire N r ×N θ The corrected measurement set obtained within the scene is:

[0124]

[0125] Return to the above steps and increase the false alarm rate until the existence probabilities of all Bernoulli components are lower than 0.5.

[0126] Specifically, in the steps of calculating the complex likelihood ratio and the squared modulus likelihood ratio for the three amplitude fluctuation types respectively:

[0127] Assume that the squared modulus vector under complex measurement is |z k | 2 , and the covariance matrix is is an N c -dimensional identity matrix. Calculate the squared modulus likelihood ratios for the amplitude fluctuation types of Swerling 0, 1, and 3 under squared measurement respectively:

[0128]

[0129]

[0130] where I0(·) is the first kind of modified Bessel function,

[0131] Calculate the complex likelihood ratios for the amplitude fluctuation types of Swerling 0, 1, and 3 under complex measurement respectively:

[0132]

[0133] Specifically, SMC prediction: Given the multi-Bernoulli posterior density at time k - 1 Each spatial probability density can be represented by a set of weighted particles , that is:

[0134]

[0135] The predicted multi-Bernoulli density can be expressed as:

[0136] For the multi-Bernoulli density of surviving targets there is

[0137]

[0138] For the multi-Bernoulli density of newly born targets there is:

[0139]

[0140] SMC update: Given the predicted multi-Bernoulli density at time k each spatial probability density can be represented by a set of weighted particles i.e.:

[0141]

[0142] Then the updated multi-Bernoulli multi-target density can be expressed as:

[0143]

[0144] wherein, note that in the present invention there are different likelihood ratios for different amplitude fluctuations.

[0145] Furthermore, similar to the standard multi-Bernoulli filter, each Bernoulli component resamples the particles after the update. To reduce the increasing number of trajectories, the components with a presence probability lower than the threshold H merge are discarded; however, this cannot accurately estimate the number of Bernoulli components, especially when the newly born Bernoulli components can also accurately estimate the true position of the target, which will cause a bias in the potential. The present invention gives the implementation of DPM in S4.

[0146] Specifically, in the steps of deleting the Bernoulli components with a presence probability lower than the threshold and merging the Bernoulli components using the DPM algorithm:

[0147] After the traditional multi-Bernoulli filter is updated, the components with a presence probability lower than the threshold H mergeThe Bernoulli components, or assuming that multiple Bernoulli components are independent within each other's given ranges, so as to reduce the increase in Bernoulli components. Under the LABer-STC-TBD algorithm, after the likelihood ratio screening and target sequential elimination of the newborn Bernoulli components, the true position of the target is represented as much as possible. After the update, the newborn targets are also left as much as possible. Then, the remaining Bernoulli components after the update are the sum of the surviving Bernoulli components at the previous moment and the Bernoulli components under adaptive newborn. To solve the problem of the linear growth of Bernoulli components after the update, an algorithm for trajectory merging based on distance and particle weights (DPM) is proposed.

[0148] The DPM algorithm first classifies the Bernoulli components according to the distance. The multiple Bernoulli components before merging can be expressed as M k|k represents the total number of components after the update. The Bernoulli components within the threshold represent the same target. At this time, the multiple Bernoulli components can be expressed as:

[0149]

[0150] Among them, represents the Bernoulli component of the same target. M k|k components are divided into M N classes in total, 1 ≤ M j ≤ M N .

[0151] Subsequently, retain the hypothesis component with the highest existence probability for the same target. Then, the Bernoulli components before selection are After selection, there is only one component for the same target, that is:

[0152]

[0153] Among them, |·| represents the cardinality of the set.

[0154] If the existence probabilities of two components are the same, that is and the distance of the Bernoulli components is within the threshold, they are merged into one Bernoulli component and resampled, while the hypothesis components outside the threshold are retained.

[0155] Specifically, in the steps of extracting the Bernoulli components and estimating the number of targets:

[0156] After the DPM algorithm ends, extract the Bernoulli components with an existence probability greater than 0.5. The number of Bernoulli components with an existence probability greater than 0.5 is the estimated number of targets. Specific Example 1:

[0158] In this embodiment, MATLAB software version 2014(a) is used for simulation experiments.

[0159] Please refer to Figure 3 , set the three target motions shown, consider a two-dimensional motion scenario, and the state of each target is defined as

[0160] where (x k , y k ) and are the position and velocity of the target in the Cartesian coordinate system, respectively.

[0161] The position (x k , y k ) is within the polar coordinate p = [r min , r max × [θ min , θ max scenario, where r min , r max and θ min , θ max are the minimum and maximum target ranges and azimuths, respectively;

[0162] The velocity is in the region:

[0163]

[0164] where v min and v max are the minimum and maximum target velocities, respectively.

[0165] The target state evolves according to uniform rectilinear motion:

[0166] x k = Fx k-1 + v k

[0167] The sensor scans 100 frames of images at a time interval T = 1s, where

[0168]

[0169] The process noise v k obeys a Gaussian distribution, and its covariance is:

[0170]

[0171] The noise standard deviation σ v = 5m, and the probability of target survival is p s,k (x) = 0.98.

[0172] For the simulation of the target, v min= 200 m / s, v max = 800 m / s, the signal-to-noise ratio is given by given below.

[0173] For the simulation of radar measurements, r min = 100 km, r max = 120 km, θ min = -75°, θ max = 75°, N r = 300, N θ = 100, σ 2 = 0.5, the noise covariance is Γ = 2σ 2 I Nc , B = 150 KHz, T e = 6.67×10 -5 s, N a = 55, λ = 3 cm, c = 3×10 8 m / s, Δ r = 400 m, Δ θ = 1°.

[0174] Note: The trajectory conditions of the three targets in this specific embodiment

[0175]

[0176] The optimal sub-pattern assignment distance (OSPA) is used to evaluate the algorithm performance. The OSPA metric can evaluate the target number estimation error and target position estimation error of a multi-target filter. Given two finite sets X = {x1, x2,... x m} and Y = {y1, y2,... y n}, the OSPA is defined as follows:

[0177]

[0178] where, d c (X, Y) = min{c, d b (X, Y)}, c > 0 is the truncation parameter, used to penalize the estimation bias of the target number, and p is the order, used to penalize the multi-target state estimation bias. In the simulation experiments in this paper, p = 1 and c = 1000 are set. The smaller the OSPA value, the more accurate the target number and state estimation. At SNR = 9 dB, the number of particles for each newborn Bernoulli component is 1000, and 100 Monte Carlo experiments are used for simulation. Based on the LABer-STC-TBD algorithm and the KpBer-TBD algorithm under different amplitude fluctuations, the following 4 filters are implemented:

[0179] 1. The first filter is labeled "LA-STC-Com", considering the LABer-STC-TBD algorithm under the complex likelihood ratio of the multi-Bernoulli filter.

[0180] 2. The second filter is labeled "LA-STC-Squ", considering the LABer-STC-TBD algorithm under the squared modulus likelihood ratio of the multi-Bernoulli filter.

[0181] 3. The third filter is labeled "Kp-Com", considering the KpBer-TBD algorithm under the complex likelihood ratio of the multi-Bernoulli filter.

[0182] 4. The fourth filter is labeled "Kp-Squ", considering the KpBer-TBD algorithm under the squared modulus likelihood ratio of the multi-Bernoulli filter.

[0183] Simulation results and analysis: Set three targets to move in a uniform straight line within the scene, and the original trajectories of the targets are as Figure 3 shown. This simulation considers verifying the generality and effectiveness of the LABer-STC-TBD algorithm and the DPM algorithm in the case of target amplitude fluctuations in the method of the present invention, and detecting and estimating multiple targets based on the LABer-STC-TBD algorithm and the KpBer-TBD algorithm under different amplitude fluctuations. In order to better reflect the effectiveness of the tracking effect of the algorithm in this paper, at SNR = 9dB, the number of particles for each newborn Bernoulli component is 1000, and the OSPA error statistics and cardinality estimation statistics of 100 Monte Carlo experiments are used to illustrate the tracking performance. The multi-Bernoulli density of the birth process is:

[0184]

[0185] where r Γ = 0.1,

[0186] P γ = diag([3000, 500, 3000, 500] T ) 2 .

[0187] Figures 4 - 9It shows two likelihood ratio calculation methods of the LABer-STC-TBD algorithm and the KpBer-TBD algorithm under three amplitude fluctuation types Swerling 0, 1, and 3. According to the Monte Carlo average OSPA distance estimation error and the average target number estimation, the results confirm that the LABer-STC-TBD algorithm under multi-Bernoulli-TBD can accurately estimate the target position and the number of targets. Although the estimation error of the KpBer-TBD algorithm is smaller than that of the LABer-STC-TBD algorithm at the initial moment, the error increases rapidly and finally shows a divergent state. This is because the KpBer-TBD algorithm is given a correct initialization, and for the first few moments, the prediction of the state transition equation happens to be close to the true state. After that, with the interference of uncertainties such as noise and clutter, the target state prediction will decline, ultimately leading to a worse and worse tracking effect and a higher and higher error. The same is true for the estimation of the number of targets. During the target amplitude fluctuation process, the target echoes at some times will be completely submerged in the noise, while the LABer-STC-TBD algorithm will use the measurement information of the previous moment to search for the location of the real target as much as possible, making the estimated number accurate, and the filter can maintain iteration even if all the target information is submerged by noise at a certain moment; while the KpBer-TBD algorithm fails to estimate the target at a certain moment, and when the target moves at a high speed, the target will not be estimated in the next moment, resulting in the failure of the filter. And Figures 4 - 9 It also shows that the filter with complex likelihood ratio is better than the filter with square modulus likelihood ratio.

[0188] By Figures 4 - 9 Comparing these four filter algorithms, the LABer-STC-TBD algorithm under complex likelihood ratio has the best effect, which proves that the introduction of phase information can improve the detection and tracking performance of the MeMBer-TBD algorithm. Moreover, the selection of the measurement threshold of the new algorithm not only reduces the computational complexity, but also the selected measurement is based on the target amplitude, and the measurement generated by the real target is selected to the greatest extent. Using the likelihood ratio to screen the Bernoulli components to eliminate the wrong estimates of the previous moment, the introduction of the STC idea avoids the influence of strong and weak target echoes at the same moment and maximally excavates the target echo information. From Figure 5 , 7, 9, it can be seen that for targets with amplitude fluctuation types Swerling 1 and 3, the LABer-STC-TBD under square modulus likelihood ratio is inaccurate in estimating the number of targets. This is because the square measurement ignores the phase information of the target. Comparing Figure 6 it can be seen that the loss of phase information is extremely obvious for fluctuating targets. Specific Embodiment 2:

[0190] The MATLAB version used in this embodiment, radar simulation, and the OSPA for evaluating the algorithm performance are the same as those in Embodiment 1, and will not be repeated here.

[0191] Please refer to Figure 10 , set the five target motions shown, consider a two-dimensional motion scenario, and the target state variables include the planar position as well as the velocity and the turning rate ω k . The state transition model is:

[0192]

[0193] ω k = ω k-1 + Δu k-1

[0194] where:

[0195]

[0196] Δ = 1s, σ ω = 15m / s 2 and σ u = π / 180m / s 2 .

[0197] Attachment: Trajectory conditions of the five targets in this specific embodiment

[0198]

[0199] Track the target trajectories in two scenarios of SNR = 7 and SNR = 5. The number of particles for each newborn Bernoulli component is 1000. Use 100 Monte Carlo experiments for simulation. Under different amplitude fluctuations, consider the LABer-STC-TBD algorithm and compare the algorithm simulations. Consider the following two filters:

[0200] The first filter is marked as "Comp mod", considering the LABer-STC-TBD filter under CLR.

[0201] The second filter is marked as "Sq mod", considering the LABer-STC-TBD filter under SLR.

[0202] Simulation results and analysis: From Figures 11 - 16The detection performances of different MB-TBD strategies for Swerling 0, 1, and 3 targets are shown respectively. The advantages of the complex likelihood ratio MB-TBD algorithm at low signal-to-noise ratios are verified. For all detection results, the MB-TBD filter using the complex likelihood ratio is superior to the MB-TBD filter using the squared modulus likelihood ratio. The introduction of phase information improves the system performance, enabling relatively accurate detection and tracking of targets even at low signal-to-noise ratios. Moreover, under the same type of fluctuation, the complex likelihood ratio only requires one calculation of the Bessel function, while the squared modulus likelihood ratio requires multiple Bessel function operations, effectively reducing the computational complexity.

[0203] Figures 11 - 12 The MB-TBD algorithm representing the case of no target fluctuation, where both the SLR and CLR can accurately estimate the target state and the number of targets; Figures 13 - 16 The MeMBer-TBD algorithm representing the cases of Swerling 1 and 3 fluctuation types still demonstrates the advantage of the complex likelihood ratio over the squared modulus likelihood ratio. However, when the signal-to-noise ratio is too low, the estimated number of targets often underestimates the true number of targets because the fluctuations in target amplitude cause the intensities of some targets to be submerged in the noise.

[0204] The present invention is based on a multiple Bernoulli filter-based track-before-detect algorithm (MB-TBD) to detect multiple weak fluctuating radar targets of Swerling 0, 1, and 3 amplitude types. First, MB-TBD usually only performs marginal integration on amplitude information without considering the fact that the measurements are complex numbers. In the present invention, in addition to considering amplitude information, phase marginalization is also performed in MB-TBD to improve the distinguishability between targets and noise. More precisely, the complex likelihood ratio (CLR) of three Swerling types is used instead of the squared modulus likelihood ratio (SLR). In addition, to adapt to the situation where the prior information of the birth of fluctuating targets is unknown, an idea of successive division of targets is borrowed to propose a TBD (LABer-STC-TBD) for adapting the multiple Bernoulli filter's birth distribution based on the measurement likelihood ratio. Compared with the existing MB-TBD adaptive birth algorithms, the new algorithm overcomes the detection difficulties when weak and strong targets appear simultaneously during target fluctuations, and after the MB-TBD update is completed, an algorithm (DPM) based on distance and particle weights is proposed to merge the Bernoulli components of the same target. Finally, the estimation and detection performances in different situations studied are compared, and the advantages of LABer-STC-TBD under target amplitude fluctuations are shown, and for the three fluctuation models, the CLR method is superior to the SLR method in both detection and estimation.

[0205] The above-disclosed is only a preferred embodiment of the present invention. Of course, the scope of the rights of the present invention cannot be limited thereby. Those of ordinary skill in the art can understand all or part of the processes of implementing the above embodiments, and the equivalent changes made according to the claims of the present invention still fall within the scope covered by the invention.

Claims

1. A pre-tracking method for detecting weak fluctuating radar targets based on multi-Bernoulli filtering, characterized in that, It includes the following steps: S1: Initialize system parameters and read the original measurement data at the (k - 1)-th and k-th moments in the radar receiver; S2: Use the LABer-STC-TBD algorithm to adaptively generate new targets for the original measurement data at the (k - 1)-th moment; S3: Obtain the complex measurement and squared measurement data at the k-th moment, calculate the complex likelihood ratio and squared modulus likelihood ratio for three types of amplitude fluctuations respectively, and give the SMC implementation of MB-TBD filtering under amplitude fluctuations; S4: Delete the Bernoulli components with probabilities lower than the threshold, and use the DPM algorithm to merge the Bernoulli components; S5: Extract the Bernoulli components and estimate the number of targets; S6: Judge whether k + 1 is greater than the total target movement time. If it is greater, the algorithm ends. Otherwise, return to S2; In the step of using the LABer-STC-TBD algorithm to adaptively generate new targets for the original measurement data at the (k - 1)-th moment: False alarm rate \(P\) of a given resolution cell fa That is, the threshold \(\gamma\) can be calculated to correct a threshold \(\gamma\) that is more suitable for the target fluctuation situation: The LABer-STC-TBD algorithm first selects the measurements from the previous moment to adaptively generate new targets, that is: The adaptive new target distribution can be expressed as: Eliminate the Bernoulli components with probabilities lower than 0.5, and use the detected Bernoulli components to correct the existing measurements to eliminate the influence of this component on detecting the remaining targets. When the detected target affects the resolution cell (l, m), the measurement of the resolution cell (l, m) after eliminating the influence of this target by using the measurement equation is: At this time, the sensor obtains the corrected measurement set within the entire N r ×N θ The corrected measurement set within the scene is as follows: Return to the above steps and increase the false alarm rate until the probabilities of existence of all Bernoulli components are lower than 0.

5.

2. The pre-tracking method for detecting radar weakly fluctuating targets based on multi-Bernoulli filtering according to claim 1, characterized in that, The system parameters include: Sampling interval T, current time k, total target movement time K, the radar scanning area in polar coordinates [r min , r max ×[θ min , θ max , the radar receives the measurement data Z k and Z k-1 , a range and azimuth surveillance radar that covers the defined area in polar coordinates. For the range, assume that the transmitted pulse is a linear frequency modulation signal with bandwidth B and duration T ε , the speed of light c, the range resolution cell For the angle, at the radar receiving end, a phased array system composed of N a linearly arranged antenna elements is adopted, with an interval of where λ is the wavelength of the carrier frequency, and the angle resolution is 3. The pre-tracking method for radar weak fluctuation target detection based on multi-Bernoulli filtering according to claim 1, characterized in that, In the step of calculating the complex likelihood ratio and squared modulus likelihood ratio for three types of amplitude fluctuations respectively: Calculate the squared modulus likelihood ratios for amplitude fluctuation types Swerling 0, 1, and 3 respectively; Calculate the complex likelihood ratios for amplitude fluctuation types Swerling 0, 1, and 3 respectively.

4. The radar pre-tracking method for detecting weak fluctuating targets based on multi-Bernoulli filtering according to claim 3, characterized in that, In the step of deleting the Bernoulli components with probabilities lower than the threshold and using the DPM algorithm to merge the Bernoulli components: The DPM algorithm first deletes Bernoulli components with probabilities lower than the threshold. Secondly, it classifies the Bernoulli components based on distance. Then, it retains the Bernoulli component with the highest probability of the same target, and there is only one component of the same target after selection; if the probabilities of two components are the same, that is and the distance of the Bernoulli components is within the threshold, then these two components are merged and a new component is redefined, specifically depending on and 5. The radar pre-tracking method for weak fluctuating targets based on multi-Bernoulli filtering according to claim 4, characterized in that, In the step of extracting the Bernoulli components and estimating the number of targets: After the DPM algorithm ends, extract the Bernoulli components with probabilities greater than 0.5, and the number of Bernoulli components with probabilities greater than 0.5 is the estimated number of targets.

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