CN103809173A - Detection and tracking integration method for frame constant false-alarm target - Google Patents

Detection and tracking integration method for frame constant false-alarm target Download PDF

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CN103809173A
CN103809173A CN201410070414.1A CN201410070414A CN103809173A CN 103809173 A CN103809173 A CN 103809173A CN 201410070414 A CN201410070414 A CN 201410070414A CN 103809173 A CN103809173 A CN 103809173A
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刘宏伟
周生华
刘红亮
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/66—Radar-tracking systems; Analogous systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/411—Identification of targets based on measurements of radar reflectivity
    • G01S7/412—Identification of targets based on measurements of radar reflectivity based on a comparison between measured values and known or stored values

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Abstract

本发明公开了一种帧恒虚警目标检测跟踪一体化方法，主要解决现有技术目标检测概率较低、目标跟踪距离较短的问题。其实现过程是：1）通过航迹起始算法得到目标的初始状态估计值和初始状态估计协方差矩阵；2）根据第k-1帧目标状态估计值和第k-1帧状态估计协方差矩阵，确定第k帧目标预测波门；3）计算第k帧目标预测波门内各个检测单元的虚警概率和检测门限；4）对目标预测波门内的回波信号进行检测，并估计目标参数，作为第k帧量测数据集合；5）对第k帧量测数据集合进行关联和滤波，得到第k帧目标状态估计值和第k帧状态估计协方差矩阵。本发明与现有检测跟踪方法相比，提高了目标的检测概率，扩展了目标的跟踪距离。

The invention discloses an integrated method for frame constant false alarm target detection and tracking, which mainly solves the problems of low target detection probability and short target tracking distance in the prior art. The implementation process is: 1) Obtain the initial state estimation value and the initial state estimation covariance matrix of the target through the track initiation algorithm; 2) According to the k-1th frame target state estimation value and the k-1th frame state estimation covariance matrix to determine the target prediction gate of the kth frame; 3) calculate the false alarm probability and detection threshold of each detection unit in the kth frame target prediction gate; 4) detect the echo signal in the target prediction gate, and estimate The target parameter is used as the measurement data set of the kth frame; 5) Correlate and filter the measurement data set of the kth frame to obtain the target state estimation value of the kth frame and the state estimation covariance matrix of the kth frame. Compared with the existing detection and tracking method, the invention improves the detection probability of the target and extends the tracking distance of the target.

Description

帧恒虚警目标检测跟踪一体化方法Frame constant false alarm target detection and tracking integrated method

技术领域 technical field

本发明属于雷达技术领域，具体的说是一种利用目标预测信息调整目标预测波门内各个检测单元虚警概率的检测跟踪方法，可用于雷达目标跟踪状态下提高目标检测概率，扩展目标跟踪距离。  The invention belongs to the field of radar technology, and specifically relates to a detection and tracking method for adjusting the false alarm probability of each detection unit in a target prediction wavegate by using target prediction information, which can be used to improve the target detection probability and expand the target tracking distance in the state of radar target tracking . the

背景技术 Background technique

现代雷达系统通常包含两大模块，即信号处理模块和数据处理模块。雷达信号处理模块作为第一次处理，将检测到的目标信息送入雷达数据处理模块做进一步处理。雷达数据处理模块在得到目标的位置、运动参数等估计量后进行预测、关联、滤波等操作，从而对雷达量测过程中的随机误差起到一定的抑制作用，使得对目标运动信息的估计更加准确，并形成稳定目标航迹。  A modern radar system usually consists of two major modules, a signal processing module and a data processing module. As the first processing, the radar signal processing module sends the detected target information to the radar data processing module for further processing. The radar data processing module performs operations such as prediction, association, and filtering after obtaining the target’s position, motion parameters, etc., so as to suppress the random error in the radar measurement process and make the estimation of the target’s motion information more accurate. Accurate and form a stable target track. the

目标检测是雷达信号处理模块的重要环节，主要的任务是对雷达接收到的回波信号进行处理，并判断目标的有无，由于噪声和干扰的影响，需要采用恒虚警方法来降低误判的概率，保证雷达信号检测具有恒虚警特性，常用的恒虚警检测算法包括单元平均恒虚警、顺序统计量恒虚警、广义似然比、自适应匹配滤波等。  Target detection is an important part of the radar signal processing module. The main task is to process the echo signal received by the radar and judge the presence or absence of the target. Due to the influence of noise and interference, it is necessary to use the constant false alarm method to reduce misjudgment The probability ensures that radar signal detection has CFAR characteristics. Commonly used CFAR detection algorithms include unit average CFAR, order statistics CFAR, generalized likelihood ratio, adaptive matched filter, etc. the

目标跟踪是基于检测得到的目标位置信息，通过滤波连续地跟踪出目标的航迹。在目标跟踪算法中，主要有线性自回归滤波，两点外推滤波，维纳滤波，加权最小二乘滤波，α-β滤波和卡尔曼滤波等，其中卡尔曼滤波可用于线性时变系统，其变形扩展卡尔曼滤波、转换量测卡尔曼滤波和不敏卡尔曼滤波可用于非线性时变系统，统计模型均采用状态方程和量测方程，且滤波方程以递推的方式计算，计算量小，实用性强，因此在目标跟踪理论中占了主导地位。  Target tracking is based on the detected target position information, and continuously tracks the track of the target through filtering. In the target tracking algorithm, there are mainly linear autoregressive filtering, two-point extrapolation filtering, Wiener filtering, weighted least square filtering, α-β filtering and Kalman filtering, among which Kalman filtering can be used for linear time-varying systems. Its deformed extended Kalman filter, converted measurement Kalman filter and insensitive Kalman filter can be used in nonlinear time-varying systems. Statistical models all use state equations and measurement equations, and the filter equations are calculated recursively. Small and practical, it has dominated the theory of object tracking. the

目标跟踪是在目标检测的基础上进行的，高的检测性能可以保证目标航迹的快速起始，而差的检测性能可以导致目标航迹的结束，因此目标的检测性能直接影响着目标的跟踪性能。对于传统的检测跟踪处理流程，首先进行目标检测并估计目标运动参数，得到量测信息后送入雷达数据处理模块，再进行预测、关联、滤波等处理，实现对目标的检测和跟踪。当目标回波信噪比较低时目标检测概率较低，将会造成目标航迹的不连续性，容易导致航迹过早地结束，因而目标跟踪距离较短。  Target tracking is carried out on the basis of target detection. High detection performance can ensure the rapid start of the target track, while poor detection performance can lead to the end of the target track. Therefore, the target detection performance directly affects the target tracking. performance. For the traditional detection and tracking processing flow, the target is detected first and the target motion parameters are estimated, and the measurement information is obtained and sent to the radar data processing module, and then the prediction, correlation, filtering and other processing are performed to realize the detection and tracking of the target. When the signal-to-noise ratio of the target echo is low, the target detection probability is low, which will cause the discontinuity of the target track, and easily lead to the premature end of the track, so the target tracking distance is short. the

发明内容 Contents of the invention

本发明的目的在于针对上述已有技术的不足，提出了一种帧恒虚警目标检测跟踪一体化方法，在保证不产生虚假航迹的条件下，调整目标预测波门内各个检测单元的虚警概率，从而提高跟踪状态下目标的检测概率，扩展目标的跟踪距离。  The purpose of the present invention is to address the deficiencies in the prior art above, and propose a frame constant false alarm target detection and tracking integration method, under the condition of ensuring that no false track is generated, adjust the virtual position of each detection unit in the target prediction wave gate. The alarm probability can be improved, thereby improving the detection probability of the target in the tracking state and extending the tracking distance of the target. the

为实现上述目的，本发明包括如下技术步骤：  To achieve the above object, the present invention comprises the following technical steps:

1）初始化参数：通过目标航迹起始算法，得到目标航迹的初始状态估计值以及初始状态估计协方差矩阵P0；  1) Initialization parameters: through the target track initial algorithm, the initial state estimation value of the target track is obtained And the initial state estimation covariance matrix P 0 ;

2）设定目标状态转移方程和雷达量测方程，根据第k-1帧目标状态估计值计算第k帧目标状态预测值

Figure BDA0000471044010000023
和第k帧目标量测的预测值
Figure BDA0000471044010000024
2) Set the target state transition equation and radar measurement equation, according to the estimated value of the target state in the k-1th frame Calculate the target state prediction value of the kth frame
Figure BDA0000471044010000023
and the predicted value of the k-th frame target measurement
Figure BDA0000471044010000024

3）根据第k-1帧状态估计协方差矩阵Pk-1和步骤2）得到的第k帧目标状态预测值 计算第k帧目标量测的预测协方差矩阵Dk|k-1；  3) According to the k-1th frame state estimation covariance matrix P k-1 and the predicted value of the k-th frame target state obtained in step 2) Calculate the prediction covariance matrix D k|k-1 of the target measurement of the kth frame;

4）根据步骤2）得到的第k帧目标量测的预测值和步骤3）得到的第k帧目标量测的预测协方差矩阵Dk|k-1，确定第k帧目标预测波门Ok；  4) According to the predicted value of the k-th frame target measurement obtained in step 2) and the prediction covariance matrix D k|k-1 of the k-th frame target measurement obtained in step 3), and determine the k-th frame target prediction gate O k ;

5）设定在连续M帧的跟踪过程中至少N帧的目标预测波门内出现虚警的概率PF，则利用下式计算第k帧目标预测波门Ok内出现虚警的概率PZ：  5) Set the probability P F of the false alarm in the target prediction gate of at least N frames in the tracking process of consecutive M frames, then use the following formula to calculate the probability P of the false alarm in the target prediction gate O k of the kth frame Z :

ΣΣ nno == NN Mm [[ Mm !! nno !! (( Mm -- nno )) !! PP ZZ nno (( 11 -- PP ZZ )) Mm -- nno ]] == PP Ff ,,

其中，n表示连续M帧的跟踪过程中目标预测波门内出现虚警的可能帧数，符号!表示阶乘运算，M、N的取值需满足M＞N≥1；  Among them, n represents the possible number of false alarms in the target prediction gate in the tracking process of consecutive M frames, the symbol ! represents the factorial operation, and the values of M and N must satisfy M>N≥1;

6）根据步骤5）得到的第k帧目标预测波门Ok内出现虚警的概率PZ，计算第k帧目标预测波门Ok内各个检测单元的虚警概率和检测门限；  6) Calculate the false alarm probability and detection threshold of each detection unit in the k-th frame target prediction gate O k according to the probability P Z of false alarms in the target prediction gate O k of the k-th frame obtained in step 5);

7）根据步骤6）得到的第k帧目标预测波门Ok内各个检测单元的检测门限，对第k帧目标预测波门Ok内的回波信号进行检测，并估计目标参数，作为第k帧量测数据集合Z(k)；  7) According to the detection threshold of each detection unit in the k-th frame target prediction gate O k obtained in step 6), detect the echo signal in the k-th frame target prediction gate O k , and estimate the target parameters, as the first k frame measurement data set Z(k);

8）根据步骤7）得到的第k帧量测数据集合Z(k)，利用关联算法筛选出第k帧有效量测集合Zk，选取第k帧有效量测集合Zk中与航迹关联度最高的量测数据，并利用跟踪算法计算第k帧目标状态估计值

Figure BDA0000471044010000031
以及第k帧状态估计协方差矩阵Pk，返回步骤2）。  8) According to the measurement data set Z(k) of the kth frame obtained in step 7), use the association algorithm to filter out the effective measurement set Z k of the kth frame, and select the effective measurement set Z k of the kth frame to be associated with the track The measurement data with the highest degree of accuracy, and use the tracking algorithm to calculate the estimated value of the target state in the kth frame
Figure BDA0000471044010000031
And the state estimation covariance matrix P k of the kth frame, return to step 2).

本发明由于在计算目标预测波门内各个检测单元的虚警概率过程中，综合考虑了目标的预测信息以及虚假航迹的抑制问题，即保证了在连续M帧的跟踪过程中至少N帧的目标预测波门内出现虚警的概率PF，恒定了每一帧出现虚警的概率PZ，从而计算出目标预测波门内各个检测单元的虚警概率和检测门限，因此具有以下优点：  In the process of calculating the false alarm probability of each detection unit in the target prediction wave gate, the present invention comprehensively considers the prediction information of the target and the suppression of false tracks, that is, guarantees the tracking of at least N frames in the continuous M frame tracking process. The probability P F of false alarms in the target prediction gate keeps the probability P Z of false alarms in each frame constant, so as to calculate the false alarm probability and detection threshold of each detection unit in the target prediction gate, so it has the following advantages:

（1）目标预测波门内的检测门限低于传统检测跟踪方法的检测门限，提高了目标的检测概率；  (1) The detection threshold in the target prediction wave gate is lower than that of the traditional detection and tracking method, which improves the detection probability of the target;

（2）在低信噪比情况下仍具有较高的检测概率，提高了目标航迹的连续性，避免了目标航迹过早地结束，扩展了目标的跟踪距离；  (2) In the case of low signal-to-noise ratio, it still has a high detection probability, which improves the continuity of the target track, avoids the premature end of the target track, and extends the tracking distance of the target;

（3）当目标突然消失时，航迹能够以很高的概率正确结束，避免了虚假航迹的产生。  (3) When the target suddenly disappears, the track can end correctly with a high probability, avoiding the generation of false tracks. the

附图说明 Description of drawings

图1是本发明的工作流程图；  Fig. 1 is a work flow chart of the present invention;

图2是本发明与传统检测跟踪方法的检测性能对比图；  Fig. 2 is the detection performance contrast figure of the present invention and traditional detection tracking method;

图3是本发明与传统检测跟踪方法的探测距离对比图；  Fig. 3 is the comparison chart of the detection distance of the present invention and traditional detection and tracking method;

图4是目标在第10帧消失的情况下各帧目标航迹存在的概率图。  Figure 4 is a probability map of the existence of the target track in each frame when the target disappears in the tenth frame. the

具体实施方式 Detailed ways

参照图1，本发明的实现步骤如下：  With reference to Fig. 1, the realization steps of the present invention are as follows:

步骤1，初始化参数：通过目标航迹起始算法，得到目标航迹的初始状态估计值

Figure BDA0000471044010000032
以及初始状态估计协方差矩阵P0。  Step 1, initialize parameters: get the initial state estimation value of the target track through the target track initial algorithm
Figure BDA0000471044010000032
and the initial state estimation covariance matrix P 0 .

步骤2，设定目标状态转移方程和雷达量测方程，根据第k-1帧目标状态估计值 计算第k帧目标状态预测值

Figure BDA0000471044010000034
和第k帧目标量测的预测值
Figure BDA0000471044010000035
Step 2, set the target state transition equation and the radar measurement equation, according to the estimated value of the target state in the k-1th frame Calculate the target state prediction value of the kth frame
Figure BDA0000471044010000034
and the predicted value of the k-th frame target measurement
Figure BDA0000471044010000035

2a）设定目标状态转移方程为：  2a) Set the target state transition equation as:

xk＝Fk-1xk-1+vk-1，  x k = F k-1 x k-1 + v k-1 ,

其中，xk表示第k帧目标的状态，Fk-1表示第k-1帧目标的状态转移矩阵，xk-1表示第k-1帧目标的状态，vk-1表示第k-1帧的过程噪声，本实例中Fk-1采用以下形式：  Among them, x k represents the state of the target in frame k, F k-1 represents the state transition matrix of the target in frame k-1, x k-1 represents the state of the target in frame k-1, and v k-1 represents the state of the target in frame k-1. The process noise of 1 frame, F k-1 in this example takes the following form:

Ff kk -- 11 == 11 ΔTΔT 00 00 00 11 00 00 00 00 11 ΔTΔT 00 00 00 11 ,,

其中，ΔT表示雷达扫描周期，本实例中取ΔT＝2s。  Among them, ΔT represents the radar scanning period, and in this example, ΔT=2s. the

2b）设定雷达量测方程为：  2b) Set the radar measurement equation as:

zk＝hk(xk)+wk，  z k =h k (x k )+w k ,

其中，zk表示第k帧目标的量测值，hk(·)表示第k帧目标的量测函数，wk表示第k帧的量测噪声；  Among them, z k represents the measurement value of the target in the kth frame, h k ( ) represents the measurement function of the target in the kth frame, and w k represents the measurement noise in the kth frame;

2c）根据第k-1帧目标状态估计值

Figure BDA0000471044010000042
计算第k帧目标状态预测值
Figure BDA0000471044010000043
2c) According to the estimated value of the target state in the k-1th frame
Figure BDA0000471044010000042
Calculate the target state prediction value of the kth frame
Figure BDA0000471044010000043

xx ^^ kk || kk -- 11 == Ff kk -- 11 xx ^^ kk -- 11 ;;

2d）根据第k帧目标状态预测值

Figure BDA0000471044010000045
计算第k帧目标量测的预测值
Figure BDA0000471044010000046
2d) According to the predicted value of the target state in the kth frame
Figure BDA0000471044010000045
Calculate the predicted value of the target measurement at the kth frame
Figure BDA0000471044010000046

zz ^^ kk || kk -- 11 == hh kk (( xx ^^ kk || kk -- 11 )) ..

步骤3，根据第k-1帧状态估计协方差矩阵Pk-1和步骤2得到的第k帧目标状态预测值

Figure BDA0000471044010000048
计算第k帧目标量测的预测协方差矩阵Dk|k-1。  Step 3, according to the state estimation covariance matrix P k-1 of the k-1th frame and the predicted value of the target state of the k-th frame obtained in step 2
Figure BDA0000471044010000048
Calculate the prediction covariance matrix D k|k-1 of the target measurement in the kth frame.

3a）根据第k帧目标状态预测值

Figure BDA0000471044010000049
计算第k帧目标量测函数的雅克比矩阵Hk：  3a) According to the predicted value of the target state in the kth frame
Figure BDA0000471044010000049
Calculate the Jacobian matrix H k of the target measurement function of the kth frame:

Hh kk == ▿▿ xx (( hh kk TT (( xx )) )) || xx == xx ^^ kk || kk -- 11 ,,

其中，▽x(·)表示对向量x求导，(·)T表示转置运算，

Figure BDA00004710440100000411
表示函数
Figure BDA00004710440100000412
在处的函数值；  Among them, ▽ x (·) represents the derivative of the vector x, (·)T represents the transpose operation,
Figure BDA00004710440100000411
express function
Figure BDA00004710440100000412
exist function value at

3b）根据第k-1帧目标状态估计协方差矩阵Pk-1和步骤3a）得到的第k帧目标量测函数的雅克比矩阵Hk，计算第k帧目标量测的预测协方差矩阵Dk|k-1：  3b) According to the estimated covariance matrix P k-1 of the target state in the k-1th frame and the Jacobian matrix H k of the target measurement function in the k-th frame obtained in step 3a), calculate the prediction covariance matrix of the target measurement in the k-th frame D k|k-1 :

DD. kk || kk -- 11 == Hh kk [[ Ff kk -- 11 PP kk -- 11 Ff kk -- 11 TT ++ QQ kk -- 11 ]] Hh kk TT ,,

其中，Qk-1表示第k-1帧的过程噪声协方差矩阵，本实例中采用以下形式：  Among them, Q k-1 represents the process noise covariance matrix of the k-1th frame, and the following form is used in this example:

QQ kk -- 11 == σσ pp 22 ΔTΔT 33 // 33 ΔTΔT 22 // 22 00 00 ΔTΔT 22 ΔTΔT 00 00 00 00 ΔTΔT 33 // 33 ΔTΔT 22 // 22 00 00 ΔTΔT 22 // 22 ΔTΔT

其中，σp表示过程噪声标准差，本实例中取σp＝0.1。  Among them, σ p represents the standard deviation of the process noise, and σ p =0.1 is taken in this example.

步骤4，根据步骤2得到的第k帧目标量测的预测值

Figure BDA0000471044010000052
和步骤3得到的第k帧目标量测的预测协方差矩阵Dk|k-1，确定第k帧目标预测波门Ok。  Step 4, according to the predicted value of the k-th frame target measurement obtained in step 2
Figure BDA0000471044010000052
and the prediction covariance matrix D k|k-1 of the target measurement in the kth frame obtained in step 3 to determine the target prediction gate O k in the kth frame.

4a）设定目标落入第k帧目标预测波门Ok的概率PG，本实例中取PG＝0.9997，通过查自由度为目标量测维数的卡方分布表，得到第k帧目标预测波门的门限γ，其中卡方分布表是概率论中卡方分布随机变量的分布函数对照表；  4a) Set the probability PG of the target falling into the target prediction gate O k in the kth frame. In this example, PG = 0.9997. By checking the chi-square distribution table with the degree of freedom as the target measurement dimension, the kth frame is obtained The threshold γ of the target prediction wave gate, wherein the chi-square distribution table is a distribution function comparison table of chi-square distribution random variables in probability theory;

4b）根据步骤4a）得到的第k帧目标预测波门Ok的门限γ，按如下公式确定第k帧目标预测波门Ok：  4b) According to the threshold γ of the target prediction gate O k of the k-th frame obtained in step 4a), determine the target prediction gate O k of the k-th frame according to the following formula:

Oo kk == {{ ythe y || (( ythe y -- zz ^^ kk || kk -- 11 )) TT DD. kk || kk -- 11 -- 11 (( ythe y -- zz ^^ kk || kk -- 11 )) ≤≤ γγ }} ,,

其中，y表示目标出现的位置，|表示条件符号，符号左边是集合元素，右边是元素满足的条件。  Among them, y indicates the position where the target appears, | indicates the condition symbol, the left side of the symbol is the set element, and the right side is the condition that the element satisfies. the

步骤5，设定在连续M帧的跟踪过程中至少N帧的目标预测波门内出现虚警的概率PF，则利用下式计算第k帧目标预测波门Ok内出现虚警的概率PZ：  Step 5, set the probability P F of the false alarm in the target prediction gate of at least N frames during the tracking process of consecutive M frames, then use the following formula to calculate the probability of false alarm in the target prediction gate O k of the kth frame P Z :

ΣΣ nno == NN Mm [[ Mm !! nno !! (( Mm -- nno )) !! PP ZZ nno (( 11 -- PP ZZ )) Mm -- nno ]] == PP Ff ,,

其中，n表示连续M帧的跟踪过程中目标预测波门内出现虚警的可能帧数，符号!表示阶乘运算，M、N的取值需满足M＞N≥1，本实例中取M＝100，N＝3，PF＝0.08；  Among them, n represents the possible number of false alarms in the target prediction gate in the tracking process of consecutive M frames, and the symbol ! represents the factorial operation, and the values of M and N must satisfy M>N≥1. In this example, M= 100, N=3, P F =0.08;

步骤6，设定雷达检波器形式，根据目标检测算法得到第k帧目标预测波门Ok内第i个检测单元的检测统计量ξ(i;k),i＝1,2,...,Nk，其中，Nk表示第k帧目标预测波门Ok内检测单元的个数；  Step 6, set the form of the radar detector, and obtain the detection statistics ξ(i;k) of the i-th detection unit in the k-th frame target prediction gate O k according to the target detection algorithm, i=1,2,... , N k , wherein, N k represents the number of detection units in the kth frame target prediction gate O k ;

所述雷达检波器的检波形式包括，平方率检波、线性检波等，本实例选用但不限于平方率检波器。  The detection form of the radar detector includes square rate detection, linear detection, etc., but not limited to the square rate detector is selected in this example. the

所述目标检测算法包括，单元平均恒虚警、顺序统计量恒虚警、广义似然比、自适应匹配滤波等，本实例选用但不限于单元平均恒虚警检测算法，即通过如下公式计算第k帧目标预测波门Ok内第i个检测单元的检测统计量ξ(i;k)：  The target detection algorithm includes unit average CFAR, sequential statistic constant false alarm, generalized likelihood ratio, adaptive matched filtering, etc. This example uses but is not limited to unit average CFAR detection algorithm, which is calculated by the following formula The detection statistic ξ(i;k) of the i-th detection unit in the k-th frame target prediction gate O k :

ξξ (( ii ;; kk )) == xx (( ii ;; kk )) ΣΣ ll == 11 NN rr ythe y (( ll ;; ii ,, kk )) ,, ii == 1,21,2 ,, .. .. .. ,, NN kk ,,

其中，x(i;k)表示第k帧目标预测波门Ok内第i个检测单元的检波器输出数据，y(l;i,k)表示第k帧目标预测波门Ok内第i个检测单元的参考窗内第l个参考单元的检波器输出数据，Nr表示参考窗内参考单元的个数，本实例中取Nr＝20。  Among them, x(i; k) represents the detector output data of the i-th detection unit in the k-th frame target prediction gate O k , and y(l; i, k) represents the k-th frame target prediction gate O k’s detector output data. The detector output data of the lth reference unit in the reference window of the i detection unit, N r represents the number of reference units in the reference window, and N r =20 in this example.

步骤7，根据步骤6得到的第k帧目标预测波门Ok内各个检测单元的检测统计量，计算第k帧目标预测波门Ok内各个检测单元的虚警概率和检测门限。  Step 7, according to the detection statistics of each detection unit in the k-th frame target prediction gate O k obtained in step 6, calculate the false alarm probability and detection threshold of each detection unit in the k-th frame target prediction gate O k .

7a）设定第k帧目标预测波门Ok内第i个检测单元的检测统计量的权值w(i;k), i＝1,2,...,Nk本实例中取w(i;k)＝1/Nk,i＝1,2,...,Nk，得到第k帧目标预测波门Ok内第i个检测单元的加权检测统计量ξ′(i;k)：  7a) Set the weight w(i;k) of the detection statistic of the i-th detection unit in the target prediction gate O k of the k-th frame, i=1,2,...,N k In this example, take w (i; k) = 1/N k , i=1,2,...,N k , to obtain the weighted detection statistic ξ'(i; k):

ξ′(i;k)＝w(i;k)ξ(i;k),i＝1,2,...,Nk；  ξ'(i;k)=w(i;k)ξ(i;k),i=1,2,...,N k ;

7b）利用如下方程组计算第k帧目标预测波门Ok内各个检测单元的虚警概率和检测门限：  7b) Use the following equations to calculate the false alarm probability and detection threshold of each detection unit in the k-th frame target prediction gate O k :

ΠΠ ii == 11 NN kk [[ 11 -- PP ff (( ii ;; kk )) ]] == 11 -- PP ZZ PP ff (( ii ;; kk )) == PrPR {{ ξξ ′′ (( ii ;; kk )) ≥&Greater Equal; TT (( kk )) || Hh 00 }} ,, ii == 1,21,2 ,, .. .. .. NN kk ,,

其中，Pf(i;k)表示第k帧目标预测波门Ok内第i个检测单元的虚警概率，H0表示目标不存在的情况，T(k)表示第k帧目标预测波门Ok内各个检测单元的检测门限，Pr{ξ′(i;k)≥T(k)|H0}表示在目标不存在的情况下第k帧目标预测波门Ok内第i个检测 单元的加权检测统计量ξ′(i;k)超过检测门限T(k)的概率。  Among them, P f (i; k) represents the false alarm probability of the i-th detection unit in the k-th frame target prediction wave gate O k , H 0 represents the situation where the target does not exist, and T(k) represents the k-th frame target prediction wave The detection threshold of each detection unit in the gate O k , Pr{ξ′(i;k)≥T(k)|H 0 } means that when the target does not exist, the target prediction of the kth frame in the gate O k The probability that the weighted detection statistic ξ'(i;k) of the detection unit exceeds the detection threshold T(k).

步骤8，根据步骤7得到的第k帧目标预测波门Ok内各个检测单元的检测门限T(k)，对第k帧目标预测波门Ok内的回波信号进行检测，并估计目标参数，作为第k帧量测数据集合Z(k)；  Step 8, according to the detection threshold T(k) of each detection unit in the k-th frame target prediction gate O k obtained in step 7, detect the echo signal in the k-th frame target prediction gate O k , and estimate the target Parameter, as the kth frame measurement data set Z(k);

步骤9，根据步骤8得到的第k帧量测数据集合Z(k)，利用关联算法筛选出第k帧有效量测集合Zk，选取该有效量测集合Zk中航迹关联度最高的量测数据。  Step 9: According to the k-th frame measurement data set Z(k) obtained in step 8, use the association algorithm to filter out the k-th frame effective measurement set Z k , and select the quantity with the highest track correlation degree in the effective measurement set Z k measurement data.

所述关联算法包括，最近邻域算法、概率数据关联算法、最优贝叶斯关联算法等，本实例选用但不限于概率数据关联算法，即按照如下步骤选取航迹关联度最高的量测数据：  The association algorithm includes the nearest neighbor algorithm, the probabilistic data association algorithm, the optimal Bayesian association algorithm, etc. This example uses but is not limited to the probabilistic data association algorithm, that is, the measurement data with the highest degree of track correlation is selected according to the following steps :

9a）利用下式计算第k帧新息协方差矩阵Sk：  9a) Use the following formula to calculate the innovation covariance matrix S k of the kth frame:

Sk＝Dk|k-1+Rk，  S k =D k|k-1 +R k ,

其中，Dk|k-1表示第k帧目标量测的预测协方差矩阵，Rk表示第k帧量测协方差矩阵；  Among them, D k|k-1 represents the prediction covariance matrix of the target measurement of the kth frame, and R k represents the measurement covariance matrix of the kth frame;

9b）设定目标量测数据被选取为有效量测的概率Pg，本实例中选取Pg＝0.9997，通过查自由度为目标量测维数的卡方分布表，获得有效量测的门限η，并确定第k帧有效量测区域Ak：  9b) Set the probability P g that the target measurement data is selected as an effective measurement. In this example, select P g = 0.9997, and obtain the threshold of effective measurement by checking the chi-square distribution table with the degree of freedom as the target measurement dimension η, and determine the effective measurement area A k of the kth frame:

AA kk == {{ zz || (( zz -- zz ^^ kk || kk -- 11 )) TT SS kk -- 11 (( zz -- zz ^^ kk || kk -- 11 )) ≤≤ ηη }} ,,

其中，z表示目标量测可能出现的位置，

Figure BDA0000471044010000072
表示第k帧目标量测的预测值，|表示条件符号，符号左边是集合元素，右边是元素满足的条件；  Among them, z represents the position where the target measurement may occur,
Figure BDA0000471044010000072
Indicates the predicted value of the k-th frame target measurement, | indicates the condition symbol, the left side of the symbol is the set element, and the right side is the condition that the element satisfies;

9c）筛选出第k帧量测数据集合Z(k)中落入第k帧有效量测区域Ak内的量测数据，作为第k帧有效量测集合Zk，并利用下式计算该有效量测集合Zk中第j个量测数据的新息vj：  9c) Screen out the measurement data that falls into the effective measurement area A k of the k-th frame from the measurement data set Z(k) of the k-th frame as the effective measurement set Z k of the k-th frame, and use the following formula to calculate the The innovation v j of the jth measurement data in the effective measurement set Z k :

vv jj == ZZ kk (( jj )) -- zz ^^ kk || kk -- 11 ,, jj == 1,21,2 ,, .. .. .. ,, mm kk ,,

其中，Zk(j)表示第k帧有效量测集合Zk中第j个量测数据，mk表示第k帧有效量测集 合Zk中量测数据个数；  Wherein, Z k (j) represents the j measurement data in the effective measurement set Z k of the kth frame, and m k represents the measurement data number in the effective measurement set Z k of the k frame;

9d）根据步骤9a）得到的第k帧新息协方差矩阵Sk和步骤9c）得到的第k帧有效量测集合Zk中第j个量测数据的新息vj，计算第k帧有效量测集合Zk中各个量测数据的航迹关联度βj：  9d) According to the innovation covariance matrix S k of the kth frame obtained in step 9a) and the innovation v j of the jth measurement data in the kth effective measurement set Zk obtained in step 9c), calculate the kth frame The track correlation degree β j of each measurement data in the effective measurement set Z k :

Figure BDA0000471044010000081
Figure BDA0000471044010000081

其中，

Figure BDA0000471044010000082
表示均值为0、方差为新息协方差矩阵Sk的高斯随机矢量在vj处的概率密度值，Pd表示第k帧目标的检测概率，Vk表示第k帧有效量测区域Ak的面积，本实例中取
Figure BDA0000471044010000083
其中，|Sk|表示第k帧新息协方差矩阵Sk的行列式；  in,
Figure BDA0000471044010000082
Indicates the probability density value of the Gaussian random vector with the mean value of 0 and the variance of the innovation covariance matrix S k at v j , P d represents the detection probability of the target in the kth frame, and V k represents the effective measurement area A k in the kth frame The area of , in this example take
Figure BDA0000471044010000083
Among them, |S k | represents the determinant of the innovation covariance matrix S k of the kth frame;

9e）选取第k帧有效量测集合Zk中各个量测数据的航迹关联度中最大值对应的量测数据。  9e) Select the measurement data corresponding to the maximum value among the track correlation degrees of each measurement data in the effective measurement set Z k of the kth frame.

步骤10，根据步骤9得到的第k帧有效量测集合Zk，利用跟踪算法计算第k帧目标状态估计值

Figure BDA0000471044010000084
以及第k帧状态估计协方差矩阵Pk，返回步骤2。  Step 10, according to the effective measurement set Z k of the kth frame obtained in step 9, use the tracking algorithm to calculate the target state estimation value of the kth frame
Figure BDA0000471044010000084
and the state estimation covariance matrix P k of the kth frame, return to step 2.

所述跟踪算法包括，卡尔曼滤波、扩展卡尔曼滤波、转换量测卡尔曼滤波、不敏卡尔曼滤波，粒子滤波等，本实例选用但不限于扩展卡尔曼滤波算法，即按照如下步骤计算第k帧目标状态估计值

Figure BDA0000471044010000085
以及第k帧状态估计协方差矩阵Pk：  The tracking algorithm includes Kalman filter, extended Kalman filter, conversion measurement Kalman filter, insensitive Kalman filter, particle filter, etc. This example uses but is not limited to the extended Kalman filter algorithm, that is, calculate the first Target state estimate for k frames
Figure BDA0000471044010000085
And the k-th frame state estimation covariance matrix P k :

10a）利用如下公式计算滤波增益矩阵Kk：  10a) Use the following formula to calculate the filter gain matrix K k :

KK kk == (( Ff kk -- 11 PP kk -- 11 Ff kk -- 11 TT ++ QQ kk -- 11 )) Hh kk TT SS kk -- 11 ,,

其中，Fk-1表示第k-1帧目标的状态转移矩阵，Pk-1表示第k-1帧目标状态估计协方差矩阵，Qk-1表示第k-1帧的过程噪声协方差矩阵，Hk表示第k帧目标量测函数的雅克比矩阵；  Among them, F k-1 represents the state transition matrix of the target in frame k-1, P k-1 represents the target state estimation covariance matrix in frame k-1, and Q k-1 represents the process noise covariance in frame k-1 Matrix, H k represents the Jacobian matrix of the kth frame target measurement function;

10b）根据步骤10a）得到的滤波增益矩阵Kk，计算第k帧目标状态估计值

Figure BDA0000471044010000087
10b) According to the filter gain matrix Kk obtained in step 10a), calculate the estimated value of the target state in the kth frame
Figure BDA0000471044010000087

xx ^^ kk == xx ^^ kk || kk -- 11 ++ KK kk ΣΣ jj == 11 mm kk ββ jj vv jj ,,

其中，

Figure BDA0000471044010000091
表示第k帧目标状态的预测值，βj表示第k帧有效量测集合Zk中第j个量测数据的航迹关联度，vj表示第k帧有效量测集合Zk中第j个量测数据的新息，mk表示第k帧有效量测集合Zk中量测数据个数；  in,
Figure BDA0000471044010000091
Indicates the predicted value of the target state in the k-th frame, β j indicates the track correlation degree of the j-th measurement data in the k-th frame effective measurement set Z k , and v j indicates the j-th measurement data in the k-th frame effective measurement set Z k The new information of measurement data, m k represents the number of measurement data in the effective measurement set Z k of the kth frame;

10c）利用下式计算第k帧状态估计协方差矩阵Pk：  10c) Calculate the k-th frame state estimation covariance matrix P k using the following formula:

PP kk == [[ II -- (( ΣΣ jj == 11 mm kk ββ jj )) KK kk Hh kk ]] (( Ff kk -- 11 PP kk -- 11 Ff kk -- 11 TT ++ QQ kk -- 11 )) ++ KK kk [[ ΣΣ jj == 11 mm kk ββ jj vv jj vv jj TT -- (( ΣΣ jj == 11 mm kk ββ jj vv jj )) (( ΣΣ jj == 11 mm kk ββ jj vv jj )) TT ]] KK kk TT ,,

其中，I表示单位矩阵。  Among them, I represents the identity matrix. the

本发明的效果通过以下仿真对比试验进一步说明：  Effect of the present invention is further illustrated by the following simulation comparison test:

1.实验场景：采用一个位于坐标原点的2D雷达，设载频fc＝3GHz，天线孔径D＝2.5m，发射信号带宽B＝2MHz，采样频率为Fs＝4MHz，雷达扫描周期为ΔT＝2s，雷达测量参数为目标的距离和方位角；设初始时刻目标在X轴、Y轴的位置均为50km，且远离雷达站匀速飞行，X轴、Y轴的速度分量均为300m/s，初始信噪比为20dB，传统检测跟踪算法中目标检测的虚警概率为10-6；航迹终结规则为：若连续三帧未检测到目标，则航迹终结，目标跟踪过程结束。  1. Experimental scenario: a 2D radar located at the origin of the coordinates is used, the carrier frequency f c = 3GHz, the antenna aperture D = 2.5m, the transmission signal bandwidth B = 2MHz, the sampling frequency is F s = 4MHz, and the radar scan period is ΔT = 2s, the radar measurement parameters are the distance and azimuth of the target; assuming that the initial position of the target on the X-axis and Y-axis is 50km, and the target is flying at a constant speed away from the radar station, the velocity components of the X-axis and Y-axis are both 300m/s, The initial signal-to-noise ratio is 20dB, and the false alarm probability of target detection in the traditional detection and tracking algorithm is 10 -6 ; the track termination rule is: if no target is detected in three consecutive frames, the track ends and the target tracking process ends.

2.仿真内容：  2. Simulation content:

仿真1：采用以上实验场景，利用传统的检测跟踪方法和本发明的检测跟踪方法，对雷达的检测性能进行仿真对比，结果如图2；  Simulation 1: Using the above experimental scene, using the traditional detection and tracking method and the detection and tracking method of the present invention, the detection performance of the radar is simulated and compared, and the results are shown in Figure 2;

仿真2：采用以上实验场景，利用传统的检测跟踪方法和本发明的检测跟踪方法，对雷达的探测距离进行仿真对比，结果如图3；  Simulation 2: Using the above experimental scene, using the traditional detection and tracking method and the detection and tracking method of the present invention, the detection distance of the radar is simulated and compared, and the results are shown in Figure 3;

仿真3：采用以上实验场景，假定第10帧目标突然消失，对各帧航迹存在的概率进行仿真，结果如图4。  Simulation 3: Using the above experimental scenario, assuming that the target suddenly disappears in the 10th frame, the probability of the existence of the track in each frame is simulated, and the result is shown in Figure 4. the

3.实验结果分析：  3. Analysis of experimental results:

通过图2可以看出，在保证同样的检测概率0.6的情况下，传统检测跟踪方法所需要的回波信噪比为13.28dB，本发明所需要的回波信噪比为9.533dB，与传统检测跟踪方法相比，本发明所需要的回波信噪比可以降低3.747dB，从而提高了雷达对目标的检测性能。  Can find out by Fig. 2, under the situation that guarantees same detection probability 0.6, the echo signal-to-noise ratio required by traditional detection and tracking method is 13.28dB, and the echo signal-to-noise ratio required by the present invention is 9.533dB, and traditional Compared with the detection and tracking method, the echo signal-to-noise ratio required by the present invention can be reduced by 3.747dB, thereby improving the detection performance of the radar to the target. the

通过图3可以看出，在保证同样的检测概率0.6的情况下，传统检测跟踪方法对目 标的最远探测距离为104.4km，本发明对目标的最远探测距离为129.3km，与传统检测跟踪方法相比提高了24.9km，提高了雷达对目标的探测距离，从而增大了雷达对目标的跟踪距离。  As can be seen from Fig. 3, under the condition of ensuring the same detection probability of 0.6, the farthest detection distance of the target by the traditional detection and tracking method is 104.4km, and the farthest detection distance of the target by the present invention is 129.3km, which is different from the traditional detection and tracking method. The method is 24.9km higher than the method, which improves the detection distance of the radar to the target, thereby increasing the tracking distance of the radar to the target. the

通过图4可以看出，当目标在第10帧消失后，正常情况下应该在第12帧消失，通过仿真结果可以看出，在第12帧目标航迹存在的概率为0.023，即航迹结束的概率为0.977，保证了目标消失后航迹能够有效的结束，抑制了虚假航迹的产生，验证了本发明中调整虚警概率的有效性，且最迟在第15帧左右便可结束航迹。  It can be seen from Figure 4 that when the target disappears in the 10th frame, it should disappear in the 12th frame under normal circumstances. From the simulation results, it can be seen that the probability of the target track existing in the 12th frame is 0.023, that is, the track ends The probability is 0.977, which ensures that the track can be effectively ended after the target disappears, suppresses the generation of false tracks, and verifies the effectiveness of adjusting the false alarm probability in the present invention, and the track can be terminated around the 15th frame at the latest. trace. the

综合上述仿真实验可以看出，在目标远离雷达站的飞行过程中，信噪比随着目标距离的增大逐渐降低，本发明相对于传统的检测跟踪方法，由于综合考虑了跟踪器对目标的预测信息以及虚假航迹抑制问题，可以在保证在不产生虚假航迹的条件下，降低目标的检测门限，从而提高了目标的检测性能，即信噪比较低时仍可保证航迹的连续性，从而增大了目标的跟踪距离。  It can be seen from the above simulation experiments that the signal-to-noise ratio decreases gradually with the increase of the target distance when the target is far from the radar station. Prediction information and false track suppression can reduce the detection threshold of the target without generating false tracks, thereby improving the detection performance of the target, that is, the continuity of the track can still be guaranteed when the signal-to-noise ratio is low Therefore, the tracking distance of the target is increased. the

Claims (5)

1. A frame constant false alarm target detection and tracking integrated method comprises the following steps:
1) initializing parameters: obtaining an initial state estimation value of the target track through a target track initial algorithm
Figure FDA0000471044000000011
And an initial state estimate covariance matrix P0；
2) Setting a target state transition equation and a radar measurement equation according to the target state estimation value of the (k-1) th frame
Figure FDA0000471044000000012
Calculating a k frame target state prediction value
Figure FDA0000471044000000013
And predicted value of k frame target measurement
3) Estimating covariance matrix P based on state of k-1 framek-1And the k frame target state predicted value obtained in the step 2)
Figure FDA0000471044000000015
Calculating a predicted covariance matrix D for the kth frame target measurementk|k-1；
4) According to the predicted value of the k frame target measurement obtained in the step 2)
Figure FDA0000471044000000016
And the prediction covariance matrix D of the k frame target measurement obtained in the step 3)k|k-1Determining a k frame target prediction gate Ok；
5) Setting probability P of false alarm in target prediction threshold of at least N frames in tracking process of continuous M framesFThen the k frame target prediction gate O is calculated using the following equationkProbability of internal false alarm PZ：
Figure FDA0000471044000000017
Wherein N represents the possible frame number of false alarms in the target prediction gate in the tracking process of continuous M frames, a symbol | represents factorial operation, and the value of M, N needs to satisfy that M is more than N and is more than or equal to 1;
6) predicting a wave gate O according to the k frame target obtained in the step 5)kProbability of internal false alarm PZCalculating a k frame target prediction gateOkFalse alarm probability and detection threshold of each detection unit;
7) according to the k frame target prediction gate O obtained in the step 6)kThe detection threshold of each detection unit is used for predicting the wave gate O for the k frame targetkDetecting echo signals in the frame, and estimating target parameters to be used as a k frame measurement data set Z (k);
8) screening out the effective measurement set Z (k) of the k frame by using a correlation algorithm according to the k frame measurement data set Z (k) obtained in the step 7)kSelecting the k frame effective measurement set ZkMeasuring data with highest correlation degree with the flight path, and calculating the estimated value of the target state of the kth frame by using a tracking algorithm
Figure FDA0000471044000000021
And the k-th frame state estimation covariance matrix PkAnd returning to the step 2).
2. The method for integrating frame constant false alarm target detection and tracking according to claim 1, wherein the step 2) of calculating the target state prediction value of the kth frame
Figure FDA0000471044000000022
And predicted value of k frame target measurement
Figure FDA0000471044000000023
The method comprises the following steps:
2a) the target state transition equation is set to:
xk＝Fk-1xk-1+vk-1，
wherein x iskIndicating the state of the target of the k-th frame, Fk-1State transition matrix, x, representing the target of frame k-1k-1Represents the state of the target of frame k-1, vk-1Process noise representing the k-1 frame;
2b) setting a radar measurement equation as follows:
zk＝hk(xk)+wk，
wherein z iskRepresents the measurement value of the k frame object, hk(. represents a measurement function of the k frame target, wkRepresenting the measurement noise of the k-th frame;
2c) according to the target state estimated value of the k-1 frame
Figure FDA0000471044000000024
Calculating a k frame target state prediction value
Figure FDA0000471044000000026
2d) Predicting the target state according to the k frame
Figure FDA0000471044000000027
Calculating a predicted value of the k frame target measurement
Figure FDA0000471044000000028
3. The method of claim 1, wherein the step 3) of calculating the prediction covariance matrix D of the k-th frame target measurementk|k-1The method comprises the following steps:
3a) predicting the target state according to the k frameCalculating a Jacobian matrix Hk of the k frame target measurement function:
Figure FDA00004710440000000211
wherein +x(. h) denotes deriving vector x, (. h)TRepresenting a transpose operation
Figure FDA00004710440000000212
Representing a function
Figure FDA00004710440000000213
In that
Figure FDA00004710440000000214
The function value of (c);
3b) estimating covariance matrix P according to target state of k-1 framek-1And step 3 a) obtaining a Jacobian matrix H of the k frame target measurement functionkCalculating the prediction covariance matrix D of the k frame target measurementk|k-1：
Figure FDA0000471044000000031
Wherein Q isk-1Representing the process noise covariance matrix for the k-1 frame.
4. The method of claim 1, wherein the step 4) of determining the k-th frame target prediction gate OkThe method comprises the following steps:
4a) target prediction gate O for setting target to fall into k framekProbability P ofGObtaining the k frame target prediction gate O by looking up the chi-square distribution table with the degree of freedom as the target measurement dimensionkWherein the chi-square distribution table is a distribution function comparison table of chi-square distribution random variables in probability theory;
4b) predicting a wave gate O according to the k frame target obtained in the step 4 a)kIs determined as followsStandard predictive wave gate Ok：
Figure FDA0000471044000000032
Where y represents the location where the target may appear, | represents the conditional symbol, the symbol left is the set element, and the right is the condition that the element satisfies.
5. The method for integrating frame constant false alarm rate target detection and tracking according to claim 1, wherein the step 6) of calculating the k frame target prediction gate OkThe false alarm probability and the detection threshold of each detection unit are carried out according to the following steps:
6a) setting the form of a radar detector, and obtaining a k frame target prediction gate O according to a target detection algorithmkThe detection statistic xi (i; k), i ═ 1,2kWherein N iskRepresenting the k frame object prediction Gate OkThe number of internal detection units;
6b) setting a k frame target prediction gate OkThe weight w (i; k) of the detection statistic of the ith detection unit is equal to 1,2kObtaining a k frame target prediction gate OkWeighted detection statistic ξ' (i; k) for the i-th detection unit:
ξ′(i;k)＝w(i;k)ξ(i;k),i＝1,2,...,Nk；
6c) calculating the k frame target prediction gate O by using the following equation systemkFalse alarm probability and detection threshold of each detection unit:
Figure FDA0000471044000000041
wherein, Pf(i; k) represents the k frame object prediction gate OkFalse alarm probability of inner i-th detection unit, H0T (k) indicates that the target does not exist, and T (k) indicates that the target in the k-th frame is predicted at the gate OkDetection threshold of each detection unit，Pr{ξ′(i;k)≥T(k)|H0Denotes a k-th frame target prediction gate O in the case where the target does not existkThe probability that the weighted detection statistic ξ' (i; k) for the ith detection cell exceeds the detection threshold t (k).
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