技术领域technical field
本发明属于雷达目标跟踪技术领域，尤其涉及目标跟踪中基于多模型优化多假设的多目标数据关联方法。The invention belongs to the technical field of radar target tracking, in particular to a multi-target data association method based on multi-model optimization and multi-hypothesis in target tracking.
背景技术Background technique
雷达作为信息化战争的“千里眼”，可对战场中的目标进行探测和跟踪，达到获得战场态势信息的目的，被广泛应用于军事领域。随着大量复杂应用背景的多源信息系统的应用，对复杂环境中的目标数据处理是实现目标精准定位的关键，因此，雷达的数据处理技术已成为军事领域乃至民用领域的重要研究方向。数据处理技术主要是通过雷达接收目标的信息，然后对接收到的信息进行一系列的处理，从而得到目标的运动轨迹，并可以得到目标的位置、速度和机动情况等信息，实现对目标的实时跟踪与监控。通过雷达数据处理，提高雷达信号处理功能，是现代军事化建设不可或缺的部分。As the "clairvoyance" of information warfare, radar can detect and track targets in the battlefield to obtain battlefield situation information, and is widely used in the military field. With the application of a large number of multi-source information systems with complex application backgrounds, target data processing in complex environments is the key to accurate target positioning. Therefore, radar data processing technology has become an important research direction in the military and even civilian fields. The data processing technology mainly receives the information of the target through the radar, and then performs a series of processing on the received information, so as to obtain the movement trajectory of the target, and obtain the information such as the position, speed and maneuvering situation of the target, so as to realize the real-time monitoring of the target. Track and monitor. Through radar data processing, improving the radar signal processing function is an indispensable part of modern military construction.
目标跟踪系统通过实时监控目标得到其状态信息，并对目标的状态进行预测，一般的目标跟踪系统是通过雷达对目标的信息进行处理。雷达的数据处理包括：数据预处理、航迹起始、数据关联和航迹关联。通过对雷达接收到的数据进行处理，确定跟踪目标的当前坐标位置和预测下一时刻目标的位置等信息，并对目标下一时刻的状态进行预测，从而得到完整的目标轨迹。The target tracking system obtains its state information by monitoring the target in real time, and predicts the state of the target. The general target tracking system processes the information of the target through radar. The data processing of radar includes: data preprocessing, track initiation, data association and track association. By processing the data received by the radar, determine the current coordinate position of the tracking target and predict the position of the target at the next moment, and predict the state of the target at the next moment, so as to obtain a complete target trajectory.
在实际应用环境中，由于目标会受到天气因素的影响，目标的运动模型是不固定的，目标在运动过程中，属于机动目标，所以对目标运动模型的预测显得尤为重要。为了减少目标跟踪的误差，需要对目标运动模型的切换做出评估，然后建立相应的运动模型并进行目标状态预测，从而提高目标跟踪系统的性能。In the actual application environment, since the target will be affected by weather factors, the motion model of the target is not fixed, and the target is a maneuvering target during the movement process, so the prediction of the target motion model is particularly important. In order to reduce the error of target tracking, it is necessary to evaluate the switching of the target motion model, and then establish the corresponding motion model and predict the target state, so as to improve the performance of the target tracking system.
在实际探测中，由于受到环境中的噪声因素和干扰信息的影响，使得对目标的探测会存在一定的误差，出现误跟或漏跟的情况，所以需要选择合适的跟踪门。跟踪门以预测量测为中心选取一块区域，区域的大小和位置决定了目标真实的量测值是否会被检测到；在此基础上，通过滤波算法将杂波和虚警过滤掉，这样可以减少杂波对点迹与航迹关联的影响；最后，通过数据关联相关算法将点迹与航迹进行关联，从而得到目标的运动轨迹，实现对目标精准跟踪的目的。In actual detection, due to the influence of noise factors and interference information in the environment, there will be certain errors in the detection of the target, and there will be false tracking or missing tracking, so it is necessary to select an appropriate tracking gate. The tracking gate selects an area centered on the predicted measurement. The size and position of the area determine whether the real measurement value of the target will be detected; Reduce the influence of clutter on the point track and track association; finally, the point track is associated with the track through the data association correlation algorithm, so as to obtain the movement trajectory of the target and achieve the purpose of accurate tracking of the target.
随着航天技术的快速发展，多目标跟踪问题成为目标跟踪的热点问题，其中对数据关联技术的研究是多目标跟踪问题的核心部分，通过将雷达探测到的数据进行处理，将接收到的回波(量测)与目标的航迹进行关联，从而得到多目标的轨迹。而在敌我双方的跟踪与反跟踪技术的不断发展中，各种“敌方”目标的信息朝着低检测率、低信噪比、低信号数据率、高干扰性和高机动性等方面发展，使得对目标的探测难度增大。因此，为了进一步提高目标的跟踪率，必须采用高效的技术对目标进行探测，实现对目标的有效跟踪，这就需要提高数据关联的精度。With the rapid development of aerospace technology, the multi-target tracking problem has become a hot issue in target tracking. The research on data association technology is the core part of the multi-target tracking problem. The wave (measurement) is correlated with the trajectory of the target to obtain the trajectory of the multi-target. In the continuous development of the tracking and anti-tracking technology of both the enemy and the enemy, the information of various "enemy" targets is developing towards low detection rate, low signal-to-noise ratio, low signal data rate, high interference and high mobility, etc. , making the detection of the target more difficult. Therefore, in order to further improve the tracking rate of the target, efficient technology must be used to detect the target and achieve effective tracking of the target, which requires improving the accuracy of data association.
发明内容SUMMARY OF THE INVENTION
为克服现有技术的不足，本发明提供了目标跟踪中基于多模型优化多假设的多目标数据关联方法。In order to overcome the deficiencies of the prior art, the present invention provides a multi-target data association method based on multi-model optimization and multi-hypothesis in target tracking.
本发明所采用的技术方案是：The technical scheme adopted in the present invention is:
目标跟踪中基于多模型优化多假设的多目标数据关联方法(IMM-OMHT)，包括以下步骤：Multi-objective data association method based on multi-model optimization and multi-hypothesis (IMM-OMHT) in object tracking, including the following steps:
步骤1：判断目标的运动模型；假设目标运动模型间的转换服从Markov(马尔科夫)过程，将多个运动模型考虑在其中，根据不同运动模型所对应的滤波器对目标的上一时刻的状态估计进行处理，实现目标状态估计的更新；Step 1: Judging the motion model of the target; assuming that the conversion between the target motion models obeys the Markov (Markov) process, and considers multiple motion models, according to the filters corresponding to different motion models. The state estimation is processed to realize the update of the target state estimation;
步骤1.1：对目标状态估计，通过IMM算法中的交互式作用，计算目标的运动模型转换概率，从模型a转移到模型j的转移概率为的计算如下式所示：Step 1.1: Estimate the state of the target, and calculate the transition probability of the target's motion model through the interaction in the IMM algorithm. The transition probability from model a to model j is: The calculation of is as follows:
步骤1.2：经过交互式作用计算后k时刻模型j的输入为：Step 1.2: After the interactive calculation, the input of the model j at time k is:
其中，为模型j的状态向量，为k-1时刻运动模型为模型j(j＝1,2,…,N)的目标状态估计，uk-1(j)为k-1时刻模型j的概率，uk-1|k-1(aj)为k-1时刻模型j转换为模型a的概率，可以表示为：in, is the state vector of model j, is the estimation of the target state when the motion model at time k-1 is model j (j=1,2,...,N), uk-1 (j) is the probability of model j at time k-1, uk-1 |k- 1 (aj) is the probability that model j is converted to model a at time k-1, which can be expressed as:
其中，为：in, for:
k-1时刻模型j的协方差为：The covariance of model j at time k-1 is:
步骤2：对目标的运动模型进行修正，将模型j的状态向量及其协方差 Poj(k-1|k-1)与量测向量Z(k)一起作为k时刻模型j的输入值，通过标准卡尔曼滤波器进行计算可获得各模型输出的状态向量和协方差Pj(k|k)；Step 2: Correct the motion model of the target, and change the state vector of model j to Its covariance Poj (k-1|k-1) and the measurement vector Z(k) are used as the input value of the model j at time k, and the standard Kalman filter is used to calculate the state vector output of each model. and covariance Pj (k|k);
步骤3：目标运动模型可行性计算，假设模型变换服从高斯分布，则模型j的可行性为：Step 3: Calculate the feasibility of the target motion model. Assuming that the model transformation obeys the Gaussian distribution, the feasibility of the model j is:
其中为k时刻模型j的可行性，为k时刻模型j的滤波残差，为k时刻模型j的协方差。in is the feasibility of model j at time k, is the filter residual of model j at time k, is the covariance of model j at time k.
步骤4：对目标的运动模型概率更新，模型j的概率更新为：Step 4: Update the probability of the motion model of the target, and the probability of model j is updated as:
其中uk(j)为k时刻模型j的概率，C为归一化因子，如下式所示：where uk (j) is the probability of model j at time k, and C is the normalization factor, as shown in the following formula:
步骤5：对目标的运动模型输出，k时刻经过交互式作用处理后的目标状态估计为：Step 5: For the output of the motion model of the target, the estimated state of the target after interactive processing at time k is:
为目标i的状态估计，uk|k(i)为时刻目标的概率； is the state estimation of the target i, and uk |k (i) is the probability of the target at the moment;
k时刻经过交互式处理后模型j的协方差为：The covariance of model j after interactive processing at time k is:
uk(j)为k时刻目标对应模型的概率；uk (j) is the probability of the corresponding model of the target at time k;
步骤6：假设的产生，设Ωk,w是至k时刻第w个雷达的关联假设集合，由Ωk-1,w和最新量测值集合得到Ωk,w，其中跟踪门内的量测值集合为：Step 6: Hypothesis generation, let Ωk,w be the associated hypothesis set of the w-th radar up to time k, obtain Ωk,w from Ωk-1,w and the latest measurement value set, in which the quantity in the tracking gate is The set of measured values is:
其中，Zw(k)为第w个雷达的量测值集合；mk为目标的个数；Ziw(k)为k时刻雷达接收到的目标量测；Among them, Zw (k) is the measurement value set of the wth radar; mk is the number of targets; Ziw (k) is the target measurement received by the radar at time k;
步骤7：假设的删减，在完成假设产生后，需要对新产生的航迹进行评估，将航迹置信度低的航迹进行删除。航迹置信度Δlk的计算公式为：Step 7: Deletion of hypotheses. After completing the generation of hypotheses, it is necessary to evaluate the newly generated tracks, and delete tracks with low track confidence. The calculation formula of the track confidenceΔlk is:
其中，Pd为探测到目标的概率，βf为虚警量测的密度空间，M为量测的维数，Pf为虚警量测的概率，d表示量测在跟踪门内，s为跟踪门的面积；Among them, Pd is the probability of detecting the target, βf is the density space of false alarm measurement, M is the dimension of measurement, Pf is the probability of false alarm measurement, d represents the measurement is in the tracking gate, s is the area of the tracking door;
步骤7.1：累计航迹置信度lk的计算，如果雷达每次扫描是独立的，式(12)的计算结果是单次扫描结果，那么经过k次扫描所得的累计航迹置信度lk可以表示为：Step 7.1: Calculation of cumulative track confidence lk , if each radar scan is independent, the calculation result of formula (12) is the result of a single scan, then the cumulative track confidence lk obtained after k scans can be Expressed as:
其中，l1为新航迹的初始置信度；Among them, l1 is the initial confidence of the new track;
通过累计航迹置信度的设置，可以对目标的航迹进行确认和删除，从而实现对假设的删减，删减的规则如下所示：By setting the accumulated track confidence, the track of the target can be confirmed and deleted, so as to realize the deletion of the hypothesis. The rules of deletion are as follows:
其中，Td为删除航迹的阈值，Ta为确认航迹的阈值，阈值的设定可以根据现场环境的需要而设定；Wherein, Td is the threshold for deleting the track, Ta is the threshold for confirming the track, and the setting of the threshold can be set according to the needs of the on-site environment;
步骤7.2：计算径向速度的置信度参数；径向速度的大小与k-1时刻到k时刻目标移动距离的大小满足：Step 7.2: Calculate the confidence parameter of the radial velocity; the magnitude of the radial velocity and the moving distance of the target from time k-1 to time k satisfy:
其中，rk-rk-1为k-1时刻到k时刻目标移动的距离，tk-tk-1为k-1时刻到k时刻所经历的时间，dk为k时刻目标的径向速度，为径向速度的平均值。Among them, rk-rk-1 is the distance that the target moves from time k-1 to time k, tk-tk-1 is the time elapsed from time k-1 to time k, and dk is the radial velocity of the target at time k , is the mean value of radial velocity.
由此得到基于径向速度的置信度参数的判断公式：From this, the judgment formula of the confidence parameter based on the radial velocity is obtained:
其中，c为常数；where c is a constant;
步骤7.3：当判断关联假设集是否为新目标航迹的时候，将连续三次扫描的结果进行判断，通过Δrd可以判断三次连续的扫描结果是否为同一目标的量测值，如果通过判断符合航迹起始的条件，那么保留该假设，否则对假设进行删除。Step 7.3: When judging whether the association hypothesis set is a new target track, the results of three consecutive scans can be judged. Through Δrd, it can be judged whether the three consecutive scan results are the measured values of the same target. The initial condition, then keep the hypothesis, otherwise delete the hypothesis.
步骤8：关联概率的计算，雷达w与当前雷达收到的量测值有关的事件θw(k)包括：ιw个源于已确认的航迹的量测，vw个源于新产生目标的量测值，Φw个虚警。Step 8: Calculation of correlation probability, events θw (k) of radar w related to measurements received by the current radar include: ιw measurements originating from confirmed tracks, vw originating from newly generated The measured value of the target, Φw false alarms.
对于雷达w的量测值q(i＝1,2,…,.mk)，定义与事件θw(k)有关的变量：For the measured value q (i=1,2,...,.mk ) of the radar w, define the variables related to the event θw (k):
在事件θw(k)中已经确认的航迹数为：The number of confirmed tracks in event θw (k) is:
在事件θw(k)中已经新确认的航迹数为：The number of tracks that have been newly confirmed in event θw (k) is:
在事件θw(k)中虚警的数量为：The number of false alarms in event θw (k) is:
Φw＝mk-τw-νw (22)Φw =mk -τw -νw (22)
对于雷达w的任一假设的概率计算为：Any assumption for radar w The probability of is calculated as:
其中，C为归一化常数因子，为雷达w的虚假量测值数量，为雷达w的新目标数的先验质量函数，V为跟踪门的体积，为雷达w探测的目标t航迹的探测概率，为雷达w与目标关联量测的高斯分布。where C is the normalization constant factor, is the number of false measurements of radar w, is the prior mass function of the number of new targets for the radar w, V is the volume of the tracking gate, is the detection probability of the target t track detected by the radar w, Gaussian distribution measured for radar w and target correlation.
步骤9：串行化处理，通过选用零扫描法，选择可能性最大的数据关联假设，来对多目标进行状态估计，将原算法中选用的卡尔曼滤波算法改为IMM算法来进行状态估计，这样更符合目标的实际运动状态；选择最大可能的数据关联假设，并增大相应的协方差矩阵，从而将相应的误相关考虑其中；最后通过关联概率的计算，求出每一个事件的概率，然后估计每一个目标的状态。每个雷达将上一个雷达的状态估计作为中间值进行状态更新，直至将w个雷达的量测值处理完成得到最终的状态估计。Step 9: Serialization processing, by selecting the zero-scan method and selecting the most likely data association hypothesis to estimate the state of multiple targets, and changing the Kalman filter algorithm selected in the original algorithm to the IMM algorithm for state estimation, This is more in line with the actual motion state of the target; select the largest possible data association hypothesis, and increase the corresponding covariance matrix, so as to take the corresponding false correlation into account; finally, through the calculation of the association probability, the probability of each event is obtained, Then estimate the state of each target. Each radar uses the state estimate of the previous radar as an intermediate value to update the state until the final state estimate is obtained by processing the measured values of the w radars.
有益技术效果：Beneficial technical effects:
(1)该发明考虑到在现实的目标跟踪环境中，目标的运动状态可能发生变化的问题，引入了IMM算法对目标的运动模型进行估计，通过Markov链的转换，对运动模型进行修正，得到接近目标实际运动模型的状态估计和协方差。(1) The invention takes into account the problem that the motion state of the target may change in the real target tracking environment, and introduces the IMM algorithm to estimate the motion model of the target. State estimates and covariances that approximate the actual motion model of the target.
(2)该发明通过加入目标径向速度信息到航迹置信度参数，对假设进行删减优化，将不符合航迹起始条件和不满足目标已确认航迹的延续的假设删除，从而减少假设数产生的数量。(2) The invention deletes and optimizes the assumptions by adding the target radial velocity information to the track confidence parameter, and deletes the assumptions that do not meet the initial conditions of the track and do not meet the continuation of the confirmed track of the target, thereby reducing the number of The quantity produced by the hypothetical number.
(3)该发明通过零扫描法，再次对假设进行删减，并且每个雷达将上一雷达的的状态估计作为中间值进行状态更新，从而对目标的状态估计进行了修正，提高了点迹与航迹的关联精度。(3) The invention uses the zero-scan method to delete the assumptions again, and each radar uses the state estimate of the previous radar as an intermediate value to update the state, thereby correcting the state estimate of the target and improving the point trace. Accuracy associated with the track.
在该发明的参数设计中，核心是通过串行结构的多雷达在杂波环境下对多目标进行有效跟踪。首先加入目标径向速度信息到航迹置信度参数，来减少假设的产生，提高数据关联的速度，并可以适当的减少对于雷达存储空间的要求。接着通过使用零扫描法再次对假设进行删减，将关联概率最高的点迹与航迹进行关联。最后每个雷达通过将上个雷达得到的状态估计作为中间值进行目标状态估计的修正，从而达到点迹与航迹的正确关联，得到接近真实目标运动的轨迹。In the parameter design of the invention, the core is to effectively track multiple targets in a clutter environment through multiple radars in a serial structure. First, add the target radial velocity information to the track confidence parameter to reduce the generation of hypotheses, improve the speed of data association, and appropriately reduce the requirements for radar storage space. The hypotheses are then pruned again by using the zero-sweep method, and the point trace with the highest association probability is associated with the track. Finally, each radar uses the state estimate obtained by the previous radar as the intermediate value to correct the target state estimate, so as to achieve the correct correlation between the point track and the track, and obtain a trajectory close to the real target movement.
附图说明Description of drawings
图1为N个运动模型的状态估计图；Figure 1 is a state estimation diagram of N motion models;
图2为本发明实施例提供的运动模型转换时，IMM-OMHT算法与MHT算法对比目标1的 x轴均方根位置误差图；Fig. 2 is the x-axis root mean square position error diagram of the IMM-OMHT algorithm and the MHT algorithm contrast target 1 during the motion model conversion provided by the embodiment of the present invention;
图3为本发明实施例提供的运动模型转换时，IMM-OMHT算法与MHT算法对比目标1的 y轴均方根位置误差图；When Fig. 3 is the motion model conversion that the embodiment of the present invention provides, IMM-OMHT algorithm and MHT algorithm contrast the y-axis root mean square position error diagram of target 1;
图4为本发明实施例提供的运动模型转换时，IMM-OMHT算法与MHT算法对比目标2的 x轴均方根位置误差图；Fig. 4 is the x-axis root mean square position error diagram of the IMM-OMHT algorithm and the MHT algorithm contrast target 2 during the motion model conversion provided by the embodiment of the present invention;
图5为本发明实施例提供的运动模型转换时，IMM-OMHT算法与MHT算法对比目标2的 y轴均方根位置误差图；When Fig. 5 is the motion model conversion that the embodiment of the present invention provides, IMM-OMHT algorithm and MHT algorithm contrast the y-axis root mean square position error diagram of target 2;
图6为本发明实施例提供的杂波密度增加，IMM-OMHT算法与MHT算法单步平均耗时对比图；Fig. 6 is the clutter density increase provided by the embodiment of the present invention, IMM-OMHT algorithm and MHT algorithm single-step average time consumption comparison diagram;
图7为本发明实施例提供的杂波密度增加，IMM-OMHT算法与MHT算法漏警率对比图；Fig. 7 is the clutter density increase provided by the embodiment of the present invention, IMM-OMHT algorithm and MHT algorithm The comparison chart of the false alarm rate;
图8为本发明实施例提供的杂波密度增加，IMM-OMHT算法与MHT算法误警率对比图；Fig. 8 is the clutter density increase provided by the embodiment of the present invention, the comparison diagram of false alarm rate of IMM-OMHT algorithm and MHT algorithm;
图9为本发明实施例提供的目标数目增加，IMM-OMHT算法与MHT算法单步平均耗时对比图；Fig. 9 is the target number increase that the embodiment of the present invention provides, IMM-OMHT algorithm and MHT algorithm single-step average time consumption comparison diagram;
图10为本发明实施例提供的目标数目增加，IMM-OMHT算法与MHT算法漏警率对比图；Fig. 10 is the target number increase that the embodiment of the present invention provides, IMM-OMHT algorithm and MHT algorithm miss-alarm rate comparison chart;
图11为本发明实施例提供的目标数目增加，IMM-OMHT算法与MHT算法误警率对比图；Fig. 11 is the target number increase that the embodiment of the present invention provides, IMM-OMHT algorithm and MHT algorithm false alarm rate comparison diagram;
具体实施方式Detailed ways
下面结合附图和实施例，对本发明的具体实施方式作进一步详细描述。以下实施例用于说明本发明，但不用来限制本发明的范围。The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and embodiments. The following examples are intended to illustrate the present invention, but not to limit the scope of the present invention.
由于在实际的目标跟踪中，目标的运动模型是不可能保持不变的，如果使用单一的运动模型就无法描述目标实际的运动情况。因此引入交互式多模型算法(InteractiveMultipleModel, IMM)，通过马尔科夫的转换过程，对每个模型的模型概率和状态估计进行计算，得到目标当前的运动模型，实现对多目标的交互式跟踪。多假设跟踪算法(MultipleHypothesisTracking, MHT)是基于延迟判断思想的算法，通过多个扫描周期，对目标的量测集进行判断，随着扫描周期的增加，假设的产生呈指数上升，因此对假设的简化具有重要意义。为了解决MHT算法假设计算量大的问题，需要合理的删减低概率的假设，将目标径向速度信息加入到航迹置信度判断中，将置信度低的航迹删除，只保留置信度高的航迹进行概率计算，保证初始航迹确认的准确性和置信度参数的可靠性。并且通过选用串行结构的多雷达，将上一个雷达处理后的状态估计作为中间值，直至将w个雷达的量测处理完，得到最终的状态估计，从而实现数据关联。目标跟踪中基于多模型优化多假设的多目标数据关联方法(InteractiveMultiple ModelOptimizationMultipleHypothesisTracking，IMM-OMHT)的具体实现过程为：Because in the actual target tracking, the motion model of the target cannot remain unchanged, if a single motion model is used, the actual motion of the target cannot be described. Therefore, the Interactive Multiple Model (IMM) algorithm is introduced. Through the Markov transformation process, the model probability and state estimation of each model are calculated to obtain the current motion model of the target and realize the interactive tracking of multiple targets. Multiple Hypothesis Tracking (MHT) is an algorithm based on the idea of delay judgment. It judges the measurement set of the target through multiple scanning periods. With the increase of scanning period, the generation of hypotheses increases exponentially. Simplification is important. In order to solve the problem that the MHT algorithm assumes a large amount of calculation, it is necessary to reasonably delete the assumptions with low probability, add the target radial velocity information to the track confidence judgment, delete the tracks with low confidence, and only keep the high confidence. The probability calculation of the track is carried out to ensure the accuracy of the initial track confirmation and the reliability of the confidence parameters. And by selecting the multi-radar with serial structure, the state estimate after processing by the previous radar is taken as the intermediate value, until the measurement of the w radars is processed, the final state estimate is obtained, so as to realize the data association. The specific implementation process of the multi-objective data association method (InteractiveMultiple ModelOptimizationMultipleHypothesisTracking, IMM-OMHT) based on multi-model optimization and multi-hypothesis in target tracking is as follows:
如图1所示，本实施例提供一种在多目标跟踪时通过IMM-OMHT算法进行目标数据关联的方法流程，具体如下所述。As shown in FIG. 1 , this embodiment provides a method flow of target data association by using the IMM-OMHT algorithm during multi-target tracking, which is specifically described as follows.
步骤1：判断目标的运动模型，假设目标运动模型间的转换服从Markov过程，将多个运动模型考虑在其中，根据不同运动模型所对应的滤波器对目标的上一时刻的状态估计进行处理，实现目标状态估计的更新；Step 1: Judging the motion model of the target, assuming that the conversion between the target motion models obeys the Markov process, taking multiple motion models into account, and processing the state estimation of the target at the previous moment according to the filters corresponding to different motion models, Implement the update of the target state estimate;
步骤1.1：对目标状态估计，通过IMM算法中的交互式作用，计算目标的运动模型转换概率，从模型a转移到模型j的转移概率为的计算如下式所示：Step 1.1: Estimate the state of the target, and calculate the transition probability of the target's motion model through the interaction in the IMM algorithm. The transition probability from model a to model j is: The calculation of is as follows:
步骤1.2：经过交互式作用计算后k时刻模型j的输入为：Step 1.2: After the interactive calculation, the input of the model j at time k is:
其中，为模型j的状态向量，为k-1时刻运动模型为模型j(j＝1,2,…,N)的目标状态估计，uk-1(j)为k-1时刻模型j的概率，uk-1|k-1(a|j)为k-1时刻模型j转换为模型a的概率，可以表示为：in, is the state vector of model j, is the estimation of the target state of the model j (j=1,2,...,N) at the time k-1, and uk-1 (j) is the probability of the model j at the time k-1, uk-1|k- 1 (a|j) is the probability that model j is converted to model a at time k-1, which can be expressed as:
其中，为：in, for:
k-1时刻模型j的协方差为：The covariance of model j at time k-1 is:
步骤2：对目标的运动模型进行修正，将状态向量及其协方差Poj(k-1k-1)与量测向量Z(k)一起作为k时刻第j个模型的输入值，通过标准卡尔曼滤波器进行计算可获得各模型输出的和Pj(k|k)；Step 2: Correct the motion model of the target and convert the state vector Its covariance Poj (k-1k-1) and the measurement vector Z(k) are used as the input value of the jth model at time k, and the standard Kalman filter is used to calculate the output of each model. and Pj (k|k);
步骤3：目标运动模型可行性计算，假设模型变换服从高斯分布，则模型j的可行性为：Step 3: Calculate the feasibility of the target motion model. Assuming that the model transformation obeys the Gaussian distribution, the feasibility of the model j is:
其中为k时刻模型j的可行性，为k时刻模型j的滤波残差，为k时刻模型j的协方差。in is the feasibility of model j at time k, is the filter residual of model j at time k, is the covariance of model j at time k.
步骤4：对目标的运动模型概率更新，模型j的概率更新为：Step 4: Update the probability of the motion model of the target, and the probability of model j is updated as:
其中uk(j)为k时刻模型j的概率，C为归一化因子，如下式所示：where uk (j) is the probability of model j at time k, and C is the normalization factor, as shown in the following formula:
步骤5：对目标的运动模型输出，k时刻经过交互式作用处理后的目标状态估计为：Step 5: For the output of the motion model of the target, the estimated state of the target after interactive processing at time k is:
为目标i的状态估计，uk|k(i)为时刻目标的概率； is the state estimation of the target i, and uk|k (i) is the probability of the target at the moment;
k时刻经过交互式处理后模型j的协方差为：The covariance of model j after interactive processing at time k is:
uk(j)为k时刻目标对应模型的概率；uk (j) is the probability of the corresponding model of the target at time k;
步骤6：假设的产生，设Ωk,w是至k时刻第w个雷达的关联假设集合，由Ωk-1,w和最新量测值集合得到Ωk,w，其中跟踪门内的量测值集合为：Step 6: Hypothesis generation, let Ωk,w be the associated hypothesis set of the w-th radar up to time k, obtain Ωk,w from Ωk-1,w and the latest measurement value set, in which the quantity in the tracking gate is The set of measured values is:
其中，Zw(k)为第w个雷达的量测值集合；mk为目标的个数；为k时刻雷达接收到的目标量测；Among them, Zw (k) is the measurement value set of the wth radar; mk is the number of targets; is the target measurement received by the radar at time k;
步骤7：假设的删减，在完成假设产生后，需要对新产生的航迹进行评估，将航迹置信度低的航迹进行删除。航迹置信度Δlk的计算公式为：Step 7: Deletion of hypotheses. After completing the generation of hypotheses, it is necessary to evaluate the newly generated tracks, and delete tracks with low track confidence. The calculation formula of the track confidenceΔlk is:
其中，Pd为探测到目标的概率，βf为虚警量测的密度空间，M为量测的维数，Pf为虚警量测的概率，d表示量测在跟踪门内，s为跟踪门的面积；Among them, Pd is the probability of detecting the target, βf is the density space of false alarm measurement, M is the dimension of measurement, Pf is the probability of false alarm measurement, d represents the measurement is in the tracking gate, s is the area of the tracking door;
步骤7.1：累计航迹置信度lk的计算，如果雷达每次扫描是独立的，式(12)的计算结果是单次扫描结果，那么经过k次扫描所得的累计航迹置信度lk可以表示为：Step 7.1: Calculation of cumulative track confidence lk , if each radar scan is independent, the calculation result of formula (12) is the result of a single scan, then the cumulative track confidence lk obtained after k scans can be Expressed as:
其中，l1为新航迹的初始置信度；Among them, l1 is the initial confidence of the new track;
通过累计航迹置信度的设置，可以对目标的航迹进行确认和删除，从而实现对假设的删减，删减的规则如下所示：By setting the accumulated track confidence, the track of the target can be confirmed and deleted, so as to realize the deletion of the hypothesis. The rules of deletion are as follows:
其中，Td为删除航迹的阈值，Ta为确认航迹的阈值，阈值的设定可以根据现场环境的需要而设定；Wherein, Td is the threshold for deleting the track, Ta is the threshold for confirming the track, and the setting of the threshold can be set according to the needs of the on-site environment;
步骤7.2：计算径向速度的置信度参数；因为目标径向速度的大小等于单位时间内目标距离的变化率；所以，径向速度的大小与k-1时刻到k时刻目标移动距离的大小相等，它们满足下列公式，即：Step 7.2: Calculate the confidence parameter of the radial velocity; because the size of the target radial velocity is equal to the rate of change of the target distance per unit time; therefore, the size of the radial velocity is equal to the size of the target moving distance from time k-1 to time k , they satisfy the following formulas, namely:
其中，rk-rk-1为k-1时刻到k时刻目标移动的距离，tk-tk-1为k-1时刻到k时刻所经历的时间，dk为k时刻目标的径向速度，为径向速度的平均值。即雷达对同一个目标连续探测两次，量测距离的变化率与径向速度的平均值是相近的。Among them, rk-rk-1 is the distance that the target moves from time k-1 to time k, tk-tk-1 is the time elapsed from time k-1 to time k, and dk is the radial velocity of the target at time k , is the mean value of radial velocity. That is, the radar detects the same target twice continuously, and the rate of change of the measured distance is similar to the average value of the radial velocity.
由此得到基于径向速度的置信度参数的判断公式：From this, the judgment formula of the confidence parameter based on the radial velocity is obtained:
其中，c为常数。由此可见，径向距离对置信度参数的影响，当量测距离的变化率与径向速度的平均值越相近，证明量测值越有可能是源于目标的，通过加入累计航迹置信度，使得量测值的关联误差变小。where c is a constant. It can be seen that the influence of the radial distance on the confidence parameter, when the change rate of the measured distance is closer to the average value of the radial velocity, it proves that the measured value is more likely to originate from the target. By adding the cumulative track confidence degree, so that the associated error of the measurement value becomes smaller.
步骤7.3：当判断关联假设集是否为新目标航迹的时候，将连续三次扫描的结果进行判断，通过Δrd可以判断三次连续的扫描结果是否为同一目标的量测值，如果通过判断符合航迹起始的条件，那么保留该假设，否则对假设进行删除。Step 7.3: When judging whether the association hypothesis set is a new target track, the results of three consecutive scans can be judged. Through Δrd, it can be judged whether the three consecutive scan results are the measured values of the same target. The initial condition, then keep the hypothesis, otherwise delete the hypothesis.
步骤8：关联概率的计算，雷达w与当前雷达收到的量测值有关的事件θw(k)包括：ιw个源于已确认的航迹的量测，vw个源于新产生目标的量测值，Φw个虚警。Step 8: Calculation of correlation probability, events θw (k) of radar w related to measurements received by the current radar include: ιw measurements originating from confirmed tracks, vw originating from newly generated The measured value of the target, Φw false alarms.
对于雷达w的量测值q(i＝1,2,…,.mk)，定义与事件θw(k)有关的变量：For the measured value q (i=1,2,...,.mk ) of the radar w, define the variables related to the event θw (k):
在事件θw(k)中已经确认的航迹数为：The number of confirmed tracks in event θw (k) is:
在事件θw(k)中已经新确认的航迹数为：The number of tracks that have been newly confirmed in event θw (k) is:
在事件θw(k)中虚警的数量为：The number of false alarms in event θw (k) is:
Φw＝mk-τw-νw (22)Φw =mk -τw -νw (22)
对于雷达w的任一假设的概率计算为：Any assumption for radar w The probability of is calculated as:
其中，C为归一化常数因子，为雷达w的虚假量测值数量，为雷达w的新目标数的先验质量函数，V为跟踪门的体积，为雷达w探测的目标t航迹的探测概率，为雷达w与目标关联量测的高斯分布。where C is the normalization constant factor, is the number of false measurements of radar w, is the prior mass function of the number of new targets for the radar w, V is the volume of the tracking gate, is the detection probability of the target t track detected by the radar w, Gaussian distribution measured for radar w and target correlation.
步骤9：串行化处理，通过选用零扫描法，选择可能性最大的数据关联假设，来对多目标进行状态估计，将原算法中选用的卡尔曼滤波算法改为IMM算法来进行状态估计，这样更符合目标的实际运动状态；选择最大可能的数据关联假设，并增大相应的协方差矩阵，从而将相应的误相关考虑其中；最后通过关联概率的计算，求出每一个事件的概率，然后估计每一个目标的状态。每个雷达将上一个雷达的状态估计作为中间值进行状态更新，直至将w个雷达的量测值处理完成得到最终的状态估计。Step 9: Serialization processing, by selecting the zero-scan method and selecting the most likely data association hypothesis to estimate the state of multiple targets, and changing the Kalman filter algorithm selected in the original algorithm to the IMM algorithm for state estimation, This is more in line with the actual motion state of the target; select the largest possible data association hypothesis, and increase the corresponding covariance matrix, so as to take the corresponding false correlation into account; finally, through the calculation of the association probability, the probability of each event is obtained, Then estimate the state of each target. Each radar uses the state estimate of the previous radar as an intermediate value to update the state until the final state estimate is obtained by processing the measured values of the w radars.
图2-图5为发明实施例提供的运动模型转换时，IMM-OMHT算法与MHT算法对比图。假设在监测系统中，使用两部雷达对两个目标进行跟踪。目标的起始坐标为 (1000m,1000m,5000m)和(2000m,18000m,5000m)，并假设目标有三种运动模型，分别为匀速运动模型CVM、匀加速运动模型CAM和语速转弯运动模型CRM。目标1的运动轨迹为：0-20s进行CVM运动，运动速度为(300m/s，173m/s，0m/s)；20s-35s以顺时针每秒1 度做CRM运动；35s-60s进行CAM运动，运动速度为(274m/s，274m/s，0m/s)，加速度为 (52m/s2，52m/s2，0m/s2)。目标2的运动轨迹为：0-20s进行CAM运动，运动速度为(200 m/s，-115.5m/s，0m/s)，加速度为(5m/s2，-2.9m/s2，0m/s2)；20s-35s以顺时针每秒1度做CRM运动；35s-60s进行CVM运动，速度为(274m/s，274m/s，0m/s)。采样周期为1s，杂波密度为0.0001，每次仿真步数为60步，进行100次仿真，通过目标x轴方向和y轴方向的位置均方根误差(RMSE)比较分析点迹与航迹的关联准确度。由图2-图5可以看出， IMM-OMHT算法的均方根位置误差要始终小于MHT算法的均方根位置误差，说明 IMM-OMHT算法得到的目标轨迹比MHT算法得到的目标轨迹更接近于目标的真实运动轨迹。并且当目标运动模型发生转换时，IMM-OMHT算法的均方根位置误差的波动小于MHT 算法的均方根位置误差的波动，说明IMM-OMHT算法可以有效的对机动目标进行跟踪。这是由于IMM-OMHT算法通过计算不同运动模型的切换概率来计算目标下一时刻可能的运动模型和状态估计，因此IMM-OMHT算法对目标的状态估计更接近于目标的真实运动状态，使得点迹与航迹的关联更加准确。2-5 are comparison diagrams between the IMM-OMHT algorithm and the MHT algorithm when the motion model conversion provided by the embodiment of the invention is performed. Suppose that in a monitoring system, two targets are tracked using two radars. The starting coordinates of the target are (1000m, 1000m, 5000m) and (2000m, 18000m, 5000m), and it is assumed that the target has three motion models, namely the uniform motion model CVM, the uniform acceleration motion model CAM and the speech rate turning motion model CRM. The movement trajectory of target 1 is: 0-20s for CVM movement, and the movement speed is (300m/s, 173m/s, 0m/s); 20s-35s for CRM movement at 1 degree clockwise per second; 35s-60s for CAM movement Movement, the movement speed is (274m/s, 274m/s, 0m/s), and the acceleration is (52m/s2 , 52m/s2 , 0m/s2 ). The movement trajectory of target 2 is: 0-20s for CAM movement, the movement speed is (200 m/s, -115.5m/s, 0m/s), and the acceleration is (5m/s2 , -2.9m/s2 , 0m /s2 ); 20s-35s do CRM motion clockwise at 1 degree per second; 35s-60s do CVM motion, the speed is (274m/s, 274m/s, 0m/s). The sampling period is 1s, the clutter density is 0.0001, the number of simulation steps is 60 steps, and 100 simulations are performed. The point trace and the track are compared and analyzed by the root mean square error (RMSE) of the target x-axis and y-axis directions. correlation accuracy. It can be seen from Figure 2 to Figure 5 that the root mean square position error of the IMM-OMHT algorithm is always smaller than the root mean square position error of the MHT algorithm, indicating that the target trajectory obtained by the IMM-OMHT algorithm is closer to the target trajectory obtained by the MHT algorithm. the real trajectory of the target. And when the target motion model is converted, the fluctuation of the root mean square position error of the IMM-OMHT algorithm is smaller than that of the MHT algorithm, indicating that the IMM-OMHT algorithm can effectively track the maneuvering target. This is because the IMM-OMHT algorithm calculates the possible motion model and state estimation of the target at the next moment by calculating the switching probability of different motion models, so the state estimation of the target by the IMM-OMHT algorithm is closer to the real motion state of the target, so that the point Track-to-track correlation is more accurate.
图6-图8为本发明实施例提供的杂波密度增加，IMM-OMHT算法与MHT算法对比图。假设在防空指挥作战系统中，使用两部雷达对两个目标进行跟踪，为了更好的对比随着杂波数目的增加，IMM-OMHT算法与MHT算法的跟踪性能，在杂波数目不同的情况下，其他的跟踪条件保持一致，进行100次仿真，杂波密度从0.0001到0.001，两种算法性能的对比如图6-图8所示。从图6-图8可以看出，随着杂波密度的增加，MHT算法计算的单步平均耗时 (关联时间)呈指数倍增长的趋势，而IMM-OMHT算法通过引入目标径向速度信息，对假设的产生进行优化，有效的减少产生假设的数量，使得计算时所需的关联时间减少，很好的保证了系统的实时性，并且IMM-OMHT算法的虚警率和误警率始终低于MHT算法。因此，随着杂波密度的不断增加，IMM-OMHT算法的跟踪能性更好。FIG. 6-FIG. 8 are the comparison diagrams between the IMM-OMHT algorithm and the MHT algorithm according to the increased clutter density provided by the embodiment of the present invention. Assuming that in the air defense command and combat system, two radars are used to track two targets, in order to better compare the tracking performance of the IMM-OMHT algorithm and the MHT algorithm as the number of clutter increases, when the number of clutter is different , other tracking conditions remain the same, 100 simulations are performed, and the clutter density ranges from 0.0001 to 0.001. The comparison of the performance of the two algorithms is shown in Figure 6-Figure 8. As can be seen from Figure 6-Figure 8, as the clutter density increases, the average time-consuming (association time) of a single step calculated by the MHT algorithm increases exponentially, while the IMM-OMHT algorithm introduces the target radial velocity information by , optimize the generation of hypotheses, effectively reduce the number of hypotheses generated, reduce the association time required for calculation, and ensure the real-time performance of the system, and the false alarm rate and false alarm rate of the IMM-OMHT algorithm are always lower than the MHT algorithm. Therefore, with the increasing clutter density, the tracking performance of the IMM-OMHT algorithm is better.
图9-图11为本发明实施例提供的目标数目增加，IMM-OMHT算法与MHT算法对比图。为了更好的对比随着目标的增加，两种算法的跟踪性能，在其他的跟踪条件保持一致的情况下，将目标的数量从2个增加到10个，进行100次仿真，其关联的单步平均耗时和准确率的对比，如图9-图11所示。从图9-图11可以看出，随着目标数目的增加，MHT算法的关联时间呈指数倍增加，而IMM-OMHT算法的关联时间比MHT算法的关联时间要少，很好的保证了系统的实时性，并且IMM-OMHT算法的关联准确率始终高于MHT算法。因此，随着目标数目的不断增加，IMM-OMHT算法的跟踪能性更好。FIG. 9-FIG. 11 is a comparison diagram of the IMM-OMHT algorithm and the MHT algorithm provided that the number of targets provided by the embodiment of the present invention is increased. In order to better compare the tracking performance of the two algorithms as the number of targets increases, under the condition that other tracking conditions remain the same, the number of targets is increased from 2 to 10, and 100 simulations are performed. The comparison of average step time and accuracy is shown in Figure 9-Figure 11. As can be seen from Figure 9-Figure 11, as the number of targets increases, the association time of the MHT algorithm increases exponentially, while the association time of the IMM-OMHT algorithm is less than that of the MHT algorithm, which ensures the system The real-time performance of the IMM-OMHT algorithm is always higher than that of the MHT algorithm. Therefore, with the increasing number of targets, the tracking performance of the IMM-OMHT algorithm is better.
最后应说明的是：以上实施例仅用以说明本发明的技术方案，而非对其限制；尽管参照前述实施例对本发明进行了详细的说明，本领域的普通技术人员应当理解：其依然可以对前述实施例所记载的技术方案进行修改，或者对其中部分或者全部技术特征进行等同替换；而这些修改或者替换，并不使相应技术方案的本质脱离本发明权利要求所限定的范围。Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that it can still be The technical solutions described in the foregoing embodiments are modified, or some or all of the technical features thereof are equivalently replaced; and these modifications or replacements do not make the essence of the corresponding technical solutions depart from the scope defined by the claims of the present invention.
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| CN201910014542.7ACN109633589A (en) | 2019-01-08 | 2019-01-08 | The Multi-target Data Associations assumed are optimized based on multi-model more in target following |
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| CN201910014542.7ACN109633589A (en) | 2019-01-08 | 2019-01-08 | The Multi-target Data Associations assumed are optimized based on multi-model more in target following |
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| CN117214881A (en)* | 2023-07-21 | 2023-12-12 | 哈尔滨工程大学 | Multi-target tracking method based on Transformer network in complex scene |
| CN117214881B (en)* | 2023-07-21 | 2024-04-30 | 哈尔滨工程大学 | Multi-target tracking method based on Transformer network in complex scene |
| CN117233745A (en)* | 2023-11-15 | 2023-12-15 | 哈尔滨工业大学（威海） | Sea maneuvering target tracking method on non-stationary platform |
| CN117233745B (en)* | 2023-11-15 | 2024-02-09 | 哈尔滨工业大学（威海） | Sea maneuvering target tracking method on non-stationary platform |
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| RJ01 | Rejection of invention patent application after publication | Application publication date:20190416 | |
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