技术领域technical field
本发明涉及雷达技术，特别涉及无源雷达目标跟踪技术。特别是跟踪区域存在多个目标、并且各个目标航迹会出现中断现象，致使跟踪滤波后的航迹呈不连续状态下的目标跟踪技术。The invention relates to radar technology, in particular to passive radar target tracking technology. In particular, there are multiple targets in the tracking area, and the track of each target will be interrupted, resulting in a discontinuous track after the tracking filter.
背景技术Background technique
在无线电探测技术领域，无源雷达自身不用发射电磁波，通过接收目标辐射的电磁信息对目标进行定位和跟踪。无源雷达系统具有作用距离远、隐蔽性好等优点，对于提高系统在电子站环境下的生存能力具有重要作用。无源雷达系统是基于目标辐射的电磁波参数来确定辐射源以及其携载平台或目标位置信息的，系统的关键技术在于量测数据的处理并形成稳定航迹。无源雷达常用的数据处理方式类似于有源雷达，主要包含有数据预处理，数据关联，航迹起始，滤波跟踪，航迹终结，形成航迹等步骤。数据预处理解决系统误差配准、时间同步、空间对准及野值剔除等问题。航迹起始与终结是目标运动在雷达观测区域下的航迹建立和航迹结束的过程，尤其航迹起始是雷达数据处理的重要过程，决定能否对目标实现跟踪。数据关联和滤波跟踪解决量测点迹与目标的关联，以及通过量测值对目标状态的估计等问题。形成航迹是将同一目标的量测集合所估计的目标状态形成同一航迹的过程。In the field of radio detection technology, passive radar itself does not emit electromagnetic waves, but locates and tracks targets by receiving electromagnetic information radiated by targets. The passive radar system has the advantages of long range and good concealment, which plays an important role in improving the system's survivability in the electronic station environment. The passive radar system determines the radiation source and its carrying platform or target position information based on the electromagnetic wave parameters radiated by the target. The key technology of the system lies in the processing of the measurement data and the formation of a stable track. The commonly used data processing method of passive radar is similar to that of active radar, mainly including data preprocessing, data association, track start, filter tracking, track end, track formation and other steps. Data preprocessing solves problems such as system error registration, time synchronization, spatial alignment and outlier elimination. The start and end of the track are the process of establishing and ending the track of the target movement under the radar observation area, especially the start of the track is an important process of radar data processing, which determines whether the target can be tracked. Data association and filter tracking solve problems such as the association between measurement points and targets, and the estimation of target states through measurement values. Track formation is the process of forming the target state estimated by the measurement set of the same target into the same track.
对于无源雷达系统预处理(时间同步、野值剔除)后的方位角量测集合进行定位跟踪，由于空间中量测方位角与目标位置具有很强的非线性关系，所以采用不敏卡尔曼滤波器(Unscented Kalman Filter,UKF)进行滤波。对于机动目标的跟踪，采用交互式多模型(Interacting Multiple Model Algorithm，IMM)的自适应算法进行跟踪。对于多个目标的数据关联，采用联合概率数据互联算法(Joint Probabilistic Data AssociationAlgorithm，JPDA)来解决杂波环境下的多目标互联问题，以及回波落入多个跟踪相关波门的相交区域的数据关联问题。对机动目标跟踪，可以将交互式多模型(IMM)算法和不敏卡尔曼滤波(UKF)算法相结合，即将IMM算法中的滤波器用UKF滤波器替换，得到IMM_UKF算法。此方法可以解决无源雷达中的跟踪问题，可以有效检测目标运动的机动性，可以提高目标跟踪的状态估计。For the positioning and tracking of the azimuth measurement set after the preprocessing (time synchronization, outlier elimination) of the passive radar system, since the measured azimuth in space has a strong nonlinear relationship with the target position, the insensitive Kalman method is used Filter (Unscented Kalman Filter, UKF) for filtering. For the tracking of maneuvering targets, an adaptive algorithm of Interactive Multiple Model Algorithm (IMM) is used for tracking. For the data association of multiple targets, the Joint Probabilistic Data Association Algorithm (JPDA) is used to solve the problem of multi-target interconnection in the clutter environment, and the data whose echo falls into the intersection area of multiple tracking correlation gates Associated issues. For maneuvering target tracking, the Interactive Multiple Model (IMM) algorithm can be combined with the Unsensitive Kalman Filter (UKF) algorithm, that is, the filter in the IMM algorithm is replaced by the UKF filter to obtain the IMM_UKF algorithm. This method can solve the tracking problem in passive radar, can effectively detect the maneuverability of target motion, and can improve the state estimation of target tracking.
通过这些基础处理方法基本可以对量测点集合形成稳定航迹。然而由于无源雷达自身不发射探测信号的固有特质，当辐射源目标不再辐射信号或者地面障碍物遮挡等情况造成目标量测数据不连续，使得采用上述方法对同一目标形成的航迹出现间断现象，尤其当复杂环境下当多个目标同时出现间断，将给目标形成同一稳定航迹带来困难。Through these basic processing methods, a stable track can basically be formed for the set of measurement points. However, due to the inherent characteristics of the passive radar itself not emitting detection signals, when the radiation source target no longer radiates signals or is blocked by ground obstacles, the measurement data of the target is discontinuous, which makes the track formed by the above method for the same target appear intermittent. Phenomenon, especially when multiple targets appear discontinuous at the same time in a complex environment, it will make it difficult for the targets to form the same stable track.
发明内容Contents of the invention
本发明的目的提供计一种无源雷达多目标跟踪方法，不仅可以对不间断的连续量测数据进行关联形成稳定航迹，也可以对阈值时间内有部分丢失的量测数据(即出现航迹中断现象)进行关联，可以对同一批多目标中的每个目标都形成与之对应的一条稳定航迹。以克服现有技术只能对目标的连续采样量测数据形成稳定航迹，不能对同一目标前后时间有中断现象的量测数据形成同一航迹的问题。The purpose of the present invention is to provide a kind of passive radar multi-target tracking method, which can not only correlate the uninterrupted continuous measurement data to form a stable track, but also can partially lose the measurement data within the threshold time (i. track interruption phenomenon) to form a corresponding stable track for each target in the same batch of multi-targets. In order to overcome the problem that the existing technology can only form a stable track for the continuous sampling measurement data of the target, but cannot form the same track for the measurement data of the same target before and after the time interruption phenomenon.
本发明解决所述技术问题，采用的技术方案是，无源雷达目标跟踪方法，包括如下步骤：The present invention solves described technical problem, and the technical scheme adopted is, passive radar target tracking method, comprises the steps:
a、跟踪预处理：根据雷达站达采集的方位角量测集合Z(k)进行交叉定位，得到与定位目标关联的量测集合U(k)；根据定位结果使用速度、加速度、角度约束进行航迹起始，并获得目标的初始状态估计和对应的协方差矩阵估计；a. Tracking preprocessing: perform cross positioning according to the azimuth measurement set Z(k) collected by the radar station, and obtain the measurement set U(k) associated with the positioning target; use speed, acceleration, and angle constraints according to the positioning results The track starts, and the initial state estimate of the target and the corresponding covariance matrix estimate are obtained;
b、航迹跟踪滤波：对满足起始航迹的目标进行目标跟踪获得目标各个时刻的航迹及状态估计；b. Track tracking filter: track the target that meets the initial track to obtain the track and state estimation of the target at each moment;
c、中断航迹预处理：对中断时刻前的旧航迹按中断时刻的多模型概率进行预测得到该目标航迹中断后Tth+Tsm时间内的旧航迹预测状态估计，其中Tth是新、旧航迹间隔的最大时间，Tsm是序贯关联时间窗长度；c. Interruption track preprocessing: predict the old track before the interruption time according to the multi-model probability of the interruption time to obtain the old track prediction state estimation within Tth +Tsm time after the interruption of the target track, where Tth is the maximum time between new and old tracks, and Tsm is the length of the sequential correlation time window;
d、中断航迹序贯关联：根据航迹中断时刻航迹中断的目标个数N，以及航迹中断后Tth+Tsm时间内新起始航迹目标个数M，初始化关联检验矩阵ΨN×M；对每个旧航迹的目标预测状态估计与新航迹逆向状态估计在序贯关联窗长度Tsm内进行序贯法关联得到检验矩阵ΨN×M；再次按照每个旧航迹最多存在一条新航迹与之对应关联、每条新航迹最多存在一条旧航迹与之关联的约束准则和置信度水平α下的检验门限γ1-α对检验矩阵ΨN×M进行处理，得到最后的关联确认矩阵ΩN×M；d. Interrupted track sequential association: According to the number N of targets whose track is interrupted at the time of track interruption, and the number M of new starting track targets within Tth + Tsm after track interruption, initialize the correlation check matrix ΨN×M ; The target prediction state estimate of each old track and the reverse state estimate of the new track are sequentially correlated within the sequential correlation window length Tsm to obtain the test matrix ΨN×M ; again according to the maximum existence of each old track A new track is associated with it, each new track has at most one old track associated with it, and the inspection threshold γ1-α under the confidence level α processes the inspection matrix ΨN×M to obtain the final Correlation Confirmation Matrix ΩN×M ;
e、航迹确认：按照关联确认矩阵ΩN×M的关联结果，对关联成功的新航迹赋以旧航迹的航迹号，并以中断时间内的旧航迹的状态预测值代替该目标中断时间段内目标状态估计值；其余新航迹的航迹号不变，并标识为新目标出现；对未关联成功的旧航迹以航迹终结处理。e. Track confirmation: According to the correlation result of the correlation confirmation matrix ΩN×M , assign the track number of the old track to the new track with successful correlation, and replace the target with the state prediction value of the old track within the interruption time The estimated value of the target state during the interruption period; the track numbers of the remaining new tracks remain unchanged, and are marked as the emergence of new targets; the old tracks that have not been successfully associated are terminated by the track.
具体的：步骤b具体为，对满足起始航迹的量测采用IMM_UKF和JPDA算法进行目标跟踪获得目标各个时刻的航迹及状态估计。Concretely: step b is specifically, use the IMM_UKF and JPDA algorithms to track the target to obtain the track and state estimation of the target at each moment for the measurement that satisfies the initial track.
具体的：选取Tsm为采样时间Ts的3～5倍。Specifically: Tsm is selected as 3 to 5 times the sampling time Ts .
进一步的：步骤c还包括，对中断时刻后Tth+Tsm时间内出现的新目标按时间逆向进行滤波得到其航迹开始的Tsm时间内的新航迹状态估计。Further: step c also includes, time-reverse filtering for new targets appearing within Tth + Tsm time after the interruption moment to obtain the new track state estimation within Tsm time when the track starts.
具体的：所述雷达站包括不在同一位置的至少3个移动和/或固定雷达站。Specifically: the radar stations include at least 3 mobile and/or fixed radar stations that are not at the same location.
具体的：所述雷达站位于同一平面上。Specifically: the radar stations are located on the same plane.
具体的：所述雷达站数量为3个。Specifically: the number of radar stations is 3.
进一步的：所述3个雷达站中，其中一个雷达站处于另外两个雷达站连接线的垂直平分线上。Further: among the three radar stations, one of the radar stations is located on the perpendicular bisector of the connecting line of the other two radar stations.
具体的：specific:
Z(k)＝{Z1(k)，Z2(k)，Z3(k)}Z(k)={Z1 (k), Z2 (k), Z3 (k)}
式中Zs(k)是k时刻第s个雷达站的方位角量测集合，且满足where Zs (k) is the azimuth measurement set of the sth radar station at time k, and satisfies
其中是k时刻第s个雷达站的第is个方位角量测；ns表示k时刻第s个雷达站的量测数目；N表示雷达站的个数；M(k)表示k时刻系统观测区域中的目标个数；当is＝0时表示没有获得量测，即漏检目标或没有目标存在。in is the is -th azimuth measurement of the s-th radar station at time k; ns represents the measurement number of the s-th radar station at time k; N represents the number of radar stations; M(k) represents the system observation at time k The number of targets in the area; when is =0, it means that no measurement is obtained, that is, no target is detected or no target exists.
具体的：步骤a中，所述交叉定位是根据方位角量测集合Z(k)解算出所有时刻内所有目标的位置坐标。Specifically: in step a, the cross positioning is to calculate the position coordinates of all targets at all times according to the azimuth measurement set Z(k).
本发明根据多站无源雷达的方向角信息进行定位，使用速度、加速度、角度约束的直观法进行航迹起始；使用IMM算法对机动目标进行跟踪，使用UKF算法解决跟踪系统非线性问题，使用JPDA方法解决多目标关联问题，从而获得目标航迹及目标状态估计。然后对某量测中断航迹进行预测，对中断时间后Tth+Tsm时间内的新航迹进行反向估计，接着使用序贯关联方法关联新旧航迹并得到检验矩阵ΨN×M，然后再对ΨN×M进行约束处理求解最优航迹关联的关联确认矩阵ΩN×M。本发明不仅可以对无源雷达多目标进行定位跟踪，提高航迹起始时间内的目标估计精度，同时也可以解决阈值时间内的中断航迹关联问题。克服了现有技术只能对目标的连续采样量测数据形成稳定航迹，不能对同一目标前后时间有中断现象的量测数据形成同一航迹的缺陷。The invention performs positioning according to the direction angle information of the multi-station passive radar, uses the intuitive method of speed, acceleration and angle constraints to start the track; uses the IMM algorithm to track the maneuvering target, and uses the UKF algorithm to solve the nonlinear problem of the tracking system, The JPDA method is used to solve the multi-target association problem, so as to obtain the target track and target state estimation. Then predict the interrupted track of a certain measurement, reverse estimate the new track within Tth + Tsm after the interrupted time, and then use the sequential correlation method to correlate the old and new tracks to obtain the test matrix ΨN×M , and then Then carry out constraint processing on ΨN×M to solve the association confirmation matrix ΩN×M of the optimal track association. The invention can not only locate and track passive radar multi-targets, improve the target estimation accuracy within the track starting time, but also solve the problem of interrupting track association within the threshold time. It overcomes the defect that the existing technology can only form a stable track for the continuous sampling measurement data of the target, and cannot form the same track for the measurement data with interruptions before and after the same target.
下面结合附图和具体实施方式对本发明做进一步的说明。本发明附加的方面和优点将在下面的描述中部分给出，部分将从下面的描述中变得明显，或通过本发明的实践了解到。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
附图说明Description of drawings
构成本申请的一部分的附图用来提供对本发明的进一步理解，本发明的具体实施方式、示意性实施例及其说明用于解释本发明，并不构成对本发明的不当限定。在附图中：The accompanying drawings constituting a part of this application are used to provide a further understanding of the present invention, and the specific implementation modes, schematic embodiments and descriptions thereof of the present invention are used to explain the present invention, and do not constitute improper limitations to the present invention. In the attached picture:
图1是跟踪单个目标的N个模型的IMM_UKF算法的示意图，图中包含N个模型，图中滤波器采用UKF滤波器。图中的是基于N个模型基础之上的状态估计，为模型j的状态估计。为模型可能性向量，uk是模型概率向量。为k-1时刻第j个滤波器的输出。为交互作用的结果，它作为k时刻滤波器j的输入。Z(k)是k时刻的方位角量测。是模型j的一步预测状态估计。Figure 1 is a schematic diagram of the IMM_UKF algorithm of N models tracking a single target. The figure contains N models, and the filter in the figure uses a UKF filter. in the picture is the state estimation based on N models, is the state estimate of model j. is the model possibility vector, uk is the model probability vector. is the output of the jth filter at time k-1. for The result of the interaction, which serves as the input of filter j at time k. Z(k) is the azimuth measurement at time k. is the one-step predictive state estimate for model j.
图2是本发明具体实施方式中三个目标120秒内的量测位置，图中圆圈表示某目标某时刻在空间中的位置坐标。Fig. 2 is the measurement positions of three targets within 120 seconds in the specific embodiment of the present invention, and the circles in the figure indicate the position coordinates of a certain target in space at a certain moment.
图3是图2中量测数据经过发明中的A、B步骤后跟踪到的6段航迹，图中包含有量测点迹，旧航迹1、旧航迹2、旧航迹3、新航迹1、新航迹2、新航迹3。Fig. 3 is the 6 sections of tracks tracked by the measurement data in Fig. 2 after the steps of A and B in the invention. The figure contains measurement point tracks, old track 1, old track 2, old track 3, New track 1, new track 2, new track 3.
图4是经过中断航迹预测得到的结果，图中包含有量测点迹，旧航迹1、旧航迹2、旧航迹3、旧航迹预测航迹1、旧航迹预测航迹2、旧航迹预测航迹3、以及三条新航迹的方向滤波航迹。Figure 4 is the result obtained by interrupted track prediction. The figure contains measurement points, old track 1, old track 2, old track 3, old track predicted track 1, old track predicted track 2. The predicted track of the old track 3, and the direction filter track of the three new tracks.
图5是图4的局部放大图。FIG. 5 is a partially enlarged view of FIG. 4 .
图6是经过步骤D、E后得到的三个目标的最终航迹。Figure 6 is the final track of the three targets obtained after steps D and E.
具体实施方式detailed description
需要说明的是，在不冲突的情况下，本申请中的具体实施方式、实施例以及其中的特征可以相互组合。现将参考附图并结合以下内容详细说明本发明。It should be noted that, in the case of no conflict, the specific implementation methods, examples and features in the present application can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and in conjunction with the following contents.
为了使本领域技术人员更好的理解本发明方案，下面将结合本发明具体实施方式、实施例中的附图，对本发明具体实施方式、实施例中的技术方案进行清楚、完整的描述，显然，所描述的实施例仅仅是本发明一分部的实施例，而不是全部的实施例。基于本发明中的具体实施方式、实施例，本领域普通技术人员在没有做出创造性劳动的前提下所获得的所有其他实施方式、实施例，都应当属于本发明保护的范围。In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the specific embodiments of the present invention and the examples will be clearly and completely described below in conjunction with the accompanying drawings in the specific embodiments of the present invention and the examples. , the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the specific implementation modes and examples in the present invention, all other implementation modes and examples obtained by persons of ordinary skill in the art without making creative efforts shall fall within the protection scope of the present invention.
本发明的技术方案，首先对无源雷达得到的方位量测集合使用视线交叉定位法、IMM、JPDA、UKF等算法对连续量测按照跟踪预处理、航迹跟踪滤波等步骤形成连续量测的稳定航迹以及估计出各个目标所对应的状态。其次在顺序时间范围内，当航迹终结时刻存在多个目标航迹(称为“旧航迹1，旧航迹2，旧航迹3，…”)终结,并在阈值时间范围出现一个或多个目标航迹(称为“新航迹1，新航迹2，新航迹3，…”)起始，将旧航迹预测航迹与新航迹逆向滤波航迹进行序贯关联形成关联检验矩阵，并对关联检验矩阵按约束条件处理，得到旧航迹与新航迹的关联确认矩阵，其中包含旧航迹与新航迹的关联配对信息，对关联成功的旧航迹用状态预测值和航迹预测值替代中断时间内的目标状态和航迹，并与新航迹组成稳定航迹，对未关联成功的旧航迹进行航迹终结处理，对未关联成功的新航迹当做新目标出现进行处理，对超出阈值范围时间的新航迹同样认为是新目标的出现。本发明的无源雷达目标跟踪方法，不但适用于固定雷达站进行目标跟踪，同样适用于移动雷达站进行目标盖章。本发明主要步骤如下：In the technical solution of the present invention, firstly, algorithms such as line-of-sight cross-location method, IMM, JPDA, and UKF are used for the azimuth measurement set obtained by passive radar to form continuous measurement according to steps such as tracking preprocessing and track tracking filtering. Stabilize the track and estimate the state corresponding to each target. Secondly, in the sequential time range, when there are multiple target tracks (called "old track 1, old track 2, old track 3, ...") at the end of the track, and one or more target tracks appear in the threshold time range Multiple target trajectories (called "new trajectories 1, new trajectories 2, new trajectories 3, ...") start, and sequentially correlate the predicted trajectories of the old trajectories with the inverse filtering trajectories of the new trajectories to form a correlation check matrix, And process the association check matrix according to the constraints to obtain the association confirmation matrix between the old track and the new track, which contains the association pairing information of the old track and the new track, and use the state prediction value and track prediction for the old track that is successfully associated The value replaces the target state and track within the interruption time, and forms a stable track with the new track, and performs track termination processing on the old track that has not been successfully linked, and treats the new track that has not been successfully linked as a new target. A new track whose time exceeds the threshold range is also considered as the appearance of a new target. The passive radar target tracking method of the present invention is not only suitable for target tracking by fixed radar stations, but also suitable for target stamping by mobile radar stations. Main steps of the present invention are as follows:
跟踪预处理步骤：根据雷达站达采集的方位角量测集合Z(k)进行交叉定位，得到与定位目标关联的量测集合U(k)；根据定位结果使用速度、加速度、角度约束进行航迹起始，并获得目标的初始状态估计和对应的协方差矩阵估计。Tracking preprocessing step: perform cross positioning according to the azimuth measurement set Z(k) collected by the radar station, and obtain the measurement set U(k) associated with the positioning target; use speed, acceleration, and angle constraints to perform navigation according to the positioning results The trace starts, and the initial state estimate of the target and the corresponding covariance matrix estimate are obtained.
航迹跟踪滤波：对满足起始航迹的目标采用IMM_UKF和JPDA算法进行目标跟踪获得目标各个时刻的航迹及状态估计。Track tracking filtering: use the IMM_UKF and JPDA algorithms to track the target that meets the initial track to obtain the track and state estimation of the target at each moment.
中断航迹预处理步骤：对中断时刻前的旧航迹按中断时刻的多模型概率进行预测得到该目标航迹中断后Tth+Tsm时间内的旧航迹预测状态估计，其中Tth是新、旧航迹间隔的最大时间，Tsm是序贯关联时间窗长度。同时对中断时刻后Tth+Tsm时间内出现的新目标按时间逆向进行滤波得到其航迹开始的Tsm时间内的新航迹状态估计。这里通常选取Tsm为系统采样时间Ts的3～5倍。Interruption track preprocessing step: predict the old track before the interruption time according to the multi-model probability of the interruption time to obtain the old track prediction state estimation within Tth +Tsm time after the interruption of the target track, where Tth is The maximum time between new and old track intervals, Tsm is the length of the sequential correlation time window. At the same time, the new target appearing in the Tth + Tsm time after the interruption time is filtered according to the time inverse to obtain the new track state estimation within the Tsm time when the track starts. Here, Tsm is usually selected as 3 to 5 times of the system sampling time Ts .
中断航迹序贯关联步骤：根据航迹中断时刻航迹中断的目标个数N，以及航迹中断后Tth+Tsm时间内新起始航迹目标个数M，初始化关联检验矩阵ΨN×M；对每个旧航迹的目标预测状态估计与新航迹逆向状态估计在序贯关联窗长度Tsm内进行序贯法关联得到检验矩阵ΨN×M；再次按照每个旧航迹最多存在一条新航迹与之对应关联、每条新航迹最多存在一条旧航迹与之关联的约束准则和置信度水平α下的检验门限γ1-α对检验矩阵ΨN×M进行处理，得到最后的关联确认矩阵ΩN×M。Sequential association steps of the interrupted track: according to the number N of the track interrupted targets at the track interrupted time, and the number M of new initial track targets within the time Tth + Tsm after the track interrupted, initialize the correlation check matrix ΨN ×M ; The target prediction state estimation of each old track and the reverse state estimate of the new track are sequentially correlated within the sequential correlation window length Tsm to obtain the test matrix ΨN×M ; again according to the fact that each old track has at most one The new track is associated with it, and each new track has at most one old track associated with it. The constraint criterion and the inspection threshold γ1-α under the confidence level α process the inspection matrix ΨN×M to obtain the final association Confirm the matrix ΩN×M .
航迹确认步骤：按照关联确认矩阵ΩN×M的关联结果，对关联成功的新航迹赋以旧航迹的航迹号，并以中断时间内的旧航迹的状态预测值代替该目标中断时间段内目标状态估计值；其余新航迹的航迹号不变，并标识为新目标出现；对未关联成功的旧航迹以航迹终结处理。Track confirmation step: according to the association result of the association confirmation matrix ΩN×M , assign the track number of the old track to the new track that is successfully linked, and replace the target interruption with the state prediction value of the old track within the interruption time The estimated value of the target state within the time period; the track numbers of the remaining new tracks remain unchanged, and are marked as the emergence of new targets; the old tracks that have not been successfully associated are terminated by the track.
这里对上述步骤做以下补充说明：Here are the following supplementary instructions for the above steps:
1)、上述跟踪预处理步骤中，以位于同一平面的3个雷达站的方位角量测集合Z(k)进行交叉定位。即1) In the above-mentioned tracking preprocessing step, cross positioning is performed with the azimuth measurement set Z(k) of three radar stations located on the same plane. which is
Z(k)＝{Z1(k),Z2(k),Z3(k)} (1)Z(k)={Z1 (k), Z2 (k), Z3 (k)} (1)
式中Zs(k)是k时刻第s个雷达站的方位角量测集合，且满足where Zs (k) is the azimuth measurement set of the sth radar station at time k, and satisfies
其中是k时刻第s个雷达站的第is个方位角量测；ns表示k时刻第s个雷达站的量测数目；M(k)表示k时刻系统观测区域中的目标个数；当is＝0时表示没有获得方位角量测，即漏检目标。in is the is azimuth measurement of the s-th radar station at time k; ns represents the measurement number of the s-th radar station at time k; M(k) represents the number of targets in the system observation area at time k; when When is =0, it means that no azimuth measurement is obtained, that is, the target is missed.
上述交叉定位就是根据方位角量测集合Z(k)解算出所有时刻内所有目标的位置坐标，其过程如下：选取k时刻方位角量测，将s1、s2两个雷达站k时刻的方位角量测数据进行视线交叉定位得到多目标的可能分布总集合T(k)，其中The above cross positioning is to calculate the position coordinates of all targets at all times according to the azimuth angle measurement set Z(k). The measurement data is used for line-of-sight cross-location to obtain the total set of possible distributions T(k) of multiple targets, where
式中Ti(k)是M(k)个目标的第i种可能分布情况；是s1、s2两个站k时刻的量测数据的视线交叉点；C(k)表示总的可能情况的个数；表示排列运算。In the formula, Ti (k) is the i-th possible distribution of M (k) targets; is the line of sight intersection of the measurement data of two stations s1 and s2 at time k; C(k) represents the total number of possible situations; Indicates a permutation operation.
计算雷达站s3对Ti(k)中的第m个目标的方位角量测估计值令Ti(k)中所有目标与s3雷达站的真实方位角量测之间的关联概率等于Calculate the estimated value of the azimuth measurement of the radar station s3 to the mth target in Ti (k) Let the correlation probability between all targets in Ti (k) and the real azimuth measurement of radar station s3 be equal to
式中m＝1,2,...,min({ns1,ns2})；is3＝1,2,...,ns3且ns3≤M(k)；α表示概率调节系数，根据测量误差取值，一般取雷达站量测误差标准差的3～5倍。进而求得T(k)中每个可能分布情况与s3雷达站的ns3个方位角量测关联的最大似然概率In the formula, m=1,2,...,min({ns1 ,ns2 }); is3 =1,2,...,ns3 and ns3 ≤M(k); α represents the probability adjustment coefficient , according to the value of the measurement error, generally 3 to 5 times the standard deviation of the measurement error of the radar station. Then obtain the maximum likelihood probability associated with each possible distribution in T(k) and the ns3 azimuth measurements of the s3 radar station
其中等于1或0，且满足in Equal to 1 or 0, and satisfy
并由对应的Ti(k)和得到雷达站s1、s2、s3的方位线关联结果，即以定位目标关联的量测集合U(k)。假设U(k)中包含有Tk个目标，则And by The corresponding Ti (k) and Obtain the bearing line association results of radar stations s1, s2, and s3, that is, the measurement set U(k) associated with the positioning target. Suppose U(k) contains Tk targets, then
Ut(k)＝{βs1,m1,βs2,m2，βs3,m3} (10)Ut (k)={βs1,m1 ,βs2,m2 ,βs3,m3 } (10)
其中Ut(k)是k时刻目标t的三个站的量测组成的方位角量测向量；且m1∈{1,2,...,ns1}，m2∈{1,2,...,ns2}，m3∈{1,2,...,ns3}。并根据Ut(k)中任意两两组合并与相应的雷达站位置计算目标的三个位置估计对其取均值得到目标位置估计为where Ut (k) is the azimuth measurement vector composed of the measurements of the three stations of the target t at time k; and m1∈{1,2,...,ns1 }, m2∈{1,2,. ..,ns2 }, m3 ∈ {1,2,...,ns3 }. And according to the combination of any two groups in Ut (k) and the corresponding radar station position, the three position estimates of the target are calculated Taking the mean value of it, the target position is estimated as
其中Xt(k)＝[xt(k),yt(k)]′表示k时刻目标t的位置坐标。k时刻目标位置集合可记为Where Xt (k)=[xt (k), yt (k)]' represents the position coordinates of the target t at time k. The set of target positions at time k can be written as
对于连续三个时刻目标关联位置集合X(k)、X(k+1)、X(k+2)，得到相应时刻的目标位置估计从三个集合中分别各取一个目标可以得到一个组合航迹，按时间顺序求得每个组合对应目标的速度，加速度，以及速度矢量夹角，再与事先约定条件:速度约束、加速度约束、角度约束等条件判断对应组合航迹是否为目标航迹来进行航迹起始。对组合航迹满足约束条件的，确认航迹起始并进行后续处理步骤。For the target associated position sets X(k), X(k+1), and X(k+2) at three consecutive times, the estimated target position at the corresponding time is obtained, and a combined navigation can be obtained by taking one target from each of the three sets. track, obtain the speed, acceleration, and velocity vector angle of each combination corresponding to the target in chronological order, and then determine whether the corresponding combined track is the target track with the pre-agreed conditions: speed constraint, acceleration constraint, angle constraint and other conditions Perform track initiation. If the combined track satisfies the constraint conditions, confirm the start of the track and perform subsequent processing steps.
2)、上述航迹跟踪滤波中，IMM_UKF算法的示意图如图1所示，图1所示是跟踪一个目标时IMM_UKF算法流程，对多个目标的跟踪时，对每个目标重复使用该算法即可，图中包含N个模型，图中滤波器采用UKF滤波器。图中的是基于N个模型基础之上的状态估计，为模型j的状态估计。为模型可能性向量，uk是模型概率向量。为k-1时刻第j个滤波器的输出。为交互作用的结果，它作为k时刻滤波器j的输入。Z(k)是k时刻的方位角量测集合。是模型j的一步预测状态估计。交互作用过程为：模型i转移到模型j的转移概率为Πij2), in the above-mentioned track tracking filtering, the schematic diagram of the IMM_UKF algorithm is shown in Figure 1, and the flow chart of the IMM_UKF algorithm is shown in Figure 1 when tracking a target. When multiple targets are tracked, the algorithm is repeatedly used for each target. Yes, the figure contains N models, and the filter in the figure uses the UKF filter. in the picture is the state estimation based on N models, is the state estimate of model j. is the model possibility vector, uk is the model probability vector. is the output of the jth filter at time k-1. for The result of the interaction, which serves as the input of filter j at time k. Z(k) is the set of azimuth angle measurements at time k. is the one-step predictive state estimate for model j. The interaction process is: the transition probability from model i to model j is Πij
用uk-1(j)表示模型j的概率，且uk-1(j)是模型概率向量uk中的第个j元素，则交互计算后N个滤波器在k时刻的输入如下Use uk-1 (j) to represent the probability of model j, and uk-1 (j) is the jth element in the model probability vector uk , then the input of N filters at time k after interactive calculation is as follows
式中In the formula
式中，In the formula,
假设模型j离散时间的系统方程为Assume that the discrete-time system equations for model j are
X(k+1)＝fj[k,X(k)]+Vj(k) (17)X(k+1)=fj [k,X(k)]+Vj (k) (17)
模型j离散时间的系统量测方程为The measurement equation of the discrete-time system of model j is
Z(k)＝hj[k,X(k)]+Wj(k) (18)Z(k)=hj [k,X(k)]+Wj (k) (18)
将和Poj(k-1|k-1)作为k时刻第j个模型的输入到UKF滤波器中，计算出(2lx+1)个δ采样点和相应的权值Wi，其中lx是的维度，Will and Poj (k-1|k-1) as the input of the jth model at time k to the UKF filter, and (2lx +1) δ sampling points are calculated and the corresponding weight Wi , where lx is dimension,
式中上标m表示状态更新中的权值；上标c表示协方差更新中的权值；κukf、αukfβukf是UKF算法参数。In the formula, the superscript m represents the weight in the state update; the superscript c represents the weight in the covariance update; κukf , αukf βukf are the parameters of the UKF algorithm.
根据系统状态方程δ采样点的一步预测δ点再利用一步预测δ点以及权值Wi得到状态预测估计和状态预测协方差One-Step Prediction of δ Points Based on System State Equation δ Sampling Points Then use the one-step prediction δ point and the weight Wi to get the state prediction estimate and state prediction covariance
式中，Qj(k)是系统的过程协方差。再根据量测方程，即公式(18)，得到量测预测δ点In the formula, Qj (k) is the process covariance of the system. Then according to the measurement equation, that is, formula (18), the measurement prediction δ point is obtained
则目标的量测预测和相应的协方差为Then the measured predictions and corresponding covariances of the target are
式中，Rj(k)是系统量测噪声协方差矩阵。假设k+1时刻传感器方位角量测为Z(k+1)，则状态更新和状态更新协方差可表示为In the formula, Rj (k) is the system measurement noise covariance matrix. Assuming that the azimuth angle measurement of the sensor at time k+1 is Z(k+1), the state update and state update covariance can be expressed as
式中，In the formula,
得到滤波器输出和Pj(k|k)后计算模型j的可能性get filter output and Pj (k|k) to calculate the possibility of model j
式中In the formula
再更新模型j的概率为The probability of updating model j again is
最后得到k时刻IMM算法的交互式输出为Finally, the interactive output of the IMM algorithm at time k is obtained as
3)、上述航迹跟踪滤波中的JPDA算法即是将方位角量测和目标跟踪航迹关联的算法,主要过程为：假设k时刻有T个目标，并有J个方位角量测落入相应的回波波门内。计算方位角量测j与目标t的关联似然概率βj,t，得到关联似然矩阵BJ×T，则3), the JPDA algorithm in the above track tracking filter is the algorithm that associates the azimuth measurement with the target tracking track, the main process is: suppose there are T targets at time k, and J azimuth measurements fall into corresponding echo gate. Calculate the associated likelihood probability βj,t between the azimuth measurement j and the target t, and obtain the associated likelihood matrix BJ×T , then
式中In the formula
式中St(k)表示k时刻目标t的新息协方差，vj(k)表示方位角量测j对应的新息，且满足其中In the formula, St (k) represents the innovation covariance of the target t at time k, and vj (k) represents the innovation corresponding to the azimuth measurement j, and satisfies in
式中，是跟踪目标t时模型j中UKF滤波器的量测预测值，是跟踪目标t时模型j中UKF滤波器量测预测值协方差。In the formula, is the measured prediction value of UKF filter in model j when tracking target t, is the covariance of the predicted value measured by the UKF filter in model j when tracking target t.
建立一个J×T维的确认关联矩阵WJ×T，并初始化其元素ωjt为0。求BJ×T矩阵最大元素所对应的行列值，并将WJ×T中对应行列的元素赋值为1；将BJ×T中对应行列的所有元素赋值为0。一直重复该步骤，直到BJ×T中所有元素都为0，得到最终的确认关联矩阵WJ×T，其中ωjt为1的表示目标t和方位角量测j关联。Establish a J×T-dimensional confirmation correlation matrix WJ×T , and initialize its element ωjt to 0. Find the value of the row and column corresponding to the largest element of the BJ×T matrix, and assign the value of 1 to the element of the corresponding row and column in WJ×T ; assign the value of 0 to all the elements of the corresponding row and column in BJ×T . This step is repeated until all elements in BJ×T are 0, and the final confirmation correlation matrix WJ×T is obtained, where ωjt is 1, which means that the target t is related to the azimuth measurement j.
4)、上述中断航迹预处理中，对间断时刻之前的目标旧航迹按中断时刻的多模型概率进行预测该目标航迹终结后Tth+Tsm时间内的旧航迹预测状态估计的方法是：假设目标n中断时刻为kn，计算目标的预测状态估计和对应的估计协方差矩阵4), in the above-mentioned interrupted trackpreprocessing , the old track of the target before theinterrupted time is predicted by the multi-model probability of the interrupted time. The method is: assuming that the target n interruption time is kn , calculate the predicted state estimate of the target and the corresponding estimated covariance matrix
其中是跟踪目标t时模型j中UKF滤波器的状态预测估计，即公式(22)；是对应的状态协方差矩阵，即公式(23)。其中kseg的取值满足in is the state prediction estimate of the UKF filter in model j when tracking target t, that is, formula (22); yes The corresponding state covariance matrix is formula (23). Among them, the value of kseg satisfies
对km时刻出现的新的新目标m，并假设其在航迹出现的时间为km～(km+Lm)，则LmTs是该目标出现总时间长度。对新目标m的逆向滤波过程为：将正常滤波过程中，所用的系统状态方程改为如下即可，For a new target m that appears at the timekm, and assuming that its appearance time on the track is km ~ (km + L m ), then L mTsisthetotal time length of the target appearance. The inverse filtering process for the new target m is: change the system state equation used in the normal filtering process to the following,
Xm,逆(k-1|k)＝F-1(k)Xm,逆(k|k)+V(k) (42)Xm, inverse (k-1|k)＝F-1 (k)Xm, inverse (k|k)+V(k) (42)
其中F(k)是正常系统的状态转移矩阵。其他处理过程和航迹跟踪滤波处理的过程类似，且不用考虑JPDA算法。where F(k) is the state transition matrix of the normal system. Other processing procedures are similar to those of track tracking and filtering, without considering the JPDA algorithm.
5)、上述中断航迹序贯关联中，对旧航迹与新航迹的序贯关联法是将根据旧航迹预测出在0～(Tth+Tsm)/Ts时间窗内的航迹其中i＝0,1,...,(Tth+Tsm)/Ts与新航迹的逆向估计航迹按序贯法进行关联，其中i＝0,1,...,Tsm/Ts。令5), in the sequential association of the above-mentioned interruption track, the sequential association method for the old track and the new track will be based on the old track Predict the track within the time window of 0～(Tth +Tsm )/Ts where i=0,1,...,(Tth +Tsm )/Ts and the reverse estimated track of the new track Correlation is performed sequentially, where i=0,1,...,Tsm /Ts . make
式中km的取值范围为0,1,2,...,Tsm/Ts。则检验量为In the formula, the value range of km is 0,1,2,...,Tsm /Ts . then test quantity for
其服从自由度的χ2分布，其中nx表示的维；进一步得到检验矩阵ΨN×M为its obedienceχ2 distribution of degrees of freedom, where nx represents Dimension; further get the test matrix ΨN×M as
再由根据每个旧航迹最多存在一条新航迹与之对应关联、每条新航迹最多存在一条旧航迹与之关联的约束条件、置信度水平α下的检验门限γ1-α、以及检验量矩阵ΨN×M得到航迹关联确认矩阵ΩN×M。其中检验量在某置信度水平α下的检验门限γ1-α满足公式(48)Then according to the constraint condition that there is at most one new track associated with each old track, there is at most one old track associated with each new track, the inspection threshold γ1-α under the confidence level α, and the inspection amount The matrix ΨN×M obtains the track association confirmation matrix ΩN×M . Among them, the amount of inspection The inspection threshold γ1-α under a certain confidence level α satisfies the formula (48)
公式(48)表示检验量小于检验门限γ1-α的概率为1-α。同时航迹关联确认矩阵ΩN×M满足Equation (48) expresses the inspection quantity The probability of being less than the inspection threshold γ1-α is 1-α. At the same time, the track association confirmation matrix ΩN×M satisfies
式中ωn,m是ΩN×M中的元素。Where ωn,m are elements in ΩN×M .
实施例Example
本实施例的无源雷达目标跟踪方法，假设无源雷达跟踪系统是二维平面上的三站固定站跟踪系统(即系统包括3个相距一定距离，处于同一平面上的固定雷达站)，并采用matlab软件进行仿真。The passive radar target tracking method of the present embodiment assumes that the passive radar tracking system is a three-station fixed station tracking system on a two-dimensional plane (that is, the system includes 3 fixed radar stations at a certain distance on the same plane), and The simulation is carried out by using matlab software.
设三个雷达站的位置坐标分别为O1(-20km,0)、O2(20km,0)、O3(0,20km)，并设三个站之间方位角量测互相独立，方位角量测误差均值为0，标准差都为σβ＝0.02°，且服从高斯分布。Suppose the position coordinates of the three radar stations are O1 (-20km,0), O2 (20km,0), O3 (0,20km), and the azimuth angle measurement between the three stations is independent of each other, and the azimuth The mean value of the angle measurement error is 0, the standard deviation is σβ =0.02°, and it obeys Gaussian distribution.
假定该系统采样间隔Ts＝1s，Tth＝22s，Tsm＝3s，仿真总时间T＝120s。Assume that the sampling interval of the system is Ts =1s, Tth =22s, Tsm =3s, and the total simulation time is T=120s.
设观测范围内有三个目标：目标T1在0～120秒内做匀速运动，其初始位置为XT1(-21km,75km)，其初始速度VT1(55m/s,60m/s)；目标T2在0～120秒内做匀速圆周运动，其初始位置为XT2(-20km,82km)，其初始速度VT2(50m/s,-50m/s)，角速度为目标T3在0～120秒内做匀速运动，其初始位置在XT3(-21km,79km)，其初始速度VT3(60m/s,0m/s)；并设定三个站同时丢失目标1在51～67s时间内的方位角量测，同时丢失目标2在51～65s时间内的方位角量测，同时丢失目标3在51～64s时间内的方位角量测。Suppose there are three targets within the observation range: target T1 moves at a constant speed within 0 to 120 seconds, its initial position is XT1 (-21km, 75km), and its initial velocity VT1 (55m/s, 60m/s); target T2 Perform uniform circular motion within 0~120 seconds, its initial position is XT2 (-20km, 82km), its initial velocity VT2 (50m/s, -50m/s), and its angular velocity is Target T3 moves at a constant speed within 0 to 120 seconds, its initial position is XT3 (-21km, 79km), and its initial velocity VT3 (60m/s, 0m/s); and set three stations to lose target 1 at the same time The azimuth measurement of target 2 during 51-65 s is lost at the same time, while the azimuth measurement of target 3 during 51-64 s is lost.
设雷达站的天线指向均为Y轴正方向，且k时刻雷达站j的位置为当此时目标i的位置为则雷达站j获得方位角量测是βji(k)为Assume that the antennas of the radar station are pointing in the positive direction of the Y axis, and the position of the radar station j at time k is At this time, the position of target i is Then the azimuth measurement obtained by radar station j is βji (k) as
式中dβ是方位角测量误差，且其协方差为where dβ is the azimuth measurement error, and its covariance is
设IMM_UKF算法中含有一个匀速运动模型的过程噪声协方差Qcv＝1.8∧2I，六个转弯运动转弯速率为转弯模型的过程噪声协方差为Qtr＝2.5∧2I。其中I表示单位矩阵。并假设IMM算法中7个模型的初始概率为u＝[0.1,0.1,0.1,0.4,0.1,0.1,0.1]′；模型之间的转移概率Assuming that the IMM_UKF algorithm contains a process noise covariance Q cv of a uniform motion model Qcv =1.8∧ 2I, the turning rate of the six turning motions is The process noise covariance of the turn model is Qtr =2.5∧ 2I. where I represents the identity matrix. And assume that the initial probability of the 7 models in the IMM algorithm is u=[0.1,0.1,0.1,0.4,0.1,0.1,0.1]'; the transition probability between the models
设UKF算的参数为：αukf＝0.01、βukf＝2、κukf＝0。It is assumed that the parameters of the UKF calculation are: αukf =0.01, βukf =2, and κukf =0.
由上述仿真条件，可以得知仿真时间120秒内，三个站每个时刻的方位角量测数目同样多，则：From the above simulation conditions, it can be known that within 120 seconds of the simulation time, the number of azimuth angle measurements of the three stations at each moment is the same, then:
1)、跟踪预处理：处理每个时刻的三个雷达站的方位角量测，假设对k时刻的三个站的方位角量测，先选取k时刻的O1和O2两个站的方位角量测根据公式(52)计算得到视线交叉点且1), tracking preprocessing: process the azimuth angle measurements of the three radar stations at each moment, assuming that the azimuth angle measurements of the three stations at the k moment, first select the O1 and O2 stations at the k moment The azimuth measurement is calculated according to the formula (52) to obtain the line of sight intersection point and
式中iO1,iO2∈{1,2,3}；where iO1 , iO2 ∈{1,2,3};
假设一个目标与一个方位角量测一一对应，则得到可能分布总集合T(k)，则Assuming a one-to-one correspondence between a target and an azimuth measurement, the total set of possible distributions T(k) is obtained, then
其中in
再求Ti(k)中三个目标在O3雷达站下的观测值取概率调节系数α＝5σβ，则得到Find the observation values of the three targets in Ti (k) under the O3 radar station Taking the probability adjustment coefficient α=5σβ , we get
式中m,is3∈{1,2,3}。进一步得到三个目标分布情况Ti(k)与O3雷达站真实方位角量测的关联概率为where m,is3 ∈{1,2,3}. Further, the correlation probability between the three target distributions Ti (k) and the real azimuth measurement of the O3 radar station is obtained as
式中等于1或0，且满足In the formula Equal to 1 or 0, and satisfy
再求取最大对应的Ti(k)和得到目标1量测关联为U1(k)＝{β11,β21,β31}，目标2的量测关联为U2(k)＝{β12,β22,β32}，目标3的量测关联为U3(k)＝{β13,β23,β33}；Then find the maximum The corresponding Ti (k) and The measurement correlation of target 1 is obtained as U1 (k) = {β11 , β21 , β31 }, the measurement correlation of target 2 is U2 (k) = {β12 , β22 , β32 }, and the target 3 The measurement correlation of is U3 (k)={β13 ,β23 ,β33 };
根据Ut(k)计算目标t的位置估计Zt(k)＝[xt(k),yt(k)]′，其中t的取值为1、2、3；则Calculate the position estimate Zt (k)=[xt (k), yt (k)]′ of the target t according to Ut (k), where the value of t is 1, 2, 3; then
式中In the formula
画出所有目标所有时刻的位置估计图如图2所示；Draw the position estimation map of all targets at all times as shown in Figure 2;
同时可以计算目标t测量误差在直角坐标系下的协方差误差为At the same time, the covariance error of the target t measurement error in the Cartesian coordinate system can be calculated as
所以根据前两个时刻的方位角量测值得到目标t的初始状态估计和估计协方差为Therefore, the initial state estimation and estimated covariance of the target t are obtained according to the azimuth measurement values at the first two moments:
2)、航迹跟踪滤波：根据跟踪预处理得到所有目标的初始状态估计和估计协方差，即公式(62)和公式(63)，带入到IMM_UKF算法中对所有进行跟踪滤波；2), track tracking filter: According to the tracking preprocessing, the initial state estimation and estimated covariance of all targets are obtained, that is, formula (62) and formula (63), which are brought into the IMM_UKF algorithm to track and filter all targets;
首先根据目标t在k-1时刻的状态估计和估计协协方差Pt(k-1|k-1)通过公式(19)到公式(26)得到量测预测值和对应的协方差矩阵First, according to the state estimation of the target t at time k-1 and the estimated co-covariance Pt (k-1|k-1) to obtain the measurement prediction value through formula (19) to formula (26) and the corresponding covariance matrix
再根据公式(35)到公式(38)得到关联似然矩阵BJ×T，建立确认关联矩阵WJ×T，并初始化其元素ωjt为0。求BJ×T矩阵最大元素所对应的行列值，并将WJ×T中对应行列的元素赋值为1；将BJ×T中对应行列的所有元素赋值为0。一直重复该步骤，直到BJ×T中所有元素都为0，得到最终的确认关联矩阵WJ×T；Then according to formula (35) to formula (38), get correlation likelihood matrix BJ×T , establish confirmation correlation matrix WJ×T , and initialize its element ωjt to 0. Find the value of the row and column corresponding to the largest element of the BJ×T matrix, and assign the value of 1 to the element of the corresponding row and column in WJ×T ; assign the value of 0 to all the elements of the corresponding row and column in BJ×T . This step is repeated until all elements in BJ×T are 0, and the final confirmation correlation matrix WJ×T is obtained;
根据WJ×T的关联结果，将与目标t与之关联的方位角量测Zt(k)带入到公式(27)到公式(34)得到所有目标t在k时刻的状态估计和估计协方差Pt(k|k)，以及k时刻目标t的多模型概率According to the correlation result of WJ×T , the azimuth measurement Zt (k) associated with the target t is brought into formula (27) to formula (34) to obtain the state estimation of all targets t at time k and the estimated covariance Pt (k|k), and the multi-model probability of the target t at time k
若某个时刻ke起连续3个Ts周期内没有方位角量测与目标t关联成功，则目标在ke时刻航迹中断；If there is no azimuth measurement successfully associated with the target t within 3 consecutive Ts cycles from a certain time ke , the target track is interrupted at the time ke ;
若某个时刻ks有方位角量测未与所有ks-1时刻的目标关联成功，则认为是新目标出现，对于新目标的航迹跟踪滤波，则按照该目标ks时刻和ks+1时刻的方位角量测，按照上述跟踪预处理中公式(58)至公式(63)的处理方式得到If the measurement of azimuth angle at a certain time ks fails to correlate successfully with all the targets at ks -1 time, it is considered that a new target appears, and for the track tracking filter of the new target, according to the time ks and ks of the target The azimuth angle measurement at +1 time is obtained according to the processing methods of formula (58) to formula (63) in the tracking preprocessing above
再利用航迹跟踪处理过程对其进行滤波；Then use the track tracking process to filter it;
最终得到经过航迹跟踪处理后的实施案例中三个目标的航迹如图3所示；Finally, the trajectories of the three targets in the implementation case after the track tracking process are obtained as shown in Figure 3;
3)、中断航迹预处理：按顺序时间搜索出现所有目标出现航迹中断的所有时刻，并对所有中断按如下航迹中断预处理进行处理：3), interrupted track preprocessing: search for all times when all targets appear track interrupted in order of time, and process all interrupts according to the following track interrupted preprocessing:
假设在中断时刻ke出现有N个旧目标中断，在ke之后阈值时间Tth+Tsm内又有M个新目标航迹出现；Assuming that there are N old target interruptions at the interruption time ke , and M new target tracks appear within the threshold time Tth +Tsm after ke ;
设旧目标n出现航迹中断时刻为kn＝ke，根据公式(39)至公式(41)得到所有N个旧目标在Tth+Tsm时间内的状态预测值和预测协方差，其中是目标n的状态预测值，Pn(kseg+1|kseg+1)是对应的预测协方差，其中kseg满足公式(41)，并将所有N个旧目标在0～Tth+Tsm时间窗内的预测值记为其中k＝1,2,...,(Tth+Tsm)/Ts；Assuming that the track interruption time of old target n is kn = ke , according to formula (39) to formula (41), the state prediction value and prediction covariance of all N old targets in the time Tth + Tsm are obtained, where is the state prediction value of target n, Pn (kseg +1|kseg +1) is The corresponding prediction covariance, where kseg satisfies formula (41), and the predicted values of all N old targets within the time window 0～Tth +Tsm are recorded as where k=1,2,...,(Tth +Tsm )/Ts ;
设新目标m在出现的时刻为km航迹总长度为LmTs，依据上述航迹跟踪处理中得到的新目标m在km+Lm时刻的估计状态和估计协方差Pm(km+Lm|km+Lm)。按照公式(42)设置系统方程的方法重新设置每个IMM模型的系统状态方程，再依据上述航迹跟踪滤波中IMM_UKF的方法进行逆向滤波，得到新航迹逆向滤波状态估计和其中i＝1,2,...,Lm，并将所有M个新目标在0～Tsm时间窗内的逆向估计记为其中i＝0,1,2,...,Tsm/Ts；Assuming that the time when the new target m appears is km and the total length of the track is Lm Ts , according to the estimated state of the new targetm at the time km + L mobtainedin the above track tracking process and estimated covariance Pm (km +Lm |km +Lm ). Reset the system state equation of each IMM model according to the method of setting the system equation in formula (42), and then perform inverse filtering according to the method of IMM_UKF in the above-mentioned track tracking filter, and obtain the state estimation of the new track inverse filter with where i=1,2,...,Lm , and the inverse estimation of all M new targets within the time window of 0～Tsm is recorded as where i=0,1,2,...,Tsm /Ts ;
至此得到各个中断航迹的预测值和新航迹的逆向估计如图4所示，其局部放大如图5所示；So far, the predicted value of each interrupted track and the inverse estimation of the new track are shown in Figure 4, and its partial enlargement is shown in Figure 5;
4)、中断航迹序贯关联：上述中断航迹预处理结果，即得到的新航迹逆向状态估计其中i＝0,1,2,...,Tsm/Ts和旧航迹的状态预测值记为其中k＝1,2,...,(Tth+Tsm)/Ts，如图4所示，根据公式(43)至公式(47)计算得到关联检验矩阵ΨN×M，再根据每个旧航迹最多存在一条新航迹与之对应关联、每条新航迹最多存在一条旧航迹与之关联的约束条件、置信度水平α下的检验门限γ1-α、以及检验量矩阵ΨN×M得到航迹关联确认矩阵ΩN×M；4) Sequential association of interrupted track: the above-mentioned interrupted track preprocessing result, that is, the reverse state estimation of the new track obtained where i=0,1,2,...,Tsm /Ts and the state prediction value of the old track are denoted as Where k=1,2,...,(Tth +Tsm )/Ts , as shown in Figure 4, the correlation test matrix ΨN×M is calculated according to formula (43) to formula (47), and then according to There is at most one new track associated with each old track, the constraint condition that there is at most one old track associated with each new track, the inspection threshold γ1-α under the confidence level α, and the inspection matrix ΨN ×M to get the track association confirmation matrix ΩN×M ;
5)、航迹确认：上述中断航迹关联结果，得到关联确认矩阵ΩN×M，根据ΩN×M将有新航迹关联的旧航迹中断时间内的状态用状态预测值代替，并和新航迹形成稳定航迹；对未与新航迹关联的旧航迹确认航迹终结；对未与旧航迹确认关联的新航迹按新目标起始航迹；最终得到仿真结果如图6所示。5) Track confirmation: the above-mentioned interrupted track association results, the association confirmation matrix ΩN×M is obtained, according to ΩN×M , the state within the interruption time of the old track associated with the new track is replaced by the state prediction value, and The new track forms a stable track; confirm the end of the track for the old track that is not associated with the new track; start the track with a new target for the new track that is not associated with the old track; the final simulation result is shown in Figure 6 .
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| RJ01 | Rejection of invention patent application after publication | Application publication date:20170725 |