基于GM-CPHD滤波算法的主动声呐目标跟踪
Active Sonar Target Tracking Based on the GM-CPHD Filter Algorithm

水下多目标运动状态估计一直是主动声呐目标跟踪的难点问题。为了实现对可变数目水下多目标运动状态的估计，将随机有限集理论应用于多目标跟踪，不仅避免了多目标跟踪数据关联问题，而且解决了多目标跟踪过程中可变数目目标运动状态估计。传统的PHD滤波算法对目标数目估计存在敏感性，虽然CPHD滤波算法引入了对势分布的估计提高了对目标数目估计的精确性，但同时也增加了其计算量。对于高斯线性目标跟踪系统，GM-CPHD滤波算法对目标数目的估计比GM-PHD滤波更加精确。利用椭圆跟踪门策略减小了GM-CPHD滤波算法的计算量。同时，结合水下目标跟踪的特点，利用声呐方程得到一定虚警概率条件下的检测概率与距离关系的解析式，提出了一种适合于水下目标跟踪的自适应检测概率GM-CPHD滤波算法，仿真结果表明：该算法在多目标跟踪中可以更有效地实现目标状态及数目的估计。
The estimation of underwater multi-target state has always been the difficult problem of active sonar target tracking. In order to get the variable number of target and their state, the random finite set theory is applied to multi-target tracking system. This theory not only effectively avoids the problem of multi-target tracking data association, and also realizes the estimation of time-varying number of targets and their states. Due to Probability Hypothesis Density(PHD) recursion propagates cardnality distribution with only a single parameter, a new generalization of the PHD recursion called Cardinalized Probability Hypothesis Density(CPHD) recursion, which jointly propagates the intensity function and the cardnality distribution, while have a big computation than PHD. Also there did not have closed-form solution for PHD recursion and CPHD recursion, so for linear Gaussian multi-target tracking system, the Gaussian Mixture Probability Hypothesis Density and Gaussian Mixture Cardinalized Probability Hypothesis Density(GM-CPHD) filter algorithm is put forward. GM-CPHD is more accurate than GM-PHD in estimation of the time-varying number of targets. In this paper, we use the ellipse gate tracking strategy to reduce computation in GM-CPHD filtering algorithm. At the same time, according to the characteristics of underwater target tracking, using active sonar equation, we get the relationship between detection probability, distance and false alarm, when fixed false alarm, analytic formula of the relationship between adaptive detection probability and distance is obtained, we puts forward the adaptive detection probability GM-CPHD filtering algorithm. Simulation shows that the combination of ellipse tracking gate strategy and adaptive detection probability GM-CPHD filtering algorithm can realize the estimation of the time-varying number of targets and their state more accuracy in dense clutter environment