光电跟踪系统的估计性能随着探测概率的下降而降低,是否存在一个临界探测概率,当跟踪系统的实际探测概率高于临界探测概率时,跟踪系统统计意义下的估计误差协方差对任意估计初值均收敛是跟踪系统设计时的一个关键问题.本文证明了跟踪系统临界探测概率的存在性,并且给出了临界探测概率的一组上下界,其上界被描述成一个非线性矩阵不等式(NMI)的最优解,其下界仅与跟踪系统状态转移矩阵的特征值有关.进一步利用摄动线性化方法给出了求解临界探测概率上界的一种迭代线性矩阵不等式(ILMI)算法,并且对跟踪系统在三种标准测试场景中的临界探测概率上界进行了仿真求解,仿真结果表明:当跟踪系统的探测概率高于50％时,其统计意义下的估计误差协方差对任意估计初值均收敛,这为跟踪系统探测概率的设计提供了理论依据.%The estimation performance of optic-electric tracking systems degrade with the decrease of detection probability. The key problem of designing a tracking system is that whether there is a critical detection probability, when the actual detection probability of a tracking system is greater than the critical detection probability, the estimation error covariance of the tracking system is convergent under the statistic significance for the arbitrary initial value of estimation. The existence of critical detection probability of tracking systems is proved, and the upper and lower bound of the critical detection probability is presented. The upper bound is described as the optimal solution of a nonlinear matrix inequality (NMI) , and the lower bound is only related to the eigenvalues of system state transition matrices. An iterative linear matrix inequality (ILMI) algorithm for solving the upper bound of critical detection probability is proposed by means of perturbation linearization, and the upper bound of the critical detection probability of tracking systems is solved by the proposed algorithm in three standard simulation scenes. The simulation results show that when detection probability of tracking systems is greater than 50%, the estimation error covariance of tracking systems is convergent under the statistic significance for the arbitrary initial value of estimation, which provides a theoretical basis for the design of the detection probability of an optic-electric tracking system.
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