Abstract:

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.

Key words: opticelectric tracking systems;intermittent observations;critical detection probability;nonlinear matrix inequality