To identify the turn rate of fighter Zigzag maneuver under one-step randomly delayed measurements and non-Gaussian measurements noise and to achieve better tracking performance

based on the idea of joint estimation and identification and Maximum Likelihood Estimation Criteria

a joint optimization algorithm based on expectation maximization for target state estimation and turning angular identification is proposed

which takes mutual coupling between target state and turning angular velocity into account. The algorithm basically contains two parts: E-step and M-step. In the E-step

the likelihood function of particle filter was firstly reconstructed by fully taking one-step randomly delayed measurements and non-Gaussian measurements noise into account

which improves the update formula of particle weight. Meanwhile

in order to avoid particle deficiencies

the particle swarm algorithm was introduced into the reconstructed particle filter to improve the sampling process. Secondly

the idea of rejection sampling was introduced into the backward simulation particle smoother

and the termination condition for rejecting the sampling was set accordingly

thus the backward simulation particle smoother was further optimized to improve the execution efficiency of the smoothing algorithm. Lastly the smooth estimation of the target state was obtained by using the improved particle filter and backward simulation particle smoother. In the M-step

a numerical optimization algorithm was used to maximize the conditional likelihood function

and the estimation of the turning angular velocity was thus obtained for the next iteration of the algorithm. The optimized solution of the closed-loop form of the turning angular velocity was obtained by the iteration of E-step and M-step. Simulation results show that the proposed algorithm performed better in state estimation and turn rate identification than the traditional augmentation method.