## 1 Introduction  
Multi-target tracking technology based on random finite sets (RFS) has achieved great development in recent years [1, 2, 3, 4]. It not only overcomes the problem of excessive association calculation due to increasing number of targets in traditional multi-target tracking technology based on the data association algorithm [5, 6]. It can also solve the tracking difficulties caused by uncertain factors, such as detection parameters and new targets in the environment with an unknown clutter rate [7, 8, 9]. The filtering technology developed by RFS has been used in many successful applications, such as aerial warning [10], marine monitoring [11, 12], computer vision [13] and sonar detection [14]. PHD filter [15, 16] is the first-moment approximation of multi-objective Bayesian filter based on random finite set, which recurses multi-objective density in the single-objective state space. Compared with the cardinalized PHD filter [17], generalized label multi-Bernoulli (GLMB) filter [18], Poisson multi-Bernoulli mixture (PMBM) filter [19] and other filters, the PHD filter is the most basic RFS filter with the lowest computational complexity. The multi-objective posterior density and cardinality propagated by the PHD filter are subjected to Poisson distribution, and the elements in each cardinality are independently and identically distributed. Take the frame structure of PHD filter into consideration, the dynamic track of the target cannot be obtained directly, and dynamic correlation cannot be automatically generated at different moments of the same target. The key to improve multi-target tracking technology is producing a PHD filter that can form the trajectory without discarding the historical state while capturing the current target state. Instead of labeling the PHD components for trajectory construction [20; 21; 22], [PERSON] et al. proposed the TPHD filter for trajectory [23], which uses the trajectory instead of target as the basic variable of trajectory space [24] under the similar structural framework to PHD filter. The trajectory state is estimated in a principled way, which requires a minimum KLD [25] to propagate an approximate PHD subject to the Poisson distribution given by a fast implementation of the Gaussian mixture. On the basis of TPHD, the jump Markov model (JMS) was recently used to achieve highly dynamic maneuvering target's trajectory, and the derivation of JMS-TPHD closed solution proved its tracking effectiveness [26]. In addition, in order to achieve the combination of target tracking and classification, trajectory information was used in [27], combined with the JTC model to classify the trajectory generated by different targets, and the trajectory showed better performance than the PHD filter after confirming the dynamic model based on posterior probability. It is unlikely to regard the covariance of the measurement noise of the target as a priori knowledge in the practical application, so the measurement noise will change with time followed by the environmental interference. When the estimated noise covariance is different from the actual covariance, PHD will have a partial estimation, resulting in inaccurate state estimation, false target error, wrong cardinality of targets along with the reduced performance and reliability of the filter. To solve the problem of unknown covariance of measurement noise, the least square method was initially used to approximate the noise error [28]. In addition, the interactive multi-model [29] and particle method [30] were also used to solve the problem of measurement noise covariance, but it required a huge amount of calculation. On the other hand, a robust filter with the minimum interference can be achieved under the worst influence of unknown measurement noise on the estimation error [31]. This kind of filter can tolerate the change of noise to the maximum extent rather than realizing adaptive estimation. Refs. [32; 33; 34] modeled a random matrix according to the conjugate prior distribution of the covariance.