An Adaptive Estimation Method for Heterogeneous Group Targets with Uncertain Multiplicative and Additive Noises

In this paper, an adaptive estimation algorithm for heterogeneous group targets considering uncertain multiplicative and additive noises is proposed. Firstly, a state-space model for heterogeneous group targets with composite multiplicative and additive noise is established. Since the coupling effect of multiplicative noise renders the marginal likelihood analytically intractable and induces heavy-tailed characteristics, a tailored hierarchical Gaussian–Gamma model is introduced for robust approximation. Second, a joint posterior probability density function incorporating the target kinematic state, extended morphology, and noise parameters is constructed. Within the variational Bayesian framework, approximate posterior distributions of these variables are derived, and fixed-point iteration is employed to compute the system state and noise statistics. Simulation results demonstrate that, under environments corrupted by unknown and time-varying multiplicative and additive noises, the proposed algorithm adaptively estimates a unified measurement noise covariance, achieving superior estimation performance compared to the random matrix model and the VB-EOT-SN method.