A student-t mixture filtering algorithm based on adaptive parametric model

The state estimation technique is the foundation and prerequisite of trajectory prediction and interception, which are critical parts of defense techniques. As a result, the increasing defense demand for re-entry vehicles requires a high-precision state estimation. Since re-entry vehicles perform cross-domain flight, unknown outliers are committed in the complex flight environment, and it is intractable for the detection system in capturing the distribution and statistical information of non-Gaussian noise, which brings in disastrous outcomes for the state estimation. Without any prior statistics of measurement noise, an adaptive variational Bayesian Student-t mixture filtering (AVBSTMF) built an adaptive parametric model based on the improved STM in variational Bayesian (VB) framework to address the non-stationary measurement noise with uncertain non-Gaussian degree to provide a high-precision state estimation. Firstly, the STM distribution as a generalized distribution taking full advantage of mixture components and the heavy-tailed characteristic of the ST distribution can mitigate the outlier effects and crack the dependency on the assumptions of measurement noises’ prior distributions. In addition, a novel parametric model termed normal Gaussian-inverse Wishart -Gamma (NIW-Gam) approximation scheme employing the VB method adaptively updates parameters online to break the dependence on the prior statistics to improve the STM distribution. Within the framework of the improved STM, the NIW distribution is introduced to characterize the unknown time-varying mean, simultaneously the Gam distribution is introduced to express DOFs to deal with uncertain non-Gaussian degree of measurement noise. As a result, grounded in the NIWGam distribution, the improved STM distribution termed STM (STMNIWGam) joint distribution can implement online adjustment of the component coefficient, mean and DOF parameters to capture the statistics of time-varying and non-stationary noise without the dependence on prior information in the complex flight environment. Finally, ground in the quantification, the design of the proposed filter is further derived analytically based on the VB algorithm. The simulation results of hypersonic skip-glide vehicles demonstrate that the proposed AVBSTMF can improve the estimation accuracy and robustness significantly. Meanwhile, the success in the state estimation implementations of the vehicle shows great potential in other application areas such as the location, navigation, and multi-sensor fusion algorithm.