Existing robust filters under generalized nonstationary noises conditions are difficult to choose suitable prior parameters, this brief proposed a Pearson-type VII distribution with adaptive parameters selection based interacting multiple model (IMM) Kalman filter (IMMPVII KF). In the model conditional filtering process, both the one-step prediction and the measurement likelihood are modeled as Pearson-type VII distributions. They are decomposed into Gaussian-Gamma Hierarchies (GGH), which are then matched to the time-varying heavy-tailed properties of the noises by pre-selecting the sets of shape and rate parameters and the variational Bayesian (VB) technique. Finally, a new model probability update method for filter under non-Gaussian conditions is derived. Simulation results show that the filter proposed in this brief has better robustness and adaptability to generalized non-stationary noises than the existing filters.

In this paper, a multi-prior mixture (MPM) distribution and arithmetic average (AA) fusion-based Student’s t filter (MPMAASTF) is proposed for the problem of non-stationary heavy-tailed noises filtering with only rough prior information available. Firstly, a MPM distribution is proposed to model the joint probability density function (PDF) for one-step prediction and measure likelihood, then the Kullback-Leibler Divergence (KLD) minimization technique and Jensen’s inequality are used to derive approximate posterior PDFs for states and parameters. A finite number of Student’s t PDF fusion algorithm based on AA fusion is developed to guarantee the closure of the filtering posterior PDF, and finally existing high precision moment matching technique is embedded. The proposed filter improves the filtering accuracy of non-stationary heavy-tailed noises by adaptive learning of the degrees of freedom (dof), the one-step prediction error scale matrix and the measurement noise scale matrix. Simulations validate the effectiveness and superiority of the proposed method.

The velocity and acceleration of geostationary transfer orbit (GTO) satellites change dramatically and periodically, and the operating area extends from hundreds of kilometers to 36,000 km above the Earth’s surface. This leads to the limitation of navigation methods of GTO satellites, the complexity of perturbation components and the increase of sensor measurement noise. Therefore, in this paper, a celestial navigation system/Beidou navigation system (CNS/BDS) integrated navigation method based on the adaptive spherical simplex unscented transformation federated Kalman filter (ASSUT-FF) algorithm is designed for GTO satellite high-precision autonomous navigation, considering the integrated navigation method and filtering algorithm. A Beidou observation model based on the relative pseudorange/pseudorange rate is established. Even when the GTO satellite moves to the high orbit region, it can still use BDS navigation information to determine the orbit. In addition, the designed adaptive algorithm can still ensure the filter stability in a complex space environment. The CNS/BDS integrated navigation method based on the ASSUT-FF algorithm proposed in this paper can realize continuous and high-precision autonomous navigation of GTO satellites. The simulation results show that the orbit determination accuracy of the proposed navigation method is 96.23% and 84.06% higher than that of the single celestial navigation method and the traditional Beidou geometric positioning correction celestial navigation method, respectively. The performance test results of the adaptive algorithm also show that the ASUT-FF algorithm has good robustness.