The INS/GNSS integration is the commonly used technique for hypersonic vehicle navigation. However, owing to the complicated flight dynamics with high maneuverability and large flight envelope, the dynamic model of INS/GNSS integration inevitably exists errors which degrades the navigation performance of a hypersonic vehicle seriously. In this paper, a new model predictive based unscented Kalman filter (MP-UKF) is proposed to address this problem. The MP-UKF employs the concept of model predictive filter for the establishment of a dynamic model error estimator, and it subsequently compensate the model error estimation to UKF for nonlinear state estimation. Since the MP-UKF could predict the dynamic model error persistently and correct the filtering procedure of UKF online, it improves the UKF adaptiveness and is promising for the performance enhancement of INS/GNSS integration for hypersonic vehicle navigation. Simulation results and comparison analysis have been conducted to demonstrate the effectiveness of the proposed method. INDEX TERMS Unscented Kalman filter, model predictive filter, hypersonic vehicle navigation, INS/GNSS integration, dynamic model error.

This paper presents a new stochastic-based method for modelling and analysis of COVID-19 spread. A new deterministic Susceptible, Exposed, Infectious, Recovered (Re-infected) and Deceased-based Social Distancing model, named SEIR(R)D-SD, is proposed by introducing the re-infection rate and social distancing factor into the traditional SEIRD (Susceptible, Exposed, Infectious, Recovered and Deceased) model to account for the effects of re-infection and social distancing on COVID-19 spread. The deterministic SEIRD(R)D-SD model is further converted into the stochastic form to account for uncertainties involved in COVID-19 spread. Based on this, an extended Kalman filter (EKF) is developed based on the stochastic SEIR(R)D-SD model to simultaneously estimate both model parameters and transmission state of COVID-19 spread. Simulation results and comparison analyses demonstrate that the proposed method can effectively account for the re-infection and social distancing as well as uncertain effects on COVID-19 spread, leading to improved accuracy for prediction of COVID-19 spread.

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