An Application of a Set-Valued State Estimator Based on Constrained Zonotopes in GNSS-INS Integration

In this paper, the problem of guaranteed state estimation and fault detection for integrated navigation systems in aerospace vehicles is considered. Global Navigation Satellite Systems (GNSS) aided Inertial Navigation System (INS) via sensor fusion is used to estimate the states of a vehicle with high accuracy and at a high sampling rate. Kalman filtering is one of the most popular techniques for state estimation of such systems in a stochastic way. However, poor initialization or parameterization, unknown-but-bounded disturbances, unavailability of statistical information about the sensors and abnormal measurements due to sensor failures is a major drawback. In more practical applications, the covariances are usually approximated by heuristic approaches which may lead to situations where the filter may not perform in an optimal or desired way. In this paper, a set-membership based approach is used to bound the vehicle states by a poly topic set representation known as Constrained Zonotopes. A minimum-variance criterion is used for optimal state estimation and the bounds can be used for integrity monitoring and fault detection for the system since these bounds are guaranteed by construction. An example of GNSS-INS integration for a Quadrotor UAV trajectory is considered and the results are compared with the Extended Kalman filter.