A novel stochastically stable variational Bayesian Kalman filter for spacecraft attitude estimation

Abstract

AbstractIn the context of nonlinear systems, variational Bayesian filters play an important and alternative role to sampling‐based Monte Carlo methods. Although they have been used in conjunction with derivatives of Kalman filters, their behavior, both in terms of convergence, stability, and a solution without a stepwise approximation procedure, has not been well explored. In this paper, we propose a novel, stochastically stable, stepwise approximation‐free variational Bayesian Kalman filter (hence, termed as VBKF) for nonlinear systems. The proposed filter, unlike other posterior distribution estimation methods, is very flexible with the number of parameters that should be known a priori, offers an excellent convergence rate, stochastic stability, and more specifically in its ability to handle non‐Gaussian, unknown, inaccurate and drifting noise models. Furthermore, one of the key advantages of the proposed solution is that it is stepwise approximation‐free, and as such, less computationally demanding. We also prove that the proposed filter is stochastically stable using the Posterior Cramér–Rao Lower Bound. In addition to the stability, by using Lyapunov function, we show that the estimation errors are exponentially bounded by the mean square error under certain conditions. In addition to this, we also demonstrate the practical applicability of the proposed approach by developing a novel filter for estimating the attitude of spacecrafts using star cameras and gyro‐sensors. We then evaluate the efficacy of the novel filter for attitude estimation, and thus that of the VBKF, using a set of detailed simulations mimicking different initialization errors that are common in attitude estimation. Our results show that the proposed approach offers an excellent convergence rate within conventional bounds, better root mean square error when compared against several of the common, and state‐of‐the‐art methods.