An Efficient Estimation Method for Dynamic Systems in the Presence of Inaccurate Noise Statistics

The uncertainty of noise statistics in dynamic systems is one of the most important issues in engineering applications, and significantly affects the performance of state estimation. The optimal Bayesian Kalman filter (OBKF) is an important approach to solve this problem, as it is optimal over the posterior distribution of unknown noise parameters. However, it is not suitable for online estimation because the posterior distribution of unknown noise parameters at each time is derived from its prior distribution by incorporating the whole measurement sequence, which is computationally expensive. Additionally, when the system is subjected to large disturbances, its response is slow and the estimation accuracy deteriorates. To solve the problem, we improve the OBKF mainly in two aspects. The first is the calculation of the posterior distribution of unknown noise parameters. We derive it from the posterior distribution at a previous time rather than the prior distribution at the initial time. Instead of the whole measurement sequence, only the nearest fixed number of measurements are used to update the posterior distribution of unknown noise parameters. Using the sliding window technique reduces the computational complexity of the OBKF and enhances its robustness to jump noise. The second aspect is the estimation of unknown noise parameters. The posterior distribution of an unknown noise parameter is represented by a large number of samples by the Markov chain Monte Carlo approach. In the OBKF, all samples are equivalent and the noise parameter is estimated by averaging the samples. In our approach, the weights of samples, which are proportional to their likelihood function values, are taken into account to improve the estimation accuracy of the noise parameter. Finally, simulation results show the effectiveness of the proposed method