Measurement bootstrapping Kalman filter

In practice, many estimation problems rely on on-line solutions, hence recusive methods are necessary. Tradition estimation approaches for linear systems subject to Gaussian noise are based on the Kalman filter and its improving algorithms. Based on the realization construction of state prediction and measurement update, Kalman filter can obtain the optimal estimation of state under the linear minimum variance criterion. However, it is known that the optimal filtering result is achieved in statistical sense, which can not meet a superior result for single filtering process because of the random characteristics effect of measurement noise. Aiming at this problem, the authors propose a novel Kalman filtering algorithm based on measurement bootstrapping strategy. In realization of algorithm, first, combining with the extraction and utilization of measurement information including the latest measurement and the prior statistical information from measurement noise modeling, the measurement bootstrapping strategy is designed and virtual measurements are sampled. Its objective is to enhance the reliability of latest measurement by increasing samples numbers. Second, virtual measurements are applied to Kalman filtering framework, and the key improvement is concentrated in the utilization of measurement information. In addition, considering the requirements in engineering application such as instantaneity, filtering precision and robustness, the distributed weighted fusion structure and the centralized consistency fusion structure are designed respectively. Finally, the theoretical analysis and experimental results verify the feasibility and efficiency of the proposed algorithm.