A State Optimization Model Based on Kalman Filtering and Robust Estimation Theory for Fusion of Multi-Source Information in Highly Non-linear Systems

Abstract

Consistent state estimation is a vital requirement in numerous real life applications from localization to multi-source information fusion. The Kalman filter and its variants have been successfully used for solving state estimation problems. Kalman filtering-based estimators are dependent upon system model assumptions. A deviation from defined assumptions may lead to divergence or failure of the system. In this work, we propose a Kalman filtering-based robust state estimation model using statistical estimation theory. Its primary intention is for multiple source information fusion, although it is applicable to most non-linear systems. First, we propose a robust state prediction model to maintain state constancy over time. Secondly, we derive an error covariance estimation model to accept deviations in the system error assumptions. Afterward, an optimal state is attained in an iterative process using system observations. A modified robust MM estimation model is executed within every iteration to minimize the impact of outlying observation and approximation errors by reducing their weights. For systems having a large number of observations, a subsampling process is introduced to intensify the optimized solution redundancy. Performance is evaluated for numerical simulation and real multi sensor data. Results show high precision and robustness of proposed scheme in state estimation.