Constrained Information-based State Estimation And Fusion

State estimation, which is also called filtering, means estimating the inner statesof a dynamic system indirectly, according to the selected principles and observationdata we can get. It is widely and successfully applied in various fields such asaeronautics and astronautics, target tracking, electric systems, pattern recognition, androbot formation. In practical applications of state estimation theory, the state vectorsalways include some constraint terms which are known in advance. Researchers canunderstand the relationship within the state components more thoroughly using thepriori information. However, the intrinsic priori constraints of a system are alwaysneglected in applications of state estimation theories. The reason is that the efficientmining and application of constraints are inadequate, not because there doesn’t existany constraints in reality. In fact, constraints change the structure of state estimationprobability model and alter the previous estimation process, making data analysis andthe realization of state estimation difficult. Should the difficulties be overcome, andthe priori constraints be rationally utilized, we will improve the accuracy of stateestimation for dynamical systems with constraints.So, it is meaningful and practical to develop research on constrained-based stateestimation and fusion. On the basis of previous scientific researches, this paperreveals several new algorithms mainly for linear equation constraint, non-linearequation constraint, unknown observation noise, and multi-sensor constrained systemswith relevant observation noise. The research work is concentrated on three aspects asfollows:1) The state estimation problem with linear and nonlinear state constraints isstudied. Constrained information is incorporated into the traditional Kalman filtering Framework. The traditional Kalman filter result without constraint is projected toconstraint subspace, and the result after projection has higher state estimationaccuracy. The constrained Kalman filter is classified as open-loop estimationprojection method and closed estimation projection method depending on whether theprojected state estimation feedback to filtering circuit. At the same time, the filteringalgorithm based on projection is extended to nonlinear systems.2) For equation-constrained cases where the statistical characteristics ofobservation noise are unknown, a fuzzy adaptive filtering algorithm is proposed. Withthe help of fuzzy inference system and covariance matching technology, observationnoise covariance matrix is adjusted on-line, real time to get closer to the real situation.Therefore, the adaptive ability to model variation of state estimation is effectivelydeveloped.3) In order to improve the accuracy and reliability of state estimation, wepropose multi-sensor equality constrained state estimation algorithm based on theprevious results. We study a new multi-sensor optimal information fusion algorithmweighted by matrices. In addition, this paper also studies the strategies of distributedfusion, eliminating the sensors with abnormal observations detected bycovariance-matching technology in the data fusion process. Finally, this paper studiesthe constraint filtering on the occasion of observation noise relevance among amulti-sensor system.