A Study Of Kalman Filtering Algorithm With Equality Constraints And Its Application

With the swift development of geomatics, the modern data processing theory is gradually being expanded, especially the development of dynamic positioning theory. Kalman filter is often used in dynamic positioning data processing methods, and is very suitable for real-time and computer operation due to its characteristic of real-time, recursive, and not need to store historical data. Kalman filter has been used more and more in dynamic positioning, such as real-time GPS positioning, inertial navigation and integrated navigation. However, the dynamic positioning data processing theory always confined to the original data processing and less use of some useful prior information. Today, especially in the area of geodesy, we could get more and more abundant observational information with the rapid development of measurement techniques and variety of observation techniques. We can establish a prior information base on these constraints, if the observation information obtained in an observation target or object of any physical and mechanical properties is enough. And if we can make full use of these priori constraints information and effective combine with Kalman filter model, we can improve calculation accuracy and accurate positioning results. Therefore, the research on the constraint filter algorithm is very necessary.This paper systematically studied equation constraints of various algorithm, and compare with each other. During this review, The equality constrained problem is transformed into a convex quadratic programming problem, then the problem turns into a LCP problem using Kuhn Tucker conditions, an explicit expression of constrained filter estimator is given by Lemke algorithm. At last We achieve good results in the experiment combined with the vehicle location. And this is also the solution of equality constrained filtering and statistical properties of a preliminary study. Specific contents are as follows:(1) This paper summaries several linear equality constraint filtering algorithms which major domestic and foreign scholars have researched. Then verifying analysis is done. In this paper, we give the explicit expression of constrained filter estimate for quadratic programming by using the Lemke algorithm.(2) The paper analyses the algorithm of robust filtering with equality constraints, and present the correction method when gross errors occur.(3) The paper analyses the statistical properties of the solution based on equality constrained Kalman Filtering, and expands equality constrained Kalman Filtering to inequality constrained Kalman Filtering.(4) The paper gives the algorithm of the equality constrained Kalman filtering in the nonlinear system.Structural framework of this paper is as follows:Chapterâ… briefly describes the source of the equality constraint model, and introduces the general form of the model; Chapterâ…¡gives the algorithm for equality constrained adjustment model and its characteristics, and the explicit expression of kalman filter estimator by Lemke algorithm; Chapterâ…¢gives the treatment by using the robust filtering with equality constraints while the observation is polluted by the outlier; Chapterâ…£analyses the statistical properties of equality constraint filtering solution; Chapterâ…¤expands equality constrained Kalman Filtering to inequality constrained Kalman Filtering; Chapterâ…¥researches the solution of the constrained filtering model in the nonlinear system; Chapterâ…¦describes the experimental procedure and data processing via an example, and verifies the effectiveness of the algorithm; Final chapter concludes the paper, and makes an prospect for future research work and the application.