Improving the Performance of Kalman Filter by Updating the Covariance Matrix of the Process Noise Random Vector

Abstract

This paper presents an investigation towards developing a better understanding of the Kalman filtration process by adding an updating equation to the covariance of the random vector process noise in the main algorithm of Kalman. This updating equation results from the theoretical proof of the relationship between Unified Least Square Technique and the Kalman algorithm. Two numerical examples are used to illustrate the effect of the new step added to Kalman algorithm. In the first example, statistical analysis is applied on the original observations. No outliers were detected in the original observations. Three solutions were applied on the data. First, Kalman Filtration without updating the covariance of random vector process noise. Second, Kalman filtration with updating equation is added to the algorithm. Third, Recursive least square technique is used. In the second numerical example, original observations were collected from GPS observations to determine the deformation of two towers supporting a Tianjin Yong Highway cable – stayed bridge in China. Original observations were suffering from outliers. Using the same previous strategy to estimate the state vector and its variance. Finally we conclude that, when the original observations suffering from outliers, Updating the equation of the covariance of the random process noise must be added to Kalman algorithm to improve the performance of filtration process and to overcome the existence of outliers. Adding the new equation improves the variance of the estimated state vector to be identical with Recursive least Square Technique.