Continuous-time nonlinear estimation filters using UKF-aided Gaussian sum representations

Thesis Type: Doctorate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Faculty of Engineering, Department of Electrical and Electronics Engineering, Turkey

Approval Date: 2014




A nonlinear filtering method is developed for continuous-time nonlinear systems with observations/measurements carried out in discrete-time by means of UKFaided Gaussian sum representations. The time evolution of the probability density function (pdf) of the state variables (or the a priori pdf) is approximated by solving the Fokker-Planck equation numerically using Euler’s method. At every Euler step, the values of the a priori pdf are evaluated at deterministic sample points. These values are used with Gaussian radial basis functions to obtain weighted sum of Gaussian approximation of a priori pdf. The locations of the sample points and mean and covariance values of Gaussian functions are found by the help of the prediction step of an Unscented Kalman Filter (UKF). The weights of the Gaussian functions are calculated using the method of least squares. The pdf of the updated state variables (or a posteriori pdf) is approximated similar to a priori case. This time Bayes rule and the help of the update step of UKF are used. In the developed filter, UKF acts as a one step look ahead mechanism to determine the high likelihood regions of the a priori and a posteriori pdfs and these pdfs are locally approximated around these high likelihood regions. As a second filtering method, particle flow is combined with UKF-aided Gaussian sum representations approach. Both filters are compared with some of the known nonlinear filtering methods by means of computational load and error levels using various scenarios .