Motivation:

State estimation is one research topic in many domains, such as to estimate the position and velocity for tracking and localization in robotics control systems,  to estimate the voltage and current in power system, or to estimate a temperature diffusion field, etc. Kalman filter (KF) as an effective tool is widely applied to finish this state estimation task for linear dynamic systems. In the real world, there exists plenty of nonlinear dynamic systems. To deal with a nonlinear state estimation problem, there are several variant KF algorithms using different methods to approximate the posterior distribution of the state variables. Unscented Kalman filter as one of them applies numerical approximation of density functions. It shows advantages when the nonlinear function of the system model is not differentiable or with higher nonlinearity.

Goal:

Study on unscented Kalman filter and understand the principle of numerical approximation using sigma points.  Compare its performance with the extended Kalman filter. Simulate different algorithms in a specific scenario, e.g., for ToA/DoA-based localization.

Requirements: 

Basic Matlab skills and background knowledge of linear estimation, Bayesian statistics are required.

[1]. E. A. Wan, and R. Van Der Merwe. "The unscented Kalman filter for nonlinear estimation." 2000.