MATLAB Implementation of Extended Kalman Filter (EKF) Code

The Extended Kalman Filter (EKF) is a powerful algorithm for state estimation in nonlinear systems. Building upon the traditional Kalman Filter framework, it addresses nonlinear problems through linearization techniques, making it widely applicable in navigation systems, robotics localization, and control systems. The core concept of EKF involves performing local linearization of nonlinear systems using Taylor series expansion, followed by applying the standard Kalman Filter framework. In MATLAB implementation, this typically requires defining the Jacobian matrices for both the state transition function and observation function to complete the linearization process. A typical MATLAB implementation includes these key steps: First, initialize the state vector and covariance matrix using appropriate initial values. In the prediction step, update the state estimate based on the system model through mathematical operations. Then, in the update step, refine the prediction by incorporating observational data. For nonlinear systems, the Jacobian matrices need to be recalculated at each iteration, which represents the primary difference between EKF and linear Kalman Filter implementations. The MATLAB code typically involves matrix operations for prediction and update equations, numerical differentiation for Jacobian calculations (using functions like jacobian or numerical differentiation techniques), and probability distribution handling for noise modeling. Key functions often include matrix multiplication, inversion operations, and statistical computations. Notably, EKF's performance heavily depends on the accuracy of initial state estimation and proper modeling of system noise. Due to the approximate linearization method, estimation bias may occur in strongly nonlinear systems, where more advanced filtering algorithms like Unscented Kalman Filter (UKF) might be considered. For MATLAB users, leveraging its powerful matrix computation capabilities and built-in functions enables efficient EKF implementation. A robust implementation typically contains modules for matrix operations, numerical differentiation, and probability distribution processing, often utilizing MATLAB's optimization tools for enhanced performance.