MATLAB Implementation of Unscented Kalman Filter (UKF) for Advanced Filtering

This document presents a MATLAB-based implementation of the Unscented Kalman Filter (UKF) algorithm designed for sophisticated filtering applications. The UKF approach employs sigma point transformation to accurately capture statistical properties of nonlinear systems, eliminating the need for Jacobian matrix calculations required in extended Kalman filters. The core implementation includes key components such as the sigma point selection mechanism using the unscented transform, nonlinear state transition functions, and measurement update procedures. The algorithm demonstrates superior performance in handling nonlinear systems with Gaussian noise, making it particularly effective for applications requiring precise state estimation and trend prediction in noisy environments. Through extensive validation testing involving multiple nonlinear system scenarios and noise conditions, the implementation has been verified to maintain numerical stability and estimation accuracy. The code includes proper initialization routines, covariance matrix management, and regularization techniques to ensure robust performance. This thoroughly tested implementation is ready for practical deployment in real-world nonlinear filtering applications across various engineering domains.