9. Unscented and Complex Unscented Kalman Filtering for Parameter Estimation of a Single and Multiple Sinusoids in the Area of Power and Communication Signals

The chapter delves into the critical problem of estimating sinusoidal parameters in white Gaussian noise, a fundamental topic with wide-ranging applications in radar, nuclear magnetic resonance, control systems, and biomedical engineering. It introduces the state-space approach and Bayesian methods for optimal parameter estimation, emphasizing the limitations of existing techniques like the Extended Kalman Filter. The Unscented Kalman Filter (UKF) is presented as a superior alternative, offering higher-order accuracy without linearization. The chapter also discusses the Cramer–Rao Lower Bound as a measure of estimator performance and compares various estimation methods, including Maximum Likelihood Estimation, Linear Predictor, and the MUSIC algorithm. The development of an adaptive UKF for real sinusoidal signals is highlighted, demonstrating improved performance under high noise conditions. This detailed exploration of UKF techniques makes the chapter a valuable resource for professionals seeking advanced solutions in signal parameter estimation.