A Comparison of Extended Kalman Filters for Parameter Estimation of Sinusoidal Signals

This paper compares the performance of three classical Extended Kalman Filters (EKF) to estimate the amplitude, frequency, and phase angle of a sinusoidal signal corrupted by white noise. Besides, two output signals are generated, one in-phase to the input signal and other in-quadrature as required in some applications. The selected EKF variants are the EKF based on the orthogonal vector model (OV-EKF), the extended complex KF (ECKF), and the one based on the so called nearly constant frequency model (NCF-EKF). The last method is computationally less demanding for real time implementation since it does not require neither a square root nor a trigonometric arctangent function nor a natural logarithm to estimate the parameters. Assuming a single sinusoidal signal, simulations are carried out with different amplitudes, frequencies, initial phase angles, and levels of signal-to-noise ratio (SNR). The results show that NCF-EKF method is the most suitable to estimate the phase angle, and it has no problems of instability and divergence.