Parameter estimation of exponentially damped sinusoids using HSVD based extended complex Kalman filter

The present study proposes two alternate model structures to represent exponentially damped sinusoids and proposes a novel method of estimating the parameters of the damped sinusoids by combining Hankel singular value decomposition (HSVD) with the extended complex Kalman filter (ECKF). The ECKF is capable of estimating the parameters and can effectively track the variations of damping constants and frequencies. However, the performance of ECKF has been found to be very sensitive to initial state estimates when one of the proposed model (called model-1) is used for representing the signal. Some of the existing methods of damped signal estimation including HSVD, which belong to the class of batch processing algorithms, are not sensitive to initial conditions. However, these are unsuitable for tracking variations of signal parameters. The proposed algorithm, therefore, uses HSVD to accurately estimate the initial states from few samples of the signal. These estimates are subsequently being used by ECKF to eliminate its sensitivity to initial conditions. The structure of Model-1 is further modified to yield another model structure (called Model-2) to represent the damped signal. The parameters of the damped signal were estimated under variety of noisy conditions by ECKF using both Model-1 & 2. Their effectiveness were compared by computing the the variances of estimates and comparing those with Cramer-Rao (CR) bound. Results of estimation show that Model-2 is more efficient compared to Model-1 and ECKF is capable of accurately tracking the variations in signal parameters.