Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Digital signal processing (3rd ed.): principles, algorithms, and applications
Digital signal processing (3rd ed.): principles, algorithms, and applications
A parameter estimation scheme for damped sinusoidal signals basedon low-rank Hankel approximation
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Iterative frequency estimation by interpolation on Fourier coefficients
IEEE Transactions on Signal Processing
Cramer-Rao lower bounds for a damped sinusoidal process
IEEE Transactions on Signal Processing
On Asymptotic Normality of Nonlinear Least Squares for Sinusoidal Parameter Estimation
IEEE Transactions on Signal Processing
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Parameter estimation of noisy damped sinusoidal signals in the frequency domain is presented in this paper. The advantage of the frequency domain approach is having the spectral energy concentrated in frequency domain samples. However, the least squares criterion for frequency estimation using frequency domain samples is nonlinear. A low complexity three-sample estimation algorithm (TSEA) for solving the nonlinear problem is proposed. Using the TSEA for initialization, a frequency domain nonlinear least squares (FD-NLS) estimation algorithm is then proposed. In the case of white Gaussian noise, it yields maximum likelihood estimates, verified by simulation results. A time domain NLS (TD-NLS) estimation algorithm is also proposed for comparison. The Cramer-Rao lower bound (CRLB) of the frequency domain estimation algorithms is derived. The theoretical analysis shows that the FD-NLS can yield a near-optimal performance with few energy-concentrated samples. On the other hand, the TD-NLS does not have the energy concentration property and requires more time domain samples to perform satisfactory estimation. Simulation results verify that the frequency domain estimation algorithms provide better tradeoff between computational complexity and estimation accuracy than time domain algorithms.