Linear prediction approach for efficient frequency estimation of multiple real sinusoids: algorithms and analyses

Abstract

Abstract-Based on the linear prediction property of sinusoidal signals, two constrained weighted least squares frequency estimators for multiple real sinusoids embedded in white noise are proposed. In order to achieve accurate frequency estimation, the first algorithm uses a generalized unit-norm constraint, while the second method employs a monic constraint. The weighting matrices in both methods are a function of the frequency parameters and are obtained in an iterative manner. For the case of a single real tone with sufficiently large data samples, both estimators provide nearly identical frequency estimates and their performance approaches Cramér-Rao lower bound (CRLB) for white Gaussian noise before the threshold effect occurs. Algorithms for closed-form single-tone frequency estimation are also devised. Computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the CRLB for different frequencies, observation lengths and signal-to-noise ratio (SNR) conditions.

Structured total least squares approach for efficient frequency estimation

“…Both the STLS2 and proposed algorithms terminate when the difference of norm of successiveâ is less than 10 −6 or the number of iterations has reached the maximum allowable value, which is set to 10. The initial value ofx is obtained by a simple consistent method [22] and that of Δx is set to 0 ×1 for both algorithms.…”

Efficient frequency estimation of a single real tone based on principal singular value decomposition

“…So and Chan [4] have shown that the PHD estimation performance can be improved if the data matrix is employed instead of the covariance matrix. By incorporating the technique of weighted least squares (WLS) into [4], the resultant algorithm [5] can provide optimum accuracy. Recently, Elasmi-Ksibi et al [6] have also extended [3] with the use of a normalized second-order infinite impulse response notch filter, whose frequency variance can attain Cramér-Rao lower bound (CRLB) [1] when ω is close to 0.5π.…”

“…Although single-tone frequency estimation has been well studied, efforts have continually been made to devise fast and accurate estimators with small threshold signal-to-noise ratio (SNR) and uniform estimation performance across the admissible frequency range. In this work, we propose to exploit the principal-singular-vector utilization for modal analysis (PUMA) [14] which is originally derived for two-dimensional sinusoidal parameter estimation, and WLS [5], in the frequency estimator development, in order to fulfil the above-mentioned challenges.…”

“…To be precise, the left principal singular vectors correspond to noisy sinusoidal sequences with frequency of ω while the frequency of the right principal singular vectors is Mω. We then utilize the WLS technique [5] to find the frequencies of the principal singular vectors. It is also proved that when K tends to infinity, the variance of the frequency estimate approaches CRLB.…”

“…Nevertheless, the factorization of a real tone is different from that of a complex tone and hence the algorithm and analy-sis are different from [15]. Simulation results are included in Section 3 to corroborate the analytical development and to evaluate the performance of the proposed algorithm by comparing with the WLS [5], ML [8], and ARMA model fitting [7] methods as well as CRLB. Finally, conclusions are drawn in Section 4.…”