In this paper, a recursive Gauss-Newton (RGN) algorithm is first developed for adaptive tracking of the amplitude, frequency and phase of a real sinusoid signal in additive white noise. The derived algorithm is then simplified for computational complexity reduction as well as improved with the use of multiple forgetting factor (MFF) technique to provide a flexible way of keeping track of the parameters with different rates. The effectiveness of the simplified MFF-RGN scheme in sinusoidal parameter tracking is demonstrated via computer simulations.

In this Letter, estimation of the phase of a real sinusoid with known frequency in white Gaussian noise is addressed. Based on the Newton-Raphson iterative procedure, two simple realizations of exact maximum likelihood phase estimators for known and unknown amplitude are devised. Computer simulations are included to contrast the performance of the proposed algorithms with the approximate maximum likelihood estimate as well as Cramér-Rao lower bound for different phase values and signal-to-noise ratios.

In this Letter, linear least squares (LLS) techniques for phase estimation of real sinusoidal signals with known or unknown amplitudes are studied. It is proved that the asymptotic performance of the LLS approach attains Cramér-Rao lower bound. For the case of a single tone, a novel LLS algorithm with unit-norm constraint is derived. Simulation results are also included for algorithm evaluation.

A new adaptive filter algorithm based on the linear prediction property of sinusoidal signals is proposed for unbiased estimation of the frequency of a real tone in white noise. Similar to the least mean square algorithm, the estimator is computationally simple and it provides unbiased as well as direct frequency measurements. Learning behavior and variance of the estimated frequency are derived and confirmed by computer simulations.

It is well known that Pisarenko's frequency estimate for a single real tone can be computed easily using the sample covariance with lags 1 and 2. In this Letter, we propose to use alternative covariance expressions, which are inspired from the modified covariance (MC) frequency estimator, in Pisarenko's algorithm. Computer simulations are included to corroborate the theoretical development of the variant and to demonstrate its superiority over the MC and Pisarenko's methods.

The modified covariance (MC) method provides a computationally attractive and closed-form solution for frequency estimation of a single real sinusoid. In this paper, the performance measures of the MC estimator, namely, mean and mean square error, are derived in closed-form and confirmed by computer simulations.

The frequency estimate for a real sinusoid provided by the periodogram has a bias which is particularly severe for a short observation interval. In this paper, two improvements to the periodogram are proposed to reduce this bias. The first method transforms the real tone to a complex sinusoid while the second algorithm subtracts the negative spectral line from the received signal, prior to applying the periodogram. The performance of the two methods is illustrated by comparing with the periodogram and Quinn's interpolation as well as Cramér-Rao lower bound.

By utilizing the second and fourth order linear prediction errors, a novel estimator for a single noisy sinusoid is devised. The frequency estimate is obtained from a solving a cubic equation and a simple root selection procedure is provided. Asymptotical variance of the estimated frequency is derived and confirmed by computer simulations. It is demonstrated that the proposed estimator is superior to the reformed Pisarenko harmonic decomposer, which is the improved version of Pisarenko harmonic decomposer.

Tufts-Kumaresan (TK) method, which is based on linear prediction approach, is a standard algorithm for estimating the frequencies of sinusoids in noise. In this Letter, the TK algorithm is improved by attenuating the noise in the observation vector with the use of the reduced rank data matrix. It is shown that the proposed modification can provide smaller mean square frequency errors with lower threshold signal-to-noise ratios than the TK method and a total least squares solution.

This paper tackles the problem of detecting a random signal embedded in additive white noise. Although the likelihood ratio test (LRT) is the well-known optimum detector for this problem, it may not be easily realized in applications such as radar, sonar, seismic, digital communications, speech analysis and automatic fault detection in machinery, for which suboptimal quadratic detectors have been extensively employed. In this paper, the relationships between four suboptimal quadratic detection schemes, namely, the energy, matched subspace, maximum deflection ratio as well as spectrum matching detectors, and the LRT are studied. In particular, we show that each of those suboptimal detectors can approach the optimal LRT under certain operating conditions. These results are verified via Monte Carlo simulations.