Adaptive Technique for Computationally Efficient Time Delay and Magnitude Estimation of Sinusoidal Signals

TL;DR

This paper introduces an adaptive, real-time method for estimating the time delay and magnitude of sinusoidal signals that is robust to noise, varying signal characteristics, and offers computational efficiency with high accuracy.

Contribution

It presents a novel adaptive gradient descent-based estimator with a quadrature carrier generator, improving robustness and efficiency over classical methods.

Findings

Accurately estimates time delay and magnitude in noisy conditions

Converges exponentially fast to true values

Achieves comparable accuracy to classical methods with lower computational cost

Abstract

An online, adaptive method of time delay and magnitude estimation for sinusoidal signals is presented. The method is based on an adaptive gradient descent algorithm that directly determines the time delay and magnitudes of two noisy sinusoidal signals. The new estimator uses a novel quadrature carrier generator to produce the carriers for an adaptive quadrature phase detector, which in turn uses an arc tan function to compute the time delay. The proposed method is quite robust and can adapt to significant variation in input signal characteristics like magnitude and frequency imposing no requirement on the magnitudes of the two signals. It even works effectively when the signals have time-varying magnitudes. The convergence analysis of the proposed technique shows that estimate converges exponentially fast to their nominal values. In addition, if the technique is implemented in the continuous time domain, the delay estimation accuracy will not be constrained by the sampling frequency as observed in some of the classical techniques. Extensive simulations show that the proposed method provides very accurate estimates of the time delay comparable to that of the popular methods like Sinc-based estimator, Lagrange estimator, and the Quadrature estimator, as well the magnitude estimate of the input signals at lower signal to noise ratio at appreciably reduced computational cost.