  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.
