We purpose algorithms to consistently estimate the time-varying delay via the coefficients of the polynomial φ(t) from a single record of the noisy observations x(t). The novel approach is shown to offer the following advantages over the existing ones. Provides a common frame-work for deterministic as well as random signals without regard to their distribution. Computationally efficient, optimal parameter estimation is possible even in non-Gaussian noise. Estimation is (theoretically) tolerant to any stationary noise. Can be generalized to maneuvering targets with varying acceleration. Sequential estimation versus multi-dimensional likelihood minimization. Preliminary simulations confirm the superior performance of these algorithms even with small data sizes and low SNR.