Efficient Parametric Signal Estimation From Samples With Location Errors

We introduce an iterative linear estimator (ILE) for estimating a signal from samples having location errors and additive noise. We assume that the signals lie in the span of a finite basis and the location errors and noise are mutually independent and normally distributed. The parameter estimation problem is formulated as obtaining a maximum likelihood (ML) estimate given the observations and an observation model. Using a linearized observation model we derive an approximation to the likelihood function. We then adopt an iterative strategy to develop a computationally efficient estimator, which captures the first order effect of sample location errors on signal estimation. Through numerical simulations we establish the efficacy of the proposed estimator for one-dimensional and two-dimensional parametric signals, comparing the mean squared estimation error against a basic linear estimator. We develop a numerical approximation of the Cramér-Rao lower bound (CRB) and the Expectation-Maximization (EM) algorithm, and for a one-dimensional signal compare our algorithm against them. We show that for high location error variance and small noise variance the mean squared error (MSE) with ILE is significantly lower when compared to the baseline linear estimator. When compared to EM, our algorithm provides comparable MSE with a significant reduction in computational time.