DocumentCode :
57873
Title :
Efficient Parametric Signal Estimation From Samples With Location Errors
Author :
Kumar, Sudhakar ; Goyal, Vivek K. ; Sarma, Sanjay E.
Author_Institution :
Mech. Eng. Dept., Massachusetts Inst. of Technol., Cambridge, MA, USA
Volume :
61
Issue :
21
fYear :
2013
fDate :
Nov.1, 2013
Firstpage :
5285
Lastpage :
5297
Abstract :
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.
Keywords :
expectation-maximisation algorithm; mean square error methods; parameter estimation; signal processing; CRB; Cramer-Rao lower bound; MSE; additive noise; expectation-maximization; iterative linear estimator; likelihood function; location error variance; location errors; maximum likelihood estimation; mean squared error; mean squared estimation error; numerical approximation; numerical simulations; one-dimensional parametric signals; parameter estimation problem; parametric signal estimation; two-dimensional parametric signals; Computational modeling; Estimation error; Jitter; Maximum likelihood estimation; Mobile communication; Sensors; Cramér-Rao lower bound; Expectation-Maximization; iterative estimation; jitter; maximum likelihood estimator; parameter estimation; unknown location;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/TSP.2013.2274641
Filename :
6568001
Link To Document :
بازگشت