Performance analysis of the approximate dynamic programming algorithm for parameter estimation of superimposed signals

We consider the classical problem of fitting a model composed of multiple superimposed signals to noisy data using the criteria of maximum likelihood (ML) or subspace fitting, jointly termed generalized subspace fitting (GSF). We analyze a previously proposed approximate dynamic programming algorith...

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Vydáno v:IEEE transactions on signal processing Ročník 48; číslo 5; s. 1274 - 1286
Hlavní autoři: Sze Fong Yau, Bresler, Y.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY IEEE 01.05.2000
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithm design and analysis
Algorithms
Applied sciences
Array signal processing
Dynamic programming
Exact sciences and technology
Heuristic algorithms
Information, signal and communications theory
Lattices
Maximum likelihood estimation
Multidimensional systems
Performance analysis
Predictive models
Signal and communications theory
Signal, noise
Studies
Telecommunications and information theory
Upper bound
Waveform
Parameter estimation
Signal estimation
Optimization method
Mean square error
Perturbation method
Model matching
Radar
Performance analysis
System identification
Dynamic programming
Cramer Rao inequality
Estimation error
Monte Carlo method
Approximate method
Non linear regression
Sonar
Frequency characteristic
Experimental result
Algorithm performance
Signal processing
Numerical simulation
Maximum likelihood
Sensor array
Signal to noise ratio
ISSN:1053-587X, 1941-0476
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Shrnutí:We consider the classical problem of fitting a model composed of multiple superimposed signals to noisy data using the criteria of maximum likelihood (ML) or subspace fitting, jointly termed generalized subspace fitting (GSF). We analyze a previously proposed approximate dynamic programming algorithm (ADP), which provides a computationally efficient solution to the associated multidimensional multimodal optimization problem. We quantify the error introduced by the approximations in ADP and deviations from the key local interaction signal model (LISMO) modeling assumption in two ways. First, we upper bound the difference between the exact minimum of the GSF criterion and its value at the ADP estimate and compare the ADP with GSF estimates obtained by exhaustive multidimensional search on a fine lattice. Second, motivated by the similar accuracy bounds, we use perturbation analysis to derive approximate expressions for the MSE of the ADP estimates. These various results provide, for the first time, an effective tool to predict the performance of the ADP algorithm for various signal models at nonasymptotic conditions of interest in practical applications. In particular, they demonstrate that for the classical problems of sinusoid retrieval and array processing, ADP performs comparably to exact (but expensive) maximum likelihood (ML) over a wide range of signal-to-noise ratios (SNRs) and is therefore an attractive algorithm.
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ISSN:1053-587X
1941-0476
DOI:10.1109/78.839975