Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
SIAM Journal on Optimization
A simple derivation of the constrained multiple parameterCramer-Rao bound
IEEE Transactions on Signal Processing
Harmonics in multiplicative and additive noise: performanceanalysis of cyclic estimators
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
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In this paper, the simultaneous estimation of the input and output frequencies of nonlinear systems is considered. As the output frequencies are generated from the input frequencies, and are integer combinations of these frequencies, it is shown in this paper that the simultaneous estimation of both the input and output frequencies can therefore be formulated as a constrained estimation problem. First, the constrained Cramer-Rao lower bound, an important general property of any unbiased estimator, is derived. The procedure and algorithm for estimating the input and output frequencies are devised based on the periodogram method. Numerical examples are presented to illustrate the performance and implementation of the proposed estimation procedure and algorithm.