Second-order polynomial estimators from uncertain observations using covariance information
Applied Mathematics and Computation
Linear recursive discrete-time estimators using covariance information under uncertain observations
Signal Processing - From signal processing theory to implementation
On the design of quadratic filters with application to image processing
IEEE Transactions on Image Processing
Polynomial fixed-point smoothing of uncertainly observed signals based on covariances
International Journal of Systems Science
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
ISCGAV'09 Proceedings of the 9th WSEAS international conference on Signal processing, computational geometry and artificial vision
Journal of Computational and Applied Mathematics
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Least-squares linear and quadratic filtering and fixed-point smoothing algorithms are derived to estimate a signal from uncertain observations perturbed by an additive white noise. The random variables describing the uncertainty are correlated only at consecutive time instants, and this correlation, as well as the probability that the signal exists in each observation, is known. Recursive algorithms are obtained without requiring the state-space model generating the signal, but just some moments of both the signal and the additive noise in the observation equation. For the linear estimation algorithms, only the second-order moments are required, and the autocovariance function of the signal must be expressed in a semi-degenerate kernel form. The quadratic estimation algorithms use, in addition, the moments up to the fourth one, and they require the autocovariance and cross-covariance functions of the signal and their second-order powers in a semi-degenerate kernel form. This form for expressing autocovariance functions is not very restrictive, since it covers many general stochastic processes, including stationary and non-stationary processes.