Abstract
The least-squares polynomial filtering and fixed-point smoothing problems of discrete-time signals from randomly delayed observations is addressed, when the Bernoulli random variables modelling the delay are correlated at consecutive sampling times. Recursive estimation algorithms are deduced without requiring full knowledge of the state-space model generating the signal process, but only information about the delay probabilities and the moments of the processes involved. Defining a suitable augmented observation vector, the polynomial estimation problem is reduced to the linear estimation problem of the signal based on the augmented observations, which is solved by using an innovation approach.
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This work is partially supported by Ministerio de Educación y Ciencia and Junta de Andalucía through projects MTM2005-03601 and P07-FQM-02701, respectively.
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Caballero-Águila, R., Hermoso-Carazo, A. & Linares-Pérez, J. Least-squares Polynomial Estimation from Observations Featuring Correlated Random Delays. Methodol Comput Appl Probab 12, 491–509 (2010). https://doi.org/10.1007/s11009-008-9117-z
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DOI: https://doi.org/10.1007/s11009-008-9117-z
Keywords
- Least-squares estimation
- Filtering and smoothing algorithms
- Polynomial estimation
- Randomly delayed observations