Covariance-based least-squares filtering algorithm under Markovian measurement delays

ABSTRACT

This paper addresses the least-squares linear filtering problem of signals from measurements which may be randomly delayed by one or two sampling times. The delays are modelled by a homogeneous discrete-time Markov chain to capture the dependence between them. Assuming that the evolution equation generating the signal is not available and that only the first- and second-order moments of the processes involved in the observation model are known, a recursive filtering algorithm is derived using an innovation approach. Recursive formulas for the filtering error variances are also obtained to measure the precision of the proposed estimators.

KEYWORDS:

• Least-squares estimation
• covariance information
• innovation approach
• Markovian delays
• recursive filtering algorithm

2010 AMS SUBJECT CLASSIFICATION:

• 60G35
• 62M20
• 93E10
• 93E11

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

M. J. García-Ligero http://orcid.org/0000-0001-5604-5599

A. Hermoso-Carazo  http://orcid.org/0000-0001-8120-2162

J. Linares-Pérez http://orcid.org/0000-0002-6853-555X

Additional information

Funding

This research is supported by Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional FEDER (grant no. MTM2014-52291-P).