# Signal Estimation with Random Parameter Matrices and Time-correlated Measurement Noises

### R. Caballero-Águila, A. Hermoso-Carazo, J. Linares-Pérez

#### Abstract

This paper is concerned with the least-squares linear estimation problem for a class of discrete-time networked systems whose measurements are perturbed by random parameter matrices and time-correlated additive noise, without requiring a full knowledge of the state-space model generating the signal process, but only information about its mean and covariance functions. Assuming that the measurement additive noise is the output of a known linear system driven by white noise, the time-differencing method is used to remove this time-correlated noise and recursive algorithms for the linear filtering and fixed-point smoothing estimators are obtained by an innovation approach. These estimators are optimal in the least-squares sense and, consequently, their accuracy is evaluated by the estimation error covariance matrices, for which recursive formulas are also deduced. The proposed algorithms are easily implementable, as it is shown in the computer simulation example, where they are applied to estimate a signal from measured outputs which, besides including time-correlated additive noise, are affected by the missing measurement phenomenon and multiplicative noise (random uncertainties that can be covered by the current model with random parameter matrices). The computer simulations also illustrate the behaviour of the filtering estimators for different values of the missing measurement probability.

Download#### Paper Citation

#### in Harvard Style

Caballero-Águila R., Hermoso-Carazo A. and Linares-Pérez J. (2019). **Signal Estimation with Random Parameter Matrices and Time-correlated Measurement Noises**.In *Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-758-380-3, pages 481-487. DOI: 10.5220/0007807804810487

#### in Bibtex Style

@conference{icinco19,

author={R. Caballero-Águila and A. Hermoso-Carazo and J. Linares-Pérez},

title={Signal Estimation with Random Parameter Matrices and Time-correlated Measurement Noises},

booktitle={Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2019},

pages={481-487},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007807804810487},

isbn={978-989-758-380-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - Signal Estimation with Random Parameter Matrices and Time-correlated Measurement Noises

SN - 978-989-758-380-3

AU - Caballero-Águila R.

AU - Hermoso-Carazo A.

AU - Linares-Pérez J.

PY - 2019

SP - 481

EP - 487

DO - 10.5220/0007807804810487