# ESTIMATION ALGORITHM FROM RANDOMLY DELAYED OBSERVATIONS WITH WHITE PLUS COLOURED NOISES

### S. Nakamori, A. Hermoso-Carazo, J. Linares-Pérez, M. I. Sánchez-Rodríguez

#### Abstract

A recursive algorithm for the least-squares linear one-stage prediction and filtering problems of discrete-time signals using randomly delayed measurements perturbed by additive white plus coloured noises are presented. It is assumed that the autocovariance function of the signal and the coloured noise are expressed in a semidegenerate kernel form and the delay is modelled by a sequence of independent Bernoulli random variables, which indicate if the measurements arrive in time or are delayed by one sampling time. The estimators are obtained by an innovation approach and do not use the state-space model of the signal, but only the covariance information about the signal and the observation noises and the delay probabilities.

#### References

- Evans, J. S. and Krishnamurthy, V. (1999). Hidden Markov model state estimation with randomly delayed observations. IEEE Transactions on Signal Procesing, 47:2157-2166.
- Matveev, A. S. and Savkin, A. V. (2003). Optimal computer control via communication channels with irregular transmission times. International Journal of Control, 76:165-177.
- Nakamori, S., Caballero, R., Hermoso, A. and Linares, J. (2004a). Fixed-interval smoothing from uncertain observations with white plus coloured noises using covariance information. IEICE Trans. Fundamentals, E87-A, No. 5:1209-1218.
- Nakamori, S., Caballero, R., Hermoso, A. and Linares, J. (2004b). Recursive estimator of signals from measurements with stochastic delays using covariance information. Applied Mathematics and Computation, (in press).
- Yaz, E. and Ray, A. (1998). Linear unbiased state estimation under randomly varying bounded sensor delay. Applied Mathematics Letters, 11:27-32.

#### Paper Citation

#### in Harvard Style

Nakamori S., Hermoso-Carazo A., Linares-Pérez J. and Sánchez-Rodríguez M. (2004). **ESTIMATION ALGORITHM FROM RANDOMLY DELAYED OBSERVATIONS WITH WHITE PLUS COLOURED NOISES** . In *Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,* ISBN 972-8865-12-0, pages 19-23. DOI: 10.5220/0001127000190023

#### in Bibtex Style

@conference{icinco04,

author={S. Nakamori and A. Hermoso-Carazo and J. Linares-Pérez and M. I. Sánchez-Rodríguez},

title={ESTIMATION ALGORITHM FROM RANDOMLY DELAYED OBSERVATIONS WITH WHITE PLUS COLOURED NOISES},

booktitle={Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},

year={2004},

pages={19-23},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001127000190023},

isbn={972-8865-12-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,

TI - ESTIMATION ALGORITHM FROM RANDOMLY DELAYED OBSERVATIONS WITH WHITE PLUS COLOURED NOISES

SN - 972-8865-12-0

AU - Nakamori S.

AU - Hermoso-Carazo A.

AU - Linares-Pérez J.

AU - Sánchez-Rodríguez M.

PY - 2004

SP - 19

EP - 23

DO - 10.5220/0001127000190023