×

zbMATH — the first resource for mathematics

Unbiased minimum-variance linear state estimation. (English) Zbl 0627.93065
A method is developed for linear estimation in the presence of unknown or highly non-Gaussian system inputs. The state update is determined so that it is unaffected by the unknown inputs. The filter may not be globally optimum in the mean square error sense. However, it performs well when the unknown inputs take extreme or unexpected values. In many geophysical and environmental applications, it is performance during these periods which counts the most. The application of the filter is illustrated in the real-time estimation of mean areal precipitation.

MSC:
93E10 Estimation and detection in stochastic control theory
93C05 Linear systems in control theory
93E11 Filtering in stochastic control theory
62M20 Inference from stochastic processes and prediction
86A10 Meteorology and atmospheric physics
93C95 Application models in control theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bras, R.L.; Colon, R., Time-averaged areal Mean of precipitation: estimation and network design, Wat. resources res., 14, 878-888, (1978)
[2] Bras, R.L.; Rodriguez-Iturbe, I., Rainfall network design for runoff prediction, Wat. resources res., 12, 1197-1208, (1976)
[3] Delhomme, J.P., Kriging in the hydrosciences, Adv. wat. resources, 1, 251-266, (1978)
[4] Gandin, L.S., ()
[5] Glover, J.D., The linear estimation of completely unknown signals, IEEE trans. aut. control, AC-14, 766-769, (1969)
[6] Hoeksema, R.J.; Kitanidis, P.K., An application of the geostatistical approach to the inverse problem in 2-D groundwater modeling, Wat. resources res., 20, 1003-1020, (1984)
[7] Kitanidis, P.K., Parameter uncertainty in estimation of spatial functions: a Bayesian approach, Wat. resources res., 22, 499-507, (1986)
[8] Kitanidis, P.K.; Bras, R.L., Adaptive filtering through detection of isolated transient errors in rainfall-runoff models, Wat. resources res., 16, 740-748, (1980)
[9] Luenberger, D.G., ()
[10] Matheron, G., ()
[11] Matheron, G., The intrinsic random functions and their applications, Adv. appl. probability, 5, 439-468, (1973) · Zbl 0324.60036
[12] Mehra, R.K., On the identification of variances and adaptive Kalman filtering, IEEE trans. aut. control, AC-15, 175-184, (1970)
[13] Rodriguez-Iturbe, I.; Mejia, J.M., On the design of rainfall networks in time and space, Wat. resources res., 10, 713-728, (1974)
[14] Sanyal, P.; Shen, C.N., Bayes’ decision rule for rapid detection and adaptive estimation scheme with space applications, IEEE trans. aut. control, AC-19, 228-231, (1974)
[15] Willsky, A.S.; Jones, H.L., A generalized likelihood ratio approach to the detection and estimation of jumps in linear systems, IEEE trans. aut. control, AC-21, 108-112, (1976) · Zbl 0316.93038
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.