STATISTICAL INFERENCE IN A LINEAR MODEL FOR SPATIALLY LOCATED SENSORS AND RANDOM INPUT

STANISŁAW GNOT^{1}, EWARYST RAFAJŁOWICZ^{2} AND AGNIESZKA URBAŃSKA-MOTYKA^{1}

1Pedagogical University, Institute of Mathematics, pl. Słowiański 9, 65-069 Zielona Góra, Poland

2Wrocław University of Technology, Institute of Engineering Cybernetics, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

(Received June 8, 1998; revised October 18, 1999)

Abstract. In the paper we consider a random linear model for observations provided by spatially located sensors measuring signals coming from one source. For this model a set of sufficient and complete statistics are found, and it is shown that the maximum likelihood estimators of unknown parameters (characteristics of the source) are functions of those statistics. The problem of nonnegative estimators of variance components of the model is shortly discussed. Comparisons of the mean squared errors of several estimators are given. Numerical example concerning hunting for defects in solar cells is considered in details.

Key words and phrases: Inverse problem, random linear model, sufficient statistics, variance components, ML estimators.