Optimal Prediction of Tessarine Signals from Multi-sensor Uncertain Observations under Tk-Properness Conditions

Abstract

: In this paper, the optimal one-stage prediction problem of tessarine signals from multi-sensor uncertain observations is approached. At each instant of time, there exists a non-null probability that the observation tessarine component coming from each sensor, contains the corresponding signal component, or only noise. To model the uncertainty, multiplicative noises modeled by Bernoulli random variables are included in the observation equations. Under correlation hypotheses between the signal and observation additive noises, a recursive algorithm to calculate the optimal least-squares linear predictor of the signal and its mean-squared error is proposed, derived by using an innovation approach. The theoretical results are illustrated by means of a numerical simulation example, in which the performance of the proposed estimator is evaluated under different uncertainty probabilities.