Seite - 57 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

3.2. Grey-boxModeling Definition Interpretation θne(k−1) =E [ θn(k−1)∣∣Ynr (k)] Estimation: expectationof θn(k−1)basedonthe currentmeasured temperatureYnr (k) θnp(k−1) = E [ θn(k−1)∣∣Ynr (k−1)] Prediction: expectationof θn(k−1)basedonthe formermeasured temperatureYnr (k−1) ene(k−1) =θn(k−1)−θne(k−1) Estimationerrorbetween θn(k−1)andθne(k−1) enp(k−1) =θn(k−1)−θnp(k−1) Predictionerrorbetween θn(k−1)andθnp(k) [Pne(k−1)] = E [ ene(k−1) ( ene(k−1) )T] Covariancematrixof theestimationerrorene(k−1)[ Pnp(k−1) ] = E [ enp(k−1) ( enp(k−1) )T] Covariancematrixof thepredictionerrorenp(k−1) Table3.1. Parametersandvectorsusedin the linearsystemidentification where ς(k) is the measurement error at timek. It is also assumed that the measurement error has zero mean value and a covariance ofσ2. Thecurrentlyavailableestimationof the temperaturevalue is Yne (k) = θ n e(k−2)Πn(k−1), (3.53) whereθne(k−2) is the former estimated coefficient vector. Following theproceduresin[KV86], thenewestimationθne(k−1)canbeobtained usingthe followingequation θne(k−1) = θne(k−2)+Kn(k−1) [ Ynr (k)−Yne (k) ] , (3.54) 57