Page - 222 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

A. Appendix where ∆Ynr (k) is the real measured/calculated value of ∆Yn(k), ς(k−1) isazero-meanmeasurement/calculationerrorwiththecovari- anceσ2 and [ε(k−1)] is a zero-mean white noise with the covariance matrix [Ω]. The definitions of parameters in EKF is shown by table A.1. Definition Interpretation [Λne(k)] = E [ [Λn(k)] ∣∣∆Ynr (k)] Estimationof [Λn(k)]basedon thecurrentmeasured temperature ∆Ynr (k)[ Λnp(k) ] = E [ [Λn(k)] ∣∣∆Ynr (k−1)] Predictionof [Λn(k)]basedon the formermeasured temperature ∆Ynr (k−1) [ene(k)] = [Λ n(k)]− [Λne(k)] Estimationerrorbetween [Λn(k)]and [Λne(k)][ enp(k) ] = [Λn(k)]−[Λnp(k)] Predictionerrorbetween [Λn(k)]and [Λnp(k)] [Pne(k)] =E [ [ene(k)] [ ene(k) T ]] Covariancematrixof the estimationerror [ene(k)][ Pnp(k) ] = E [[ enp(k) ][ enp(k) T ]] Covariancematrixof thepredictionerror[enp(k)] TableA.1. ParametersandvectorsusedinEKF Accordingtothedefinitions intable A.1, therelationshipbetweenthe estimationandthepredictionofΛn(k)canbeexpressedby[ Λnp(k) ] =E [ [Λn(k)] ∣∣∆Ynr (k−1)] =E [ [Λn(k−1)]+[ε(k−1)]∣∣∆Ynr (k−1)] =E [ [Λn(k−1)]∣∣∆Ynr (k−1)] = [Λne(k−1)] (A.6) 222