Seite - 226 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

A. Appendix Using the above expression, equation A.14 can be further simplified as [Pne(k)] = ( [IM]− [Kn(k)][Jn(k)] )[ Pnp(k) ]−([Pnp(k)][Jn(k)]T − [Kn(k)][Jn(k)][Pnp(k)][Jn(k)]T −σ2 [Kn(k)] ) [Kn(k)] T = ( [IM]− [Kn(k)][Jn(k)] )[ Pnp(k) ]−[[Pnp(k)] [Jn(k)]T − [Kn(k)]([Jn(k)][Pnp(k)][Jn(k)]T+σ2)][Kn(k)]T = ( [IM]− [Kn(k)][Jn(k)] )[ Pnp(k) ]−([Pnp(k)][Jn(k)]T −[Pnp(k)] [Jn(k)]T) [Kn(k)]T = ( [IM]− [Kn(k)][Jn(k)] )[ Pnp(k) ] (A.17) Combining equations A.6, A.8, A.12, A.14 and A.16, the entire updaterule inEKFis representedas in the following. Predictionpart: [ Λnp(k) ] = [Λne(k−1)] ,[ Pnp(k) ] = [Pne(k−1)]+[Ω]. Estimationpart: [Kn(k)] = [ Pnp(k) ] [Jn(k)] T ( [Jn(k)] [ Pnp(k) ] [Jn(k)] T +σ2 [I] )−1 , [Λne(k)] = [ Λnp(k) ] +[Kn(k)] ( ∆Ynr (k)−ΓT(k) [ Λnp(k) ] Γ(k) ) , [Pne(k)] = ( [IM]− [Kn(k)][Jn(k)] )[ Pnp(k) ] , with [Jn(k)] = Γ(k)ΓT(k). 226