Changeset 917 for applications/dual/SIDP/text/ch2.tex
- Timestamp:
- 04/24/10 13:29:41 (14 years ago)
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applications/dual/SIDP/text/ch2.tex (modified) (6 diffs)
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applications/dual/SIDP/text/ch2.tex
r891 r917 32 32 Proto�e v �e $t$ nem� k dispozici p�stav syst� $x_t$, ale pouze informa� vektor $I_t$, nem� pou��postup z p�oz�apitoly. P��je pot�� vhodn�ransformovat. Za t�o �m zap�me informa� vektor ve tvaru 33 33 \begin{equation} 34 \label{nep} 34 35 I_0=y_0,\qquad I_{t+1}=(I_t,u_t,y_{t+1}), \qquad t=1,\ldots,N-1. 35 36 \end{equation} … … 60 61 \begin{equation} 61 62 \label{poz2} 62 y_0=h_0(\theta,v_0),\qquad y_t=h_t( \theta, I_{t-1},u_{t-1},v_t), \qquad t=1,\ldots,N-1,63 y_0=h_0(\theta,v_0),\qquad y_t=h_t( I_{t-1},\theta,u_{t-1},v_t), \qquad t=1,\ldots,N-1, 63 64 \end{equation} 64 65 65 66 Ztr�v�unkce je nyn�\begin{equation} 66 67 \label{los2} 67 g(y_{0:N},u_{0:N-1}, w_{0:N-1})=g_N(y_N)+\sum_{t=0}^{N-1}g_t(y_t,u_t,w_t).68 g(y_{0:N},u_{0:N-1},v_{0:N-1})=g_N(y_N)+\sum_{t=0}^{N-1}g_t(y_t,u_t,v_t). 68 69 \end{equation} 69 70 … … 71 72 \begin{equation} 72 73 \label{the} 73 \theta_{t+1}=f_t( \theta_t,I_t,y_{t+1},u_t), \qquad t=1,\ldots,N-1.74 \theta_{t+1}=f_t(I_t,\theta_t,u_t,y_{t+1}), \qquad t=1,\ldots,N-1. 74 75 \end{equation} 75 76 Rovnici \eqref{the} m� pova�ovat za rovnici syst� \eqref{sys} pro stav $(\theta_t,I_t)$ a vstup $(y_{t+1},u_t)$ bez p�nosti �umu. Do rovnice \eqref{poz2} dosad� za $\theta$ jeho aktu��dhad, tedy 76 Rovnici \eqref{the} m� podobn�ako \eqref{nep} pova�ovat za rovnici syst� \eqref{sys} pro stav $(I_t, \theta_t)$, vstup $u_t$ s �umem $y_{t+1}$. Do rovnice \eqref{poz2} dosad� za $\theta$ jeho aktu��dhad, tedy 77 77 \begin{equation} 78 78 \label{poz3} … … 152 152 kter��e�en�\begin{equation} 153 153 \label{Kt} 154 K_t= \frac{P_tA_t}{A_t^TP_tA_t+Q_t}154 K_t=P_tA_t(A_t^TP_tA_t+Q_t)^{-1} 155 155 \end{equation} 156 156 Dosazen�\eqref{Kt} do \eqref{Pt+1} po ��ostaneme … … 160 160 \end{equation} 161 161 Celkov�edy od p�� odhadu parametru $N(\hat{\theta}_t,P_t)$ k nov� $N(\hat{\theta}_{t+1},P_{t+1})$ p�me pomoc�\begin{equation} 162 K_t= \frac{P_tA_t}{A_t^TP_tA_t+Q}162 K_t=P_tA_t(A_t^TP_tA_t+Q_t)^{-1} 163 163 \end{equation} 164 164 \begin{equation} … … 169 169 \end{equation} 170 170 171 Tato odhadovac�rocedura se naz�lman�ltr .171 Tato odhadovac�rocedura se naz�lman�ltr [ref].
