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##ã«ã«ãã³ãã£ã«ã¿ãšã¯ ã颿£æéã·ã¹ãã ã®åºåãããã·ã¹ãã ã®ç¶æ ãæå°äºä¹ã®æå³ã§æšå®ããã ##åé¡èšå® ä»åã¯ãã£ãšãç°¡åãªç·åœ¢æäžå€ã®æ¹çšåŒ $ x(k+1)= A x(k) + Bu(k) + Gw(k)$ $ y(k) = Cx(k) + v(k)$ ãèããã ããã§ã$w(k),v(k)$ã¯ããããçœè²ã¬ãŠã¹ãã€ãºã§ããããšãä»®å®ãããã®å¹³åãšå ±åæ£ã¯ $E[w(k)] = E[(v_k)] = 0$ $E[w(k)w(k)^T] = Q, E[v(k)v(k)^T] = R$ ã§ãããšããã$w(k)$ãš$v(k)$ã®éã«çžé¢ã¯ãªããã®ãšããã åæå€ãã¬ãŠã¹ã§ãããšãããã®å¹³åãšåæ£ã¯ $E[x(0)] = \bar x(0)$ $E[(x(0)-\bar x(0))(x(0)-\bar x(0))^T] = \Sigma_0$ ã§ãããšããã ä»ãæå»$k-1$ãŸã§ã®å ¥å${u(0),\ldots,u(k-1)}$(以åŸ$U_0^{k-1}$ãšè¡šç€º)ãšæå»$k$ãŸã§ã®åºå${y(1),\ldots,y(k)}$(以åŸ$Y_1^{k}$ãšè¡šç€º)ãããã£ãŠãããšããã ###åé¡ $\hat x(k) = \text{argmin} E[(x(k)-\hat x(k))^T(x(k)-\hat x(k))]$ ãæºãã$\hat x(k)$ãæ±ããã ##ã¢ã€ã㢠äžèšã®åé¡ã¯ãå³èŸºãèšç®ããããšã§ $\hat x(k) = \text{argmin} E[(x(k)-\hat x(k))^T(x(k)-\hat x(k)) | Y_1^k, U_0^{k-1}]$ ãšæžãæããããã ãããæŽã«å€åœ¢ããŠãããšã $\hat x(k) = E[x(k)|Y_1^k, U_0^{k-1}]$ ...