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By Cornelius T. Leondes
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L. C. KRAMER, and M. ÄTHANS, "Information Flow in Event-Driven Large-Scale Systems, " ALPHATECH Technical Report TR-127, October 1981. 17. Y. C. HO, "Team Decision Theory and Information Structures," Proa. IEEE 68 (6) (1980). 18. T. YOSHIKAWA, "Decomposition of Dynamic Team Decision Problems," IEEE Trans. Autom. Control AC-23 (4) (1978). 19. A. N. SHIRYAYEV, "On Optimum Methods in Quickest Detection Problems," Theory Probab. Appl. 16, 712-717 (1971). 20. D. TENEKETZIS, "The Decentralized Wald Problem," Proceedings of the Large Scale Systems Symposium, Virginia Beach, October, 1982.
Optimal estimation in linear Gaussian systems yield N k E (t) l k 1 Z (t)" k = M (t)" 1 1 l k 1 + £ = M (t)" 1 T -i 1 C (k) 1 C (k) (V ) 1 T 1 1 T 1 1 (23) 1 + C (k) (V ) C (k) (24) k x (t) = x N t ) N k + Z (t) ]T C (k) (V ) -1 (25) i=l χ ik (y (t) - c (k)x (t) - d (k)) 1 i k i ik x (t) = x (t) lk 1 T 1 + Z (t)C (k) (V ) χ 1 1 (26) lk x (y (t) - C ( k ) x ( t ) - d (k)) 1 using the independence of the random vectors v ( t ) f v-* (t) , for i ^ j. Equations (26) and (24) imply ik 1 ik i k 1 i k E (t)" x (t) = M (t)" x (t) i T 1 1 i i + C ( k ) ( V ) ( y ( t ) - d (k)).
F u M| where u\(i) = -P 1 (i) Β j (i) Φ [N(k + 1) , i + 1] χ Fj[N(k + 1) ]Kj (Nk)y_.