Download e-book for iPad: A Kalman Filter Primer by Randall L. Eubank

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By Randall L. Eubank

ISBN-10: 0824723651

ISBN-13: 9780824723651

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J as well as the innovations ε(1), . . , ε(k). The common component in all these factors is the innovation vectors whose computation is linked directly to the Cholesky factorization of Var(y). Consequently, the Cholesky decomposition is the unifying theme for all that follows and is the perspective we will adopt for viewing developments throughout the text. 30). Then, in Chapter 3, we show how this structure can be exploited to obtain a computationally efficient, modified Cholesky factorization of Var(y) as well as Var−1 (y).

3 29 State and innovation covariances The stage has now been set to accomplish the goals of this chapter. 6). 4 below. 4 Let S(1|0) := Var(x(1)) = F (0)S(0|0)F T (0) + Q(0). Then, for t = 1, . 15) and, for j ≤ t − 1, Cov(x(t), ε(j)) = F (t − 1) · · · F (j)S(j|j − 1)H T (j). 16) Let M (t) = F (t)−F (t)S(t|t−1)H T (t)R−1 (t)H(t). 17) Then, for t = n − 1, . , 1 and j ≥ t + 1, Cov(x(t), ε(j)) = S(t|t − 1)M T (t)M T (t + 1) · · · M T (j − 1)H T (j). 19) as well as the BLUPs of the signal and state vectors.

A(t, t − 1) as a result of the update formula A(t + 1, j) = F (t)A(t, j), j = 1, . , t − 1. This idea produces the following algorithm. 1 This algorithm evaluates L row by row beginning with the upper left hand row block.

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A Kalman Filter Primer by Randall L. Eubank

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