. Control theory with applications to naval hydrodynamics. Control theory; Calculus of variations; Dynamic programming. dP dt = A P + P AT- T -1 P H R H P - Q () p(0) = r () This set of equations finishes the solution of the filter problem. The optimal filter is a feedback system which is described by the stochastic differential equation (). It is obtained by taking the measurements z(t), forming the error signal z(t) - H(t) x(t), and feed- T -1 ing the error forward with a gain P(t) H (t) R (t). P(t), the error variance, is obtained as a solution to the nonlinear Riccati-type equa
. Control theory with applications to naval hydrodynamics. Control theory; Calculus of variations; Dynamic programming. dP dt = A P + P AT- T -1 P H R H P - Q () p(0) = r () This set of equations finishes the solution of the filter problem. The optimal filter is a feedback system which is described by the stochastic differential equation (). It is obtained by taking the measurements z(t), forming the error signal z(t) - H(t) x(t), and feed- T -1 ing the error forward with a gain P(t) H (t) R (t). P(t), the error variance, is obtained as a solution to the nonlinear Riccati-type equation (), H(t) is a known transformation matrix, and R is v the variance of the Wiener process dv. A block diagram of the filter is shown in Figure 8. The variables appearing in this diagram are vectors, and the boxes represent matrices operating on vectors. The double lines which indicate direction of signal flow serve as a reminder that multiple signals rather than a single one are being Figure 8 — Optimal Filter 62. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Timman, R. (Reinier), 1917-1975; David W. Taylor Naval Ship Research and Development Center. Bethesda, Md. : David W. Taylor Naval Ship Research and Development Center
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