or 
dP IL 
oT AP+PA-P HR 
ae Bl BP = @ Gal 
EGO) eal (5.18) 
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 (5.13). It is obtained by taking the 
measurements z(t), forming the error signal z(t) - H(t) &(t), and feed-— 
ing the error forward with a gain P(t) H(t) mC) P(t), the error 
variance, is obtained as a solution to the nonlinear Riccati-type 
equation (5.17), H(t) is a known transformation matrix, and RY is 
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 directed. 
Figure 8 -- Optimal Filter 
62 
