## Curved space (CERN lectures) by Williams. PDF By Williams.

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9 (x) (25) Using lto's formula (26) The associated Zakai equation (Stranovich calculus) is du (t ,z) = 1 { - 8 zz 2 U 1 + [2 g' 1 +[g(-g" (27) 2 We can eliminate the first order term in (27) using the exponential transformation tI (t ,z) = z 1{J(z) = The equation for tI f (L o 9 u (t ,z ) e - .!.. g' 2 (t ,z) is (Stratonovich calculus) ,,(z) )(,p-l(X» dx (28) A MACSYMA I EXPERT SYSTEM FOR NONLINEAR FILTERING 33 1 + dv(t,z)=[=O .. 2 g '? + g (Lg - 1 g')' -2 ](¢-I(Z)) (30) Since the Laplacian in (29) is "isolated," we can use the formulas in  to evaluate it.

Size,j,k) real xinput(l). observ(l), e. ze)+xinput(k) observ(j )=( e*xinput(j )**2+xinput(j) )*size+grand( 0}*sqrt(size )+obse 1 rv(k) return end 47 G. L. BLANKENSHIP ET AL. 2. A vector system including the Benes problem To illustrate the facility of the system to deal with vector problems we shall treat the following example dXII = dX 2t XII = + X2t tanh X2t + + dwu dW 2t dy 11 = XII + dv 11 dY2t = X2! + dV 2t (49) The system goes through the same steps as before, computing the estimation algebra which is a product of two versions of the estimation Lie algebra for the Kalman filtering problem [21,34J.

T 2' .... tN = .... am for some m ~ 1 and some prespecifled T. v)dv (36) -00 with