Kaplan, Sargent and Goodman 
where 
H(x,T) = Pe] (31) 
(' symbol represents transpose of matrix), Q is a normalizing 
matrix used to weight the observation errors in the minimization 
procedure, the function k(x, T) is a coefficient of the unknown input 
forcing function (as in Equation (21), but for the vector case , and 
the function V(x, T) is defined by 
V (xc, 3) = Me Ge Wier le (2c 2) (32) 
with W the weighting matrix for the errors in the basic equations 
due to the input disturbances. In the estimator equations the term 
[HOA Y(t) = hiGe, T)t] 2 is an nxn matrix with i‘ column given 
by 
=e [HQ { Y(T) - h(x, T)}] (33) 
The basic equations of the system and its observations are similar 
to those of Equations (21) and (22) but generalized to the vector 
case. With x and n-vector, P(T) is an nxn matrix, so that the 
number of equations required to be solved are n* + n which can 
become a large computational task. Some possible simplification 
could occur in some cases where the P-matrix has symmetry for 
the off-diagonal terms, depending on the form of the functions H, 
Q, etc., thereby leading to a reduction of the number of equations 
to be solved. 
In the case where identification of parameters is considered, 
the constant (but unknown) parameters, denoted as a vector a (with 
m elements), satisfy the differential equation 
Bekich i9 (34) 
and the m elements of a can be considered as additional elements 
in the state vector, i.e. they are adjoined to the state vector elements 
(£ elements) so that n = £+ m is the total number of elements in 
the state variable x, which also includes the estimates of the m 
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