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Genetic Algorithm(GA) and the MCF by Higuchi[3], we developed an algorithm implementing an GA
operation into the MCF to speed up convergence of the MCF to identify the non-stationary structural
parameters.
STATISTICAL FILTER THEORIES
State Space Model
The general form of state space model, with non-linear and non-Gaussian characteristics, can be
described by the following state transfer equation and observation equation.
X* = F(*/i-l>Wj (1)
in which \ ;J is the state vector, w, 7 the system noise, z /7 the observation vector, H the observation
matnx, v the observation noise vector.
Kalman Filter(KF)
The KF is easily derived if the state transfer and observation equation are linear, and noises are
Gaussian. The linear state transfer and observation equation are described as follows:
in which
„_, is the state transfer matrix, r n _, the state transfer matnx for system noise.
The KF algorithm is defined by the following steps:
1. Define an initial value of the state vector x 0 and its covanance matrix P 0 as well as the
co variance matrix of the observation noise R,, .
2. Calculate the pre-estimation value of the state vector x /7 and its covanance matrix M ;J from
*„= „-!*„-! +r n _,w, 7 _ 1 (5)
M fl =„_,„_,