State
estimation of a
system having multidimensional parameters, which are unknown, arbitrarily time-varying, but bounded, in addition to state variables, is performed by initializing the state estimate and matrices representing its
covariance and bias coefficients which linearly relate initial state
estimation errors to the parameter errors.
System matrices Φ, Γ, F, G and the mean value λ of unknown, time-varying, but bounded parameters λ are determined. A matrix Λ is generated, representing their physical bounds. The state estimate {
circumflex over (x)}(k|k) and matrices M(k|k) and D(k|k), characterizing the effects of measurement errors and parameter uncertainty, are extrapolated to generate {
circumflex over (x)}(k+1|k), M(k+1|k), and D(k+1|k). The measurement
noise covariance N is determined. The
filter gain matrix K is calculated. The state estimate is updated with the
filter gain matrix K weighting the measurement z(k+1) and the extrapolated state estimate {
circumflex over (x)}(k+1|k) to generate the current
system estimate {circumflex over (x)}(k+1|k+1), by minimizing its total
mean square error due to measurement errors and parameter uncertainty. The matrices M(k+1|k) and D(k+1|k) are updated with the
filter gain matrix K to generate M(k+1|k+1) and D(k+1|k+1).