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 } and matrices m and d , characterizing the effects of measurement errors and parameter uncertainty , are extrapolated to generate }, m , and d . 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 and the extrapolated state estimate } to generate the current system estimate }, by minimizing its total mean square error due to measurement errors and parameter uncertainty . the matrices m and d are updated with the filter gain matrix k to generate m and d .