Patent ID: 7009554
Filing Date: 2006-03-07
Classification: G01S

Abstract:
1. A method for recursively estimating the state of a system having multidimensional parameters λ in addition to state variables x(k) at time t k for k=1,2,3, . . . , which parameters λ are unknown, arbitrarily time-varying, but bounded, and driven by the input function u(x(k),λ) and governed by the state equation where Φ,Γ are system matrices dependent on the discrete time interval T=t k+1 −t k : said method comprising the following steps: measuring aspects of the state of the system to produce initial measurements; initializing state estimates {circumflex over (x)}(k where using the update interval T=t determining the mean value {overscore (λ)} of unknown but bounded parameters λ, and the input vector u({circumflex over (x)}(t|k),{overscore (λ)}); measuring aspects of the state of the system governed by the measurement equation  where n(k) is the measurement noise with covariance N and measurement matrix H at time t determining if the measurement is time-late by testing T<0; (a) if the measurement is time-late determining F,G as follows generating a parameter matrix Λ, representing physical bounds on the parameters λ that are not state variables of the system; extrapolating said state estimates {circumflex over (x)}(t|k) and matrices M(t|k), D(t|k), to {circumflex over (x)}(k+1|k), M(k+1|k), D(k+1|k), and calculating S(k+1|k) as in determining covariance of the residual Q as in determining the filter gain matrix K as in determining the matrix L as in  where I is the identity matrix; updating the state estimate {circumflex over (x)}(t|k) as updating the matrices M(t|k) and D(t|k) as  respectively, and generating the total mean square error S(t|k+1) as in (b) and if the measurement is not time-late determining F,G using and, generating a parameter matrix Λ, representing physical bounds on those parameters that are not state variables of the system; extrapolating said state estimates {circumflex over (x)}(k|k) and matrices M(k|k), D(k|k), S(k|k) to {circumflex over (x)}(k+1|k), M(k+1|k), D(k+1|k), and S(k+1|k) as in determining covariance of the residual Q as in determining the filter gain matrix K as in determining the matrix L as in  where I is the identity matrix; updating the state estimate {circumflex over (x)}(k+1|k) as updating the matrices M(k+1|k) and D(k+1|k) as and, respectively, and generating the total mean square error S(k+1|k+1) as after