Patent ID: 7180443

Claim:
A method for estimating the state of a system having multidimensional parameters, which parameters have known bounded values, said method comprising the following steps: measuring aspects of the state of the system to produce measurements, and initializing state estimates {circumflex over (x)}(k 0 |k 0 ) and the matrices M(k 0 |k 0 ), D(k 0 |k 0 ); where matrix M(j|k) is defined as the covariance of the state estimation errors at time t j due only to the errors in the measurements z(i) for 1≦i≦k and a priori initial information that is independent of the parameter uncertainty; and matrix D(j|k) is defined as the matrix of bias coefficients, which linearly relates state estimation errors to the parameter errors, at time t j (after processing k=0, 1, 2, . . . measurements); determining the system transition matrices Φ, Γ, and the mean value λ of unknown but bounded parameters λ; determining F, G using F = Φ + Γ ⁢ ∂ u ∂ x  x = x ^ ⁡ ( k ❘ k ) , λ = λ _ ( 38 ) G = Γ ⁢ ∂ u ∂ λ  x = x ^ ⁡ ( k ❘ k ) , λ = λ _ ( 39 ) 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 {circumflex over (x)} ( k+ 1 |k )=Φ{circumflex over ( x )}( k|k )+Γ u ({circumflex over ( x )}( k|k ), λ ) (40) M ( k+ 1 |k )= FM ( k|k ) F′ (41) D ( k+ 1 |k )= FD ( k|k )+ G (42) S ( k+ 1 |k )= M ( k+ 1 |k )+ D ( k+ 1 |k )Λ D ( k+ 1 |k )′ (43) determining the noise covariance N; determining covariance of the residual Q as in Q=HS ( k+ 1 |k ) H′+N (44) determining the filter gain matrix K as in K=S ( k+ 1 |k ) H′Q −1 (45) determining the matrix L as in L=I−KH (46) where I is the identity matrix; measuring at least one aspect z(k+1) of the state of the system; updating the state estimate {circumflex over (x)}(k+1|k) as {circumflex over (x)} ( k+ 1 |k+ 1)={circumflex over ( x )}( k+ 1 |k )+ K[z ( k+ 1)− H{circumflex over (x)} ( k+ 1 |k )] (47) updating the matrices M(k+1|k) and D(k+1|k) as M ( k+ 1 |k+ 1)= LM ( k+ 1 |k ) L′+KNK′ (48) D ( k+ 1 |k+ 1)= LD ( k+ 1 |k ) (49) respectively, and generating the total mean square error S(k+1|k+1) as in S ( k+ 1 |k+ 1)= M ( k+ 1 |k+ 1)+ D ( k+ 1 |k+ 1)Λ D ( k+ 1 |k+ 1)′ (50).