Patent ID: 7375679
Filing Date: 2008-05-20
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=0, 1, 2, . . . , which parameters λ are unknown, arbitrarily time-varying, but bounded, and driven by the input function u(x(k), λ), which may be nonlinear, and expressed 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 expressed by the measurement equation for 1≦k≦k 0 , where, if no measurements are used in the initialization of the filter, k 0 =0, where b is an unknown arbitrarily time-varying, but bounded, measurement bias vector with covariance B, whose components correspond to the different sensors, and where the sensor selector matrix J selects the appropriate components of sensor bias, and where n(k) is the measurement noise with covariance N and measurement matrix H at time t k ; initializing state estimates {circumflex over (x)}(k where determining the time t determining the system transition matrices Φand Γ using the update interval T=t determining the mean value measuring aspects of the state of the system expressed by the measurement equation where b is an unknown arbitrarily time-varying, but bounded, measurement bias vector with covariance B, whose components correspond to the different sensors, and where the sensor selector matrix J selects the appropriate components of sensor bias, and 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), E(t|k) to {circumflex over (x)}(k+1|k), M(k+1|k), D(k+1|k), E(k+1|k) as in and calculating P(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), D(t|k), E(t|k) to yield M(t|k+1), D(t|k+1), and E(t|k+1) as in 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 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), and E(k|k), to {circumflex over (x)}(k+1|k), M(k+1|k), D(k+1|k), and E(k+1|k) as determining covariance of the residual Q as determining the filter gain matrix K as determining the matrix L as where I is the identity matrix; updating the state estimate {circumflex over (x)}(k+1|k) as updating the matrices M(k+1|k), D(k+1|k), E(k+1|k) as respectively, and generating the total mean square error S(k+1|k+1) as