Patent ID: 7277047
Filing Date: 2007-10-02
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 i 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 l k ; initializing state estimates {circumflex over (x)}(k where 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 i k for k≦k 0 ; determining the system transition matrices Φ and Γ using the update interval T=t determining the mean value 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), E(k|k), S(k|k) to {circumflex over (x)}(k+1|k), M(k+1|k), D(k+1|k), E(k+1|k) and S(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