초록 ▼

A method for the estimation of the state variables of nonlinear systems with exogenous inputs is based on improved extended Kalman filtering (EKF) type techniques. The method uses a discrete-time model, based on a set of nonlinear differential equations describing the system, that is linearized abou

A method for the estimation of the state variables of nonlinear systems with exogenous inputs is based on improved extended Kalman filtering (EKF) type techniques. The method uses a discrete-time model, based on a set of nonlinear differential equations describing the system, that is linearized about the current operating point. The time update for the state estimates is performed using integration methods. Integration, which is accomplished through the use of matrix exponential techniques, avoids the inaccuracies of approximate numerical integration techniques. The updated state estimates and corresponding covariance estimates use a common time-varying system model for ensuring stability of both estimates. Other improvements include the use of QR factorization for both time and measurement updating of square-root covariance and Kalman gain matrices and the use of simulated annealing for ensuring that globally optimal estimates are produced.

대표청구항 ▼

[ What is claimed is:] [1.] A method for estimation of state variables of a physical nonlinear system with physical exogenous inputs that can be modeled by a set of continuous-time nonlinear differential equations, including input signals representing the physical exogenous inputs to the system, and

[ What is claimed is:] [1.] A method for estimation of state variables of a physical nonlinear system with physical exogenous inputs that can be modeled by a set of continuous-time nonlinear differential equations, including input signals representing the physical exogenous inputs to the system, and measurement signals representing accessible measurements that are indicative of the state variables to be estimated, the method comprising:a) creating a nonlinear differential equation model of a nonlinear system using initial estimated state variables;b) obtaining the nonlinear system measurement signals in response to the nonlinear system input signals, wherein the nonlinear differential equation model is given by x=f(x,u)+w and z=h(x,u)+v where x is the state x is a time derivative of the state variable vector x, f(x,u) is a nonlinear function of x and input vector u, z is a measurement vector which includes function h(x,u) of both x and u, and w and v are mutually independent noise vectors and wherein a state variable estimate, x.sub.k, for time t=kT is propagated to a state variable estimate, x.sub.k+1, for time t=(k+1)T by integrating the nonlinear differential equation model over a time interval of T as follows: ]EQU12 ] where f.sub.k =f(x.sub.k.vertline.k,u.sub.k) evaluated at time t=(kT), and A.sub.k is a discrete state feedback matrix, evaluated at time t=kT, from a linearized approximation to f(x,u);c) creating an updated nonlinear differential equation model using the nonlinear differential equation model, the nonlinear system input and measurement signals, and a state variable estimation method for refining the initial estimated state variables, the state variable estimation method for producing updated estimated state variables using integration methods for state variable estimation of the nonlinear system with exogenous inputs, wherein integrating is performed by evaluating a matrix exponential as follows: ]EQU13 ] so that a time propagated state vector is obtained as follows, EQU x.sub.k+1.vertline.k =x.sub.k.vertline.k +G.sub.k,and, by QR factorization, an updated conditional square-root covariance, S.sub.k+1.vertline.k, for time (k+1) is obtained from ]EQU14 ] where S.sub.k.vertline.k is a conditional square-root covariance matrix for time k, Q.sub.k is the process noise vector covariance, Q is a QR transformation matrix, and T represents a matrix transpose operator thereby using a same computational model for updating the estimated state variable and associated covariance;d) using a discrete-time covariance matrix update; ande) using a common discrete-time time-varying linear system signal model for estimating the updated state variables and a corresponding updated covariance matrix.