US 6,285,971 B1 · Method for real-time nonlinear system state estimation and control

Abstract

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.

Claims25

Dependent claims

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;
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;
d) using a discrete-time covariance matrix update;
and
e) using a common linear perturbation signal model for estimating the updated state variables and a corresponding updated covariance matrix, wherein the linear perturbation model is a discrete-time time-varying linear system model.

3 more elements

A state vector estimation method for a real-time nonlinear system with exogenous inputs, the system represented by a set of continuous-time nonlinear differential state equations that include a state vector representing the system state vector that are to be estimated, and a nonlinear system matrix that defines the functional relationship between the input vector, the state vector, and the time-derivative of the state vector, the state vector being estimated from a set of accessible measurements that are representative of the state variables, the set of measurements, labeled as a measurement vector, taken at prescribed times and represented by a measurement vector, both the state vector and the measurement vector respectively contaminated by a state noise vector and a measurement noise vector, the method comprising the following steps:

(a) constructing a set of state equations representing the nonlinear system with exogenous inputs;
(b) establishing a set of state variable values for a current-time state vector, and a set of matrix element values for one each covariance matrix for a current-time state vector, for a current-time state noise vector, for a current-time input noise vector, and for a current-time output measurement noise vector;
(c) acquiring a current-time measurement vector;
(d) updating the state covariance matrices using the current-time measurement noise covariance vector;
(e) estimating an updated current-time state vector from the current time measurement vector by use of a state vector estimating filter that operates on the current-time state vector using the current-time measurement vector, the covariance matrices for the current time state vector, for the current time state, and for the current-time measurement noise vector, the estimated updated state vector representing the state vector at the measurement current-time;
(f) projecting the estimated updated state vector by integrating the system state equations over the prescribed time interval between the prescribed measurement current-time and the next prescribed measurement current-time for obtaining a current state vector using a discrete-time covariance matrix update;
(g) projecting the updated state vector covariance matrix using the results of the system equation integration of step (f) using a linear perturbation signal model for estimating the updated state variables and a corresponding updated covariance matrix, wherein the linear perturbation model is a discrete-time time-varying linear system model;
and
(h) at the next measurement time, iterating steps (c)-(g).

6 more elements

Dependencies are inferred from the claim text.

Method for real-time nonlinear system state estimation and control

Life of this patent

Method for real-time nonlinear system state estimation and control

Life of this patent

Abstract

Claims25