Parameter estimation of linear systems in the presence of process noise using the Maximum Likelihood method.
Abstract:ESDU 89032 extends methods of parameter identification in ESDU 87039 and ESDU 88011 that treated systems with measurement noise alone to deal with the case of a system subject to both measurement and process noise. The method used is to formulate an Objective Function in terms of the maximum likelihood estimator and minimise it by a Gauss-Newton iterative procedure to find the unknown parameters. State estimation is formulated in terms of both time-varying and steady-state Kalman filters. The procedure is first developed for a first-order state system with only a single unknown parameter and driven by a combination of known and random inputs. For the time-varying Kalman filter the unknown parameter set is the unknown in the state equation and the variances of the measurement noise and of the process noise. For the steady-state Kalman filter the variance of the process noise is replaced by the constant Kalman gain in the set of unknown parameters and is subsequently found once the parameter set has been determined. An example of an aircraft executing a pure rolling manoeuvre illustrates the procedure. The fully generalised method for a multiparameter system with many degrees of freedom is described.
|Data Item ESDU 89032|