Data driven weighted estimation error benchmarking for estimators and condition monitoring systems

A simple method of benchmarking filters, predictors, smoothers or condition monitoring estimators is presented, which can avoid the need for system model knowledge. A weighted least-squares estimation problem is established, where the solution is shown to involve a term that is independent of the choice of estimator and a term that can be set to zero when using the optimal estimator. The minimum estimation error cost is therefore dependent upon the independent term in the expression and these may be computed using a simple online least-squares algorithm. The level of suboptimality, reflected in the estimation error power is then readily calculable. This enables the quality of estimation to be determined for systems which may not be completely known. If an estimator is used for condition monitoring and fault detection, the benchmark enables the deterioration in the quality of estimation to be determined. It is then possible to judge when fault estimates are sufficiently reliable. Moreover, if the system is nonlinear and fault estimators are defined for different operating conditions, then the benchmark measure can be used online to determine which estimator is best and whether the estimate is optimal in a small signal change sense.