Stable approximate stochastic partial realizations from noisy covariances. (English) Zbl 0607.93058
Modelling, identification and robust control, Sel. Pap. 7th Int. Symp. Math. Theory Networks Syst., Stockholm 1985, 489-498 (1986).
[For the entire collection see Zbl 0592.00037.]
Partial stochastic realization procedures are sensitive to perturbations. Applications are often based on not necessarily nonnegative definite covariance sequence estimates. This violates the usual assumption in reduced order modeling procedures that an underlying stable realization exists. Yet, the desired result is a stable filter that approximates well the uncertain information reflected in the covariance estimate.
An iterative projection approach is used to impose required constraints. Examples illustrate that this procedure can be effective even if the given sequence is not nonnegative definite.
Partial stochastic realization procedures are sensitive to perturbations. Applications are often based on not necessarily nonnegative definite covariance sequence estimates. This violates the usual assumption in reduced order modeling procedures that an underlying stable realization exists. Yet, the desired result is a stable filter that approximates well the uncertain information reflected in the covariance estimate.
An iterative projection approach is used to impose required constraints. Examples illustrate that this procedure can be effective even if the given sequence is not nonnegative definite.
MSC:
| 93E12 | Identification in stochastic control theory |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 93E10 | Estimation and detection in stochastic control theory |
| 93E25 | Computational methods in stochastic control (MSC2010) |
| 93B35 | Sensitivity (robustness) |
