A new sequential data assimilation method. (English) Zbl 1178.93139
Summary: A new sequential data assimilation method named “Monte Carlo \(H_{\infty }\) filter” is introduced based on \(H_{\infty }\) filter technique and Monte Carlo method in this paper. This method applies to nonlinear systems in condition of lacking the statistical properties of observational errors. In order to compare the assimilation capability of Monte Carlo \(H_{\infty }\) filter with that of the ensemble Kalman filter (EnKF) in solving practical problems caused by temporal correlation or spatial correlation of observational errors, two numerical experiments are performed by using Lorenz (1963) system and shallow-water equations respectively. The result is that the assimilation capability of the new method is better than that of EnKF method. It is also shown that Monte Carlo \(H_{\infty }\) filter assimilation method is effective and suitable to nonlinear systems in that it does not depend on the statistical properties of observational errors and has better robustness than EnKF method when the statistical properties of observational errors are varying. In addition, for the new method, the smallest level factor founded by search method is flow-dependent.
MSC:
| 93E11 | Filtering in stochastic control theory |
| 62H20 | Measures of association (correlation, canonical correlation, etc.) |
| 93C10 | Nonlinear systems in control theory |
Keywords:
sequential data assimilation; Monte Carlo \(H_{\infty }\) filter; correlation of observational errors; robustness; flow-dependentSoftware:
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