Identification of unknown noise statistics for non-stationary state space systems, страница 4

Figure 3. Adaptive estimation of non-stationary trajectory of random walk in the conditions of unequally-spaced observations.               Modeling true values of variances ; ; The minimal time interval between measurements  can increase in accordance with number of missed measurements (); observation period .

As Figure shows, the estimations of expectation substantially repeat the law of its true evolution in the conditions of unequally-spaced observations and the adaptive Kalman filter provides the robust character of prediction.

4. CONCLUSION

In this paper the new identification methods were developed to estimate the noise statistics for the non-stationary state space models with time-varying state-transition matrix and time-varying input matrix. These methods are based on the creation of m-dependent sequences of the pseudo-measurements of estimated parameters. The consistent estimates of time-invariant noise statistics were obtained by time averaging of created pseudo-measurements. To estimate the time-varying noise covariances and expectations for the model with time-varying state-transition matrix and time-varying input matrix, the method of exponential smoothing was used.

The modeling results of corresponding algorithms are given for non-stationary two-dimensional and one-dimensional state space models in the conditions of unequally-spaced observations. Examined type of models is widely used in the problems of trajectory estimation, aircraft control, prediction of financial and economical series and others.

The simplicity and high accuracy of estimation of proposed algorithms evidence about the possibility of extension of practical application field of adaptive filtration in the conditions of a priory uncertainty.

5. REFERENCES

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