Abstract:
We present a practical excitation Sompi method. The excitation Sompi method is a non-stationary time-series method developed for the analysis of physical phenomena that obey time-invariant linear processes. Hence, the model is a discrete form of an inhomogeneous linear differential equation. In contrast with previous methods, this method has three advantages: (1) the method estimates both the eigen coefficients of the dynamic system and the excitation sequence almost simultaneously; (2) the excitation sequence is without statistical constraints and can have a wide variety of characteristics; (3) the parameter estimation method is constructed to be robust for practical use: parameters with small error can be estimated even if the assumed model conditions are not fully satisfied. We demonstrate the usefulness of the present method by applying it to the analysis of the Earth's polar motion. We analysed SPACE95 data from 1976 to 1996 with a three-day sampling interval. As a result, a real eigenfrequency between $2.33 × 10-3 $ and $2.39 × 10-3 cpd$ was estimated. This is slightly larger than the previously estimated value of $2.30 × 10-3 cpd$. Because the previous methods, which lack these three advantages, tend to estimate biased parameters, our result is thought to be closer to the true value. On the other hand, Q, which was estimated to be from several tens to a thousand by previous methods, was estimated by the present method to fall in a range from 90 to 346. Using the present method, we thus succeeded in estimating a less biased real eigenfrequency and in restricting the range of Q. This will also be a powerful method for the analysis of other kinds of physical phenomena that obey linear time-invariant dynamic processes.
