Study Of Robust Parameter Estimation And Its Applications

Multiscale parameter estimation utilizes wavelet transform and Kalman filtering to dothe parameter estimation of dynamic systems. Dynamic parameter estimation has manyimportant applications in a variety of areas, such as real-time control system, maneuveringtarget tracking, video tracking, image processing and so on. The multiscale method mainlytakes advantage of Kalman filtering, which is a real-time recursive algorithm and has lowrequirement of signal, and the wavelet transform, which has well decorrelating property andsound distinguish ability of signal and noise, respectively.Willsky first introduced the multi-scale method to area of estimation. Hong forwardedthe subject with a great effort. They have obtained many useful results, algorithms andapplications. But there remains some challenge problems.As the previous algorithm aimed at decomposing the random signals into several scales,and then applying the Kalman filter to one or several scales to deal with the conventional stateestimation problem, without more direct and thorough exploitation of wavelet transform,the thesis developed a new algorithm which introduced the wavelet de-noising operation toarea of multi-scale state estimation. The new algorithm applies the wavelet thresholdingde-noising method to shrinking the noise level of the measurements which Kalman filteringrelies on. Moreover, as the wavelet threshold de-noising operation is independent with thesystem model, the new algorithm behaves some robustness to the model. A set of MonteCarlo simulation reveals that the new approach has better performance.In many application cases, we need know the properties of the residual noise processedby the de-noising algorithm. Thus, the thesis did some research on the basic statistics prob-lem, and derived some useful results. It reveals that if the original noise is Gaussian whitenoise with i.i.d., and the signal and noise are well distinguished, the residual noise remainsiid, and more importantly, it can be considered within a white noise frame.The thesis introduced the concepts"total variation"and"local variation"of functionsto the areas of wavelet transform and state estimation, and then raised the concept of"Con-traction Coefficients". The contraction coefficients mainly contract the noise in the detail...