摘要：Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov-Bayes recursion, e.g., recursion from a gaussian or gaussian mixture （GM） prior to a gaussian/GM posterior （termed ＇gaussian conjugacy＇ in this paper）, form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality （including target maneuver）, intractable uncertainties （such as unknown inputs and/or non-gaussian noises） and constraints （including circular quantities）, etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity.

摘要：In this paper we present a novel image decomposition method via credible data fitting with local total variation filter. The oscillation rate is used to measure the image complexity and characteristics. The filter parameter can be determined by a fitting curve which is reconstructed by oscillation rate. In addition, the approximate gaussian algorithm and integral image are used to reduce the algorithm computation and the sensitivity of the filter window selection. Experiments show the new method is better than the exist- ing methods.