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...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.展开更多
基金Project supported by the Marie Sk?odowska-Curie Individual Fellowship(H2020-MSCA-IF-2015)(No.709267)the Open Project Program of Ministry of Education Key Laboratory of Measurement and Control of Complex Systems of Engineering,Southeast University,China(No.MCCSE2017A01)
文摘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.
