摘要：Recently, the conditions of observers that can estimate directly Kx（t） for an arbitrarily given K, and that are free of the effect of time delayed states of the system, are formulated. This paper points out that, because of the equivalence in formulation, the existing conditions for unknown input observers can be used to establish directly a new set of sufficient conditions for that recent observer. This new set of sufficient conditions is much simpler, and therefore much more useful and significant, than the sufficient conditions derived in that recent paper. This new set of sufficient conditions also reveals some basic mistakes of that recent paper. In addition, this paper reveals the severe restrictiveness of this new set of conditions and proposes a fundamentally new observer design formulation that can relax that set of conditions significantly.

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.