Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

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

AN INTELLIGENT NAVIGATION SYSTEM FOR AN AUTONOMOUS UNDERWATER VEHICLE

The work in this thesis concerns with the development of a novel multisensor data fusion (MSDF) technique, which combines synergistically Kalman filtering, fuzzy logic and genetic algorithm approaches, aimed to enhance the accuracy of an autonomous underwater vehicle (AUV) navigation system, formed by an integration of global positioning system and inertial navigation system (GPS/INS). The Kalman filter has been a popular method for integrating the data produced by the GPS and INS to provide optimal estimates of AUVs position and attitude. In this thesis, a sequential use of a linear Kalman filter and extended Kalman filter is proposed. The former is used to fuse the data from a variety of INS sensors whose output is used as an input to the later where integration with GPS data takes place. The use of an adaptation scheme based on fuzzy logic approaches to cope with the divergence problem caused by the insufficiently known a priori filter statistics is also explored. The choice of fuzzy membership functions for the adaptation scheme is first carried out using a heuristic approach. Single objective and multiobjective genetic algorithm techniques are then used to optimize the parameters of the membership functions with respect to a certain performance criteria in order to improve the overall accuracy of the integrated navigation system. Results are presented that show that the proposed algorithms can provide a significant improvement in the overall navigation performance of an autonomous underwater vehicle navigation. The proposed technique is known to be the first method used in relation to AUV navigation technology and is thus considered as a major contribution thereof.J&S Marine Ltd., Qinetiq, Subsea 7 and South West Water PL