Continuous rotation north-finding algorithm based on constrained adaptive Kalman filter

As an orientation measurement system,north-finder has been playing a significant role in both military and civilian fields of orientation and control.In this paper,to deal with drawbacks in the conventional north-finding systems,a dynamic strategy based on continuous rotation modulation to measure the rotational angular velocity of the earth is proposed.By modeling the dynamic error,optimizing the process constraint and estimating dynamic noise,a method combining delay compensation and hardware adjustment,and a constrained adaptive Kalman filter(CAKF)algorithm are designed for the north-finding strategy.According to simulation and experiments,the proposed algorithm can achieve the high-precision north-finding with robust and anti-noise performance.

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.