A new navigation filter
This dissertation describes a new self-learning navigation filter associated with probability space and non-Newtonian dynamics. This new filter relies basically on the information contained in measurements on the vehicle: position fixes, velocities and their error statistics. The basic idea behind this new navigation filter is twofold: (1) A cluster of the observed position fixes contains true kinematic information about the vehicle in motion, (2) A motion model of the vehicle associated with the error statistics of the position fixes should be able to get, to a large extent, the information out of the measurements for use. We base the new filter on an analogy. We consider the statistical confidence region of every position fix as “source" tending to “attract" the undetermined trajectory to pass through this region. With these position fixes and their error statistics, a virtual potential field is constructed in which an imaginary mass particle moves. To make the new filter flexible and responsive to a changing navigation environment, we leave some parameters free and let the filter determine their values, using a sequence of observations and the criterion of least squares of the observation errors. We show that the trajectory of the imaginary particle can well represent the real track of the vehicle. The new navigation filter has been tested with both simulated and real navigation data, as an estimator, predictor, smoother and blunder detector. Its ability to accept navigator's intervention has also been tested. Compared with the Kalman filter, the new filter requires the uncertainties of observations to be known only relatively (cofactor matrix) and is able to offer a better navigation when the vehicle is under dynamic maneuvers and the data rate is small, but with a slower processing speed.