The Bearings-only tracking problem is to estimate the state of a moving object from noisy
observations of its direction relative to a sensor. The Kalman filter, which provides least
squares estimates for linear Gaussian filtering problems is not directly applicable because
of the highly nonlinear measurement function of the state, representing the bearings
measurements and so other types of filters must be considered. The shifted Rayleigh filter (SRF) is a highly effective moment-matching bearings-only tracking algorithm which has
been shown, in 2D, to achieve the accuracy of computationally demanding particle filters in situations where the well-known extended Kalman filter and unscented Kalman filter often fail.
This thesis has two principal aims. The first is to develop accurate and computationally efficient algorithms for bearings-only tracking in 3D space. We propose algorithms based
on the SRF, that allow tracking, in the presence of clutter, of both nonmaneuvering
and maneuvering targets. Their performances are assessed, in relation to competing
methods, in highly challenging tracking scenarios, where they are shown to match the
accuracy of high-order sophisticated particle filters, at a fraction of the computational cost.
The second is to design accurate and consistent algorithms for bearings-only simultaneous
localization and mapping (SLAM). The difficulty of this problem, originating
from the uncertainty in the position and orientation of the sensor, and the absence of
range information of observed landmarks, motivates the use of advanced bearings-only
tracking algorithms. We propose the quadrature-SRF SLAM algorithm, which is a
moment-matching filter based on the SRF, that numerically evaluates the exact mean
and covariance of the posterior. Simulations illustrate the accuracy and consistency of its
estimates in a situation where a widely used moment-matching algorithm fails to produce
consistent estimates. We also propose a Rao-Blackwellized SRF implementation of a
particle filter, which, however, does not exhibit favorable consistency properties.