Few of the methods presented thus far take into consideration the possibility of combining multiple observations of the environment. That is, the robot may wish to consider integrating data from multiple sensors, data acquired over time, or even previous pose estimates in its computation of the current pose. The most popular technique for achieving this goal is Kalman filtering. Kalman filtering has been used in a variety of application domains for computing estimates from uncertain data acquired over time. In the context of mobile robotics, Self, Smith and Cheeseman derive a method for combining uncertain reference frames (known as Approximate Transforms or ATs) using a Kalman filter [52, 53]. ATs are represented mathematically by a mean estimate and associated covariance matrix and represent transformations between reference frames such as that between a robot's internal representation of the environment and a global reference frame.
Leonard and Durrant-Whyte have applied the Extended Kalman Filter (EKF) to the problem of localisation using sonar data which is obtained over time [36]. Like the Kalman Filter, EKF methods allow for the integration of multiple sources of data and allows prior data to be weighted according to how well it predicts the current observations. Leonard et al. apply the EKF to sonar data which has been preprocessed into geometric beacons, which are employed as landmarks. As these landmarks are indistinguishable, the robot relies heavily on a good a priori estimate in order to obtain an accurate position estimate.
Extended Kalman filtering techniques have been used in a variety of robotic tasks such as road-following, visual map-building and egomotion estimation and other related navigational applications such as ship navigation and missile tracking [18, 3, 32, 43, 24]. One significant disadvantage of both the Kalman filter and the EKF is that they make a locally linear approximation to the true relationship between position and observations. That is, the Kalman filtering techniques tend to rely on a good a priori estimate. For this reason Kalman filtering methods can suffer from lack of robustness or failure to converge altogether.
Several researchers have proposed alternative methods for approaching the task of optimising the correspondence between sensor measurements and a known map. Beveridge, Weiss and Riseman, and Lu and Milios propose solutions which seek out an optimal registration of sensor data in the least squares sense [9, 39]. The solution proposed by Beveridge and colleagues uses an iterative match-and-perturb technique to arrive at a locally optimal correspondence, whereas Lu and Milios seek out an estimate which results in globally optimal sensor data registration. Similarly, Boley, Steinmetz and Sutherland employ a method which computes a least-squares position estimate from all the data that is available to it, and supports real-time implementation by deriving a recursive method to incorporate new measurements incrementally [11]. These works tend to depend critically on the availability of good range data and limited input error. In other work, Thrun derives a Bayesian probabilistic solution to the localisation problem which subsumes the Kalman filter [56]. In that work, the computational intractability of the derived probabilities leads to a neural-network based implementation.
While most optimisation approaches seek out a least-squares optimum in the correspondence error, several other measures have been suggested, such as the generalised Hough transform, geometric hashing and the Hausdorff distance [15, 49, 35, 28, 37].