In many practical systems there is a delay in some of the sensor devices, for instance vision measurements that m a y have a long processing time. How to fuse these measurements in a Kalman filter is not a trivial problem if the computational delay is critical. Depending on how much time there is at hand, the designer has to make trade offs between optimality and computational burden of the filter. In this paper various methods in the literature along with a new method proposed by the authors will be presented and compared. The nem method is based on "extrapolaiing" the measurem.ent to present time using past and present estimates of the Kalman filter and calculating an optimal gain for this extrapolated m.easurement.

E m a i l tdlOiau.dtn.dk mX: +45 to make an accurate dynamical model of the robot contemplating all the nonlinearities caused by for instance friction forces, is not a trivial task and is hardly ever seen in the literature (one example though is found in[l]). The problem (besides the noulinearities) is that a lot of parameters that change with for instance time and temperature are required to be known quite precisely.

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In many practical Kalman filter applications, the quantity of most significance for the estimation e m r w the process noise matrix. When filters are stabilized or performance is sought improved, tuning of this matrix is the most common method. This tuning process cannot be done before the filter is implemented, OS it is primarily made necessary by modelling errors. In this paper two different methods for modelling the process noise are described and evaluated; a traditional one based on Gaussian noise models and a new one based on propagating modelling uncertainties. It will be discvssed which method to use and how to tune the filter to achieve the lowest estimation errors.

This paper describes the phenomenon of systematic errors in odometry models in mobile robots and looks at various ways of avoiding it by means of auto-calibration. The systematic errors considered are incorrect knowledge of the wheel base and the gains from encoder readings to wheel displacement. By auto-calibration we mean a standardized procedure which estimates the uncertainties using only on-board equipment such as encoders, an absolute measurement system and filters; no intervention by operator or off-line data processing is necessary. Results are illustrated by a number of simulations and experiments on a mobile robot.