Seminar Details
2010-09-07 (14.00) : Bias in localization problems
At Euler building
Organized by Mathematical Engineering
Speaker :
Anderson, Brian D.O.
Abstract :
A common task in controlling formations or multi-robotic systems is the need to localize objects using various types of measurement, e.g. range, bearing,
time-difference-of-arrival, etc., These measurements are introduced into equations, which are generally nonlinear, whose solution yields the position
coordinates of the object. When the number of pieces of sensed data equals the ambient spatial dimension, the presence of any noise in the measurements,
coupled with the fact of the nonlinearity, will lead to a bias in the solution. When the dimension of the sensed data vector exceeds that of the ambient
space dimension, the equations themselves will generally be overdetermined, and they become insoluble in the presence of noise. Localization then usually
involves some kind of optimization problem, based on extremizing a maximum likelihood function. Again, bias is to be expected when the measurements are
contaminated by noise.
The seminar will discuss methods for computing the bias. What makes this problem unusually challenging is that the localization map, from sensed data
to estimated object position, is frequently not available in analytic form. What is available, normally in analytic form, is the mapping from object
position to noiseless sensed data. The technical issue is to establish how knowledge of this map can yield an expression for the bias in the localization
map.
Simulation data and data from flight trials demonstrate the improvement in localization quality that bias elimination can bring.