The sample measurements have constant
uncertainty ??2
z = var(zi). The sampling space ??– can be a grid. Constants
" > 0, p ?‰? 1 are given.
Step1 (initialize): Sample at least n0 ?‰? m initial locations, where m is
the number of field model basis functions gj . These initial sampling locations
could be randomly chosen close to a starting robot location. Remove these
sampling points from ??–. Denote the remaining sampling space as ??–n0 . After
Step1, the robot will be at location xn0 .
Step2: For n ?‰? n0 form measurement vector Z = (zj)i?‰¤j?‰¤n after n samples.
Form basis function matrix Mn as shown in equation (4).
Step3: For all sampling points x in the parameter space ??–n, calculate
m(x) using equation (6). Select the next sampling location to be xnext for
which m(x) is minimal.
Step4: Command the robot to move from location xn to location xnext.
While in transit, sample at k discrete locations xn+1, xn+2, ..., xn+k = xnext.
The number k can be chosen depending on the length of travel. Remove these
points from ??–n to form ??–n+k.
Step5: Calculate the parameter uncertainty measure
var( ?† An) = ??2
z ||(MT
n Mn)??’1||p.
If ??–n+k is empty (the whole space has been sampled), or if var( ?† An) ?‰¤ " (the
parameter uncertainty measure is below a threshold), exit. Otherwise, set n
to be n + k and repeat Step2.
For a 2D spatially distributed field variable, a particularly common basis
that can be used to approximate the field is a sum of Gaussians (SOG)
distribution.
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