This paper investigates map-making using sonar sensors. The technique
is to mark regions of the map as empty, occupied, or unknown. Multiple
sensors are placed on the mobile robot and measurements are taken from
different positions which are progressively added into the map and enhance
its detail. Three steps are used to remove some of the error before
measurements are processed. These steps are thresholding, averaging,
and clustering. Probability density functions are then used to reduce
uncertainty [actually, to represent the information from a sonar reading].
These functions are projected onto a horizontal plane to generate map information.
The paper includes a brief mathematical description of the probability
density functions used. A sonar map is represented as a 2D array
of cells containing a value which represents its occupancy and degree of
uncertainty. The values are between -1 and 1 with 0 meaning unknown.
Every new reading for a cell will increase or decrease its certainty of
being occupied/empty. Also, empty and occupied probabilities are
treated differently. [Explain why!] This paper also considers
a procedure for matching two maps. A slow method for doing this is
to compute the sum of products of corresponding cells. The paper
does not mention what a reasonable sum would be for this method.
[This is correlation --- you look for the maximum.] A quicker method
uses a transformation to match cells in the maps. [They are doing
matching to _determine_ the transformation between maps!] A sum of
products is taken in this method as well. This method can be sped
up further by creating cells corresponding to a 2x2 grouping of cells in
the map. The authors found that in practice, blurring was necessary
to account for noise in the measurements.