In the BAT location system, only three ultrasound receivers are used by default to obtain a 3D
position whereas four satellites are required to obtain a 3D position in satellite navigation. Why is
there a difference?

What will be an ideal response?

As a matter of geometry, only three non-colinear reference points are required (given that we can eliminate
solutions on the ‘wrong’ side of the plane formed by the reference points, e.g. eliminating solutions above a
ceiling). But that presupposes that all distances are known.
In the BAT system, all times are computed by the difference between electronic and ultrasound signals and
distances are measured using an estimate of the speed of sound. If we used a fourth reference point, then in
principle we could solve for the actual speed of sound and thus determine position more accurately.
In the case of a satellite navigation system such as GPS, however, the receiving unit does not have an accurate
way of measuring the signal propagation times from satellite to receiver directly. In this case, a fourth
satellite’s data is used to solve for the unit’s clock offset from the satellites; it then becomes possible to deduce
the propagation times from timestamps inserted by the satellites. The unit then estimates distances using an
estimated speed of electromagnetic propagation (taking some account of atmospheric conditions)
If an object is at a known altitude (e.g. sea level) then only three satellites are needed.