multilateration tdoa is the process of location of a source of signal position in two (respectively three) dimensions by solving for the mathematical intersection of multiple hyperbolas (or hyperboloids) based on the time difference of arrival (tdoa) between the signal reception at multiple sensors.
hyperboloid is defined as a surface, which has a constant distance difference from the two points (in our case receivers). using two hyperbolas (three receivers) we can obtain 2d target position, while using at minimum three hyperboloids (four receivers) we can reach full 3d position.
in some areas, additional receivers can serve for the position accuracy improvement.
fig. 1 shows principle of operation of multilateration system. the signal transmitted from the target is received at receiving station l,r,q,c and the time information is concentrated at one point, where the tdoa is evaluated and hyperbolas or hyperboloids intersection is computed.
math 1
the set of equations math 1 defines the mathematical problem to be solved in real time.
the values x,y,z are the unknown coordinates of the targets. the other values are given by the system configuration, or are measured by the central processing station.
