  The changes in phase, time and frequency suffered by signals when
retransmitted by a remote and inaccessible transponder and the propagation
delays are major constraints to obtain accurate ranging measurements in various
related applications. We present a new method and system to determine these
delays for every single pulsed signal transmission. The process utilizes four
ground-based reference stations, synchronized in time and installed at well
known geodesic coordinates. The repeater station is located within the fields
of view common to the four reference bases, such as in a platform transported
by a satellite, balloon, aircraft, etc. Signal transmitted by one of the
reference bases is retransmitted by the transponder, received back by the four
bases, producing four ranging measurements which are processed to determine
uniquely the time delays undergone in every retransmission process. The
repeater's positions with respect to each group of three out of four reference
bases are given by a system of equations. A minimization function is derived
comparing repeater's positions referred to at least two groups of three
reference bases. The minimum found by iterative methods provide the signal
transit time at the repeater and propagation delays, providing the correct
repeater position. The method is applicable to the transponder platform
positioning and navigation, time synchronization of remote clocks, and location
of targets. The algorithm has been fully demonstrated simulated for practical
situation with the transponder carried by an aircraft moving over bases on the
ground. The errors of the determinations have been evaluated for uncertainties
in clock synchronization, in propagation time delays and other system
parameters.
