Time Difference of Arrival and Frequency Difference of Arrival Geo-Location Techniques

The basic concept of geo-location using time difference of arrival (TDOA) measurements can be illustrated by considering a pair of spatially separated receivers and a signal source at an unknown location. Given the assumptions of line of sight propagation paths and fixed-signal propagation velocity, the signals observed at the receivers arrive with delays proportional to the distances from the signal source to the receivers. The difference in delays corresponds to the TDOA.

Given a TDOA measurement and knowledge of the signal-propagation velocity and the receiver locations, the locus of possible transmitter positions can be solved. If the problem is simplified to two dimensions by assuming the signal source and receivers lie on a plane, then the resulting line of position is a hyperbola. Given three or more receivers, the hyperbolic lines of position obtained for the different pairs of receivers will intersect at the signal source location if sources of error can be neglected.

Two basic approaches are used for measuring TDOAs. The first is applicable if a time domain feature of the signal waveform can be easily identified. For example, the time of arrival (TOA) of a pulse modulated signal can be measured by performing amplitude demodulation to obtain the pulse waveform and measuring the absolute time that corresponds to a suitable reference point on the leading edge of the pulse waveform, such as the point where the pulse reaches a fixed fraction of the peak power level.

The TDOA can then be obtained by taking the difference between the corresponding TOAs observed at two locations. The second requires that the signals from the receiver sites be relayed to a single site where the relative time differences are measured using signal processing techniques, such as cross-correlation.

TDOA based geo-location techniques involve several complications. The requirement for the accurate measurement of very small relative time delays necessitates carefully designed and engineered systems. If the signals received at the separate sites must be relayed to a common site for processing, then the requirements for suitable data links may involve issues of cost and practicality.

Nevertheless, TDOA geo-location techniques have some attractive advantages:
- specialized receiving antennas are not required;
- the orientation of the receiving antenna is not critical;

- several methods can be used to confirm that a signal received at different sites is from the same transmitter;
- the accuracy is relatively unaffected by multipath propagation that occurs in the immediate vicinity of the receiver sites.

The differential frequency shifts that result from relative motions of the transmitters and receivers complicates the signal processing needed for TDOA estimation. With suitable processing, these frequency differences can be estimated and used to define lines or surfaces on which the signal source lies. FDOA based techniques are primarily applicable to airborne or satellite platforms and can be combined with geo-location based techniques based on TDOA measurements.