ABSTRACT
Precise estimation of time of delay (time of arrival [ToA]/time difference of arrival [TDoA]) is crucial for localization. The cross-correlation function will peak at τ=τ0, making it very easy to determine the actual time delay. The eigenvector corresponding to the largest eigenvalue is the desired filter, whose role is essentially to align all sensor outputs so that they are in phase. In Capon's method, a filter is sought that minimizes the filter power output subject to the constraint that it maintains unit response toward a sensor with prescribed ToA. An adaptive notch filter is of interest where the notch frequency is changing with time. By observing the instantaneous frequency spectrum, the delay, which depends on the travel time, can be ascertained from relative position of a frequency jump. A multitone signal consisting of harmonically related sinusoids is used as a localizing signal. Frequency difference of arrival (FDoA) is then derived from the time gradient of time varying delay.
