A 1-D SEARCH SOLUTION FOR LOCALIZATION FROM FREQUENCY MEASUREMENTS

A source that emits a constant frequency tone and moves at a constant course and speed can be localized through measurements of the Doppler shifted frequencies (DSF). With five unknowns, namely, the rest freque ncy and the positions and speeds in the x - y directions, five separat e sensors would normally be necessary to give five DSF measurements fo r instantaneous localization. The equations are nonlinear, and the sta ndard solution is by grid search or iteration. The high dimensionality leads to a large computational requirement. By incorporating DSF rate s, a quantity available from frequency line trackers, a one-dimensiona l grid search solution is possible which requires only three sensors a nd reduces the computational load. The derivation of the grid search t echnique is given, together with simulation results. The conclusion is that at high signal-to-noise ratios (SNR), the scheme reaches the thr ee-sensor Cramer-Rao lower bound; at lower SNR's or with increased sen sors, the grid search answer is a good initializer for a nonlinear opt imization algorithm that gives a maximum likelihood estimate.