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For wide-band transmission, geolocation modeling using the wide-band cross-ambiguity function (WBCAF) is preferable
to conventional CAF modeling, which assumes that the transmitted signal is essentially a sinusoid. We compare
the accuracy of two super-resolution techniques for joint estimation of the time-scale (TS) and TDOA
parameters in the WBCAF geolocation model. Assuming a complex-valued signal representation, both techniques
exploit the fact that the maximum value of the magnitude of the WBCAF is attained when the WBCAF is real-valued.
The first technique enhances a known joint estimation method based on sinc interpolation and 2-D Newton root-finding
by (1) extending the original algorithm to handle complex-valued signals, and (2) reformulating the original algorithm
to estimate the difference in radial velocities of the receivers (DV) rather than time scale, which avoids machine
precision problems encountered with the original method. The second technique makes a rough estimate of TDOA on
the sampling lattice by peak-picking the real part of the cross-correlation function of the received signals. Then, by
interpolating the phase of the WBCAF, it obtains a root of the phase in the vicinity of this correlation peak, which
provides a highly accurate TDOA estimate. TDOA estimates found in this way are differentiated in time to obtain DV
estimates. We evaluate both super-resolution techniques applied to simulated received electromagnetic signals which
are linear combinations of complex sinusoids having randomly generated amplitudes, phases, TS, and TDOA. Over a
wide SNR range, TDOA estimates found with the enhanced sinc/Newton technique are at least an order of magnitude
more accurate than those found with conventional CAF, and the phase interpolated TDOA estimates are 3-4 times
more accurate than those found with the enhanced sinc/Newton technique. In the 0-10 dB SNR range, TS estimates
found with the enhanced sinc/Newton technique are a little more accurate than those found with phase interpolation.
Moreover, the TS estimate errors observed with both super-resolution techniques are too small for a CAF-type grid
search to realize in comparable time.
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