US: Prominent mathematician, Ingrid Daubechies, who’s pioneering work on wavelets is the foundation for various consumer products and GNSS applications, has received a $1.5 million grant from the Simons Foundation. Daubechies is the James B. Duke Professor of Mathematics and Electrical and Computer Engineering at Duke University in Durham, North Carolina.
The Math + X Investigator award provides research funds to professors at American and Canadian universities to encourage novel collaborations between mathematicians and researchers in another field of science or engineering.
“The mathematical technique of wavelet analysis is being used in several different GNSS applications,” said GPS World’s Innovation columnist Richard Langley. In the October 2003 Innovation article “Wavelet Multiresolution Analysis,” Langley provides a general introduction to wavelet techniques:
“Wavelet analysis is an extension of Fourier analysis, the classical technique that decomposes a signal into its frequency components. However, Fourier analysis cannot determine the exact time at which a particular frequency occurred in the signal.
“Wavelet analysis, on the other hand, allows scientists and engineers to study the frequency structure of time-varying signals with unprecedented time resolution.
“In fact, a signal can be decomposed to obtain a time history of the different frequency bands making up the signal — an approach termed multi-resolution analysis. Wavelet analysis can also compress data for more efficient storage and transmission, replacing the original data values with far fewer wavelet transform coefficients.”
Langley explains that to improve GPS accuracy, wavelet analysis is used to “de-noise” GPS pseudorange measurements, detect and eliminate cycle slips in GPS carrier-phase measurements, and separate biases such as multipath from high-frequency receiver noise.