On Quantized Analog Compressive Sensing Methods for Efficient Resonator Frequency Estimation

In many applications such as gravimetric sensing, there is a need to rapidly estimate the center resonant frequency of the sensor system. This paper proposes and compares different quantized analog compressive sensing approaches for rapid frequency estimation. In particular, we discuss (a) Atomic norm Soft Thresholding - Semidefinite Programming (AST-SDP), (b) Atomic norm Soft Thresholding - Alternating Direction Method of Multipliers (AST-ADMM) and (c) Superfast Line Spectral Estimation (LSE) algorithms. As a result of this comparison we report that Superfast LSE achieves a good trade-off between computational speed, quantization, and error in frequency estimation among the three approaches. We further compare the compressive sensing approaches to several classical methods such as the Prony's algorithm and the Pisarenko's algorithm and show that compressive sensing based approaches remain robust to higher quantization errors. Finally, experimental results are shown for a quartz crystal and a MEMS based gravimetric sensor. Frequency measurement results with the quartz crystal show that a resolution of 0.1 ppm RMSE is achieved with the compressed sensing approach.