Method and Apparatus for Compressive Parameter Estimation and Tracking

• US 20100241378A1
• Filed: 03/19/2010
• Published: 09/23/2010
• Est. Priority Date: 03/19/2009
• Status: Active Grant

• Current Assignee: Rice University
• Original Assignee: Rice University
• Inventors: Davenport, Mark A., Schnelle, Stephen R., Laska, Jason N., Baraniuk, Richard G., Boufounos, Petros T.
• Granted Patent: US 8,566,053 B2
• Time in Patent Office: Days
• US Class Current: 702/66
• CPC Class Codes: H03L 7/07 using several loops, e.g. for redundant clock signal generation
• CPC Class Codes: H03L 7/0805 the loop being adapted to provide an additional control signal for use outside the loop
• CPC Class Codes: H03L 7/087 using at least two phase detectors or a frequency and phase detector in the loop
• CPC Class Codes: H03L 7/091 the phase or frequency detector using a sampling device H03L7/087 takes precedence

Abstract

We have developed a new method and apparatus for tracking and estimating parameters of locally oscillating signals from measurements that approximately preserve the inner product among signals in a class of signals of interest. Random demodulation, random sampling, and coset sampling are three prime examples of these techniques.

One example of this is a compressive phase locked loops (PLL), which has a wide variety of applications, including but not limited to communications, phase tracking, robust control, sensing, and frequency modulation (FM) demodulation. The design modifies classical PLL designs to operate with CS-based sampling systems. By introducing a compressive sampler at the output of the oscillator and by appropriately adjusting the phase difference estimator we enable the use of PLLs with modern CS sampling technology. Other modifications can be made to reduce concerns such as normalization of the measurements, for example using the QCS-PLL.

The concept of democracy is also introduced into a CS-PLL with quantization effects. Due to the universality of compressive measurements, we can drop a few saturated measurements, yet still get just as good or better performance than if we had allowed the quantizer to saturate.

The CS-PLL and QCS-PLL enable one to track oscillating signals in very large bandwidths using a small number of measurements. In addition to potentially operating below the Nyquist rate, however, our new PLL designs offer very low computational complexity that does not involve intermediate compressive sensing signal reconstruction.

Claims

1. A method for estimating and tracking locally oscillating signals, the method comprising the steps of:

taking measurements of an analog or digital input signal that approximately preserve the inner products among signals in a class of signals of interest; and

computing an estimate of parameters of the input signal from its inner products with other signals.

2. A method according to claim 1 wherein said step of taking measurements is linear and approximately preserves inner products.

3. A method according to claim 1 wherein said step of taking measurements is non-linear and approximately preserves inner products.

4. A method according to claim 2 wherein said step of taking measurements is nonadaptive.

5. A method according to claim 1 wherein said step of taking measurements comprises compressive sensing.

6. A method according to claim 5, wherein said compressive sensing comprises projection using one of a random matrix, a pseudorandom matrix, a sparse matrix and a code matrix.

7. A method according to claim 6 further comprising the step of tracking said signal of interest with a phase-locked loop operating on compressively sampled data.

8. A method of claim 6, further comprising the step of tracking phase and frequency of a signal of interest by operating on compressively sampled frequency modulated data, tracking phase and frequency.

9. A method according to claim 1, wherein said step of taking measurements comprises taking measurements using one of a random demodulator, a random sampler, or another compressive sensing sensor.

10. A method according to claim 9, wherein said step of computing an estimate comprises estimating the parameters with a feedback loop.

11. A method according to claim 1 wherein the signals of interest are locally periodic signals with time-varying fundamental frequency and/or phase.

12. A method according to claim 1 wherein the signals of interest are sinusoids with time varying frequency and/or phase.

13. A method according to of claim 1 wherein said step of computing an estimate of the parameters comprises estimating the phase and/or frequency with a single feedback loop.

14. A method according to claim 13 wherein said single feedback loop operates in real-time.

15. A method for estimating and tracking locally oscillating signals, the method comprising the following steps:

taking measurements of an analog or digital input signal that is a stable embedding between a class of signals of interest;

computing an estimate of parameters of the input signal from its inner products with other signals.

16. A method according to claim 15 wherein the step of taking measurements comprises a linear measurement technique and said linear measurement technique is a stable embedding between a class of signals of interest.

17. A method according to claim 16 wherein said linear measurement technique is nonadaptive.

18. A method according to claim 15 wherein said step of taking measurements comprises compressive sensing comprising projection using random matrix, pseudorandom matrix, sparse matrix, and code matrix.

19. A method according to claim 18 wherein said compressive sensing is performed using a random demodulator, random sampler, or other compressive sensing sensor.

20. A system for estimating and tracking locally oscillating signals, the system comprising:

means for taking measurements of an analog or digital input signal that approximately preserve inner products among signals in a class of signals of interest; and

means for computing an estimate of parameters of the input signal from its inner products with other signals.