Signal source localization using compressive measurements
In one aspect, a method for performing signal source localization is provided. The method comprises the steps of obtaining compressive measurements of an acoustic signal or other type of signal from respective ones of a plurality of sensors, processing the compressive measurements to determine time delays between arrivals of the signal at different ones of the sensors, and determining a location of a source of the signal based on differences between the time delays. The method may be implemented in a processing device that is configured to communicate with the plurality of sensors. In an illustrative embodiment, the compressive measurements are obtained from respective ones of only a designated subset of the sensors, and a non-compressive measurement is obtained from at least a given one of the sensors not in the designated subset, with the time delays between the arrivals of the signal at different ones of the sensors being determined based on the compressive measurements and the non-compressive measurement.
1. A processing device comprising:
interface circuitry configured to receive compressive measurements of a signal from respective ones of a subset of a plurality of sensors and to receive a non-compressive measurement of the signal from at least a given one of the sensors not in the subset;
a delay determination module configured to process the compressive measurements in order to determine time delays between arrivals of the signal at different ones of the sensors; and
a source localization module configured to determine a location of a source of the signal based on the time delays;
wherein the delay determination module is configured to determine respective time delays between arrivals of the signal at different ones of the sensors based at least in part on respective impulse response vectors, the respective impulse response vectors being sparse vectors characterizing impulse responses of respective channels between the signal source and respective ones of the sensors; and
wherein the delay determination module is configured to compute respective ones of the impulse response vectors using the non-compressive measurement and a corresponding one of the compressive measurements.
2. The processing device of claim 1 wherein the signal comprises an acoustic signal.
3. The processing device of claim 1 wherein the non-compressive measurement comprises a relatively high sampling rate measurement and the compressive measurements comprise relatively low sampling rate measurements.
4. The processing device of claim 1 further comprising a processor coupled to a memory, wherein at least one of the delay determination module and the source localization module are implemented at least in part in the form of software stored in the memory and executed by the processor.
5. The processing device of claim 1 wherein the delay determination module is further configured to compute respective ones of the impulse response vectors utilizing sampling matrices corresponding to respective ones of the sensors in the subset, and wherein rows of a given one of the sampling matrices are formed using respective shifted maximum length sequences.
6. The processing device of claim 5 wherein entries of the given sampling matrix correspond to entries in respective ones of the shifted maximum length sequences.
7. The processing device of claim 1 wherein the delay determination module is configured to compute a given one of the impulse response vectors based at least in part on a minimization problem involving a sparsity basis formed using the non-compressive measurement, a compressive measurement from a given one of the sensors in the subset, and a sampling matrix corresponding to the given sensor.
8. A sensor comprising:
a signal detector;
a compressive sampling module for generating a compressive measurement from a detection output of the signal detector; and
interface circuitry configured to transmit the compressive measurement to a processing device;
wherein the processing device utilizes the transmitted compressive measurement and a non-compressive measurement received from another sensor to compute an impulse response vector, the impulse response vector being a sparse vector characterizing an impulse response of a channel between a signal source and said sensor.
9. The sensor of claim 8 wherein said sensor is a given one of a plurality of sensors of a sensor network and wherein the given sensor operates at a lower sampling rate than said other sensor of the sensor network that does not generate a compressive measurement for transmission to the processing device.
10. The sensor of claim 8 wherein the compressive sampling module generates the compressive measurement as a product of a signal vector and a sampling matrix.
11. The sensor of claim 10 wherein the sampling matrix is formed using maximum length sequences.
12. The sensor of claim 10 wherein rows of the sampling matrix are formed using respective shifted maximum length sequences.
13. The sensor of claim 12 wherein entries of the sampling matrix correspond to entries in respective ones of the shifted maximum length sequences.
14. The sensor of claim 12 further comprising one or more linear feedback shift registers for computing the shifted maximum length sequences.
15. The sensor of claim 10 wherein entries of the sampling matrix are determined according to
φ ij =1−2 p (j+i)mod N ,i= 1 , . . . ,M,j= 1 , . . . ,N
where p denotes a binary maximum length sequence generated from a polynomial and the sampling matrix φ comprises an M×N matrix.
16. A method for performing localization of a signal source, comprising:
obtaining compressive measurements of a signal from respective ones of a subset of a plurality of sensors;
obtaining a non-compressive measurement of the signal from at least a given one of the sensors not in the subset;
processing the compressive measurements to determine time delays between arrivals of the signal at different ones of the sensors based at least in part on respective impulse response vectors, the respective impulse response vectors being sparse vectors characterizing impulse responses of respective channels between the signal source and respective ones of the sensors; and
determining a location of the signal source based on differences between the time delays;
wherein respective ones of impulse response vectors aer computed using the non-compressive measurement and a corresponding one of the compressive measurements.
17. The method of claim 16 wherein the signal comprises an acoustic signal.
18. A non-transitory computer-readable storage medium having embodied therein executable program code that when executed by a processing device causes the processing device to perform the steps of the method of claim 16 .
19. A system comprising:
a sensor network comprising a plurality of sensors; and
a processing device configured to receive compressive measurements of a signal from respective ones of a subset of the sensors of the sensor network, to receive a non-compressive measurement of the signal from at least a given one of the sensors not in the subset, to process the compressive measurements in order to determine time delays between arrivals of the signal at different ones of the sensors, and to determine a location of a source of the signal based on the time delays;
wherein the processing device is configured to determine respective time delays between arrivals of the signal at different ones of the plurality of sensors based at least in part on respective impulse response vectors, the respective impulse response vectors being sparse vectors characterizing impulse responses of respective channels between the signal source and respective ones of the sensors; and
wherein the processing device is configured compute respective ones of the impulse response vectors using the non-compressive measurement and a corresponding one of the compressive measurements.
20. The system of claim 19 wherein the sensors in the subset that generate the respective compressive measurements each operate at a lower sampling rate than that utilized by the given sensor that generates the non-compressive measurement.