Method and apparatus for remote object sensing employing compressive sensing

• US 9,274,221 B2
• Filed: 02/01/2013
• Issued: 03/01/2016
• Est. Priority Date: 02/01/2013
• Status: Active Grant

• Current Assignee: GM Global Technology Operations LLC (General Motors Company)
• Original Assignee: GM Global Technology Operations LLC (General Motors Company)
• Inventors: Raz, Guy, Bilik, Igal
• Primary Examiner(s): Sotomayor, John B
• Assistant Examiner(s): Windrich, Marcus
• Application Number:
  US13/756,606
• Publication Number:
  US 20140218226A1
• Time in Patent Office: 1,124 Days
• Field of Search: 342/70, 342/118, 342/195
• US Class Current: 1/1
• CPC Class Codes: G01S 13/343 using sawtooth modulation
• CPC Class Codes: G01S 13/345 using triangular modulation
• CPC Class Codes: G01S 13/867 Combination of radar systems with cameras
• CPC Class Codes: G01S 13/931 of land vehicles
• CPC Class Codes: G01S 2013/93271 in the front of the vehicles
• CPC Class Codes: G01S 2013/93275 in the bumper area
• CPC Class Codes: G01S 7/354 Extracting wanted echo-signals Doppler systems G01S13/50
• CPC Class Codes: G01S 7/356 involving particularities of FFT processing

Abstract

A method for remote object sensing on-board a vehicle includes employing compressive sensing to analyze a waveform originating from an on-vehicle low-resolution radar imaging system and reflected from a remote object. The compressive sensing includes generating a matrix including a temporal projection, a Fourier transform, and an integral term configured to analyze the reflected waveform. Leading and trailing edges of the remote object are identified by employing a norm minimization procedure to reconstruct a range profile based upon the reflected waveform analyzed by the compressive sensing.

Claims

1. A method for remote object sensing on-board a vehicle, comprising:

operating an analog-to-digital (A/D) converter at a sampling rate proportional to a compressibility of sensed objects to generate a digitized form of an on-vehicle low-resolution radar imaging system and reflected from a remote object;

within a signal processor;

employing compressive sensing to analyze the digitized form of the waveform originating from an on-vehicle low-resolution radar imaging system and reflected from the remote object, said compressive sensing including generating a matrix comprising a temporal projection which is predetermined in an off-line environment, a Fourier transform, and an integral term configured to analyze the reflected waveform; and

identifying leading and trailing edges of the remote object by employing a norm minimization procedure to reconstruct a range profile based upon the reflected waveform analyzed by said compressive sensing;

wherein employing a norm minimization procedure includes finding a minimum of the reflected waveform employing linear programming; and

providing an estimate of an actual location of the remote object based on the identified leading and trailing edges of the remote object.

2. The method of claim 1, wherein said waveform originating from the on-vehicle low-resolution radar imaging system comprises a reflected linear frequency modulation (LFM) waveform.

3. The method of claim 2, wherein said radar imaging system comprises a low bandwidth radar device, and said LFM waveform comprises a high frequency waveform that is less than 200 MHz.

4. The method of claim 1, wherein the norm minimization procedure comprises an Ll norm minimization procedure.

5. The method of claim 1, wherein said radar imaging system comprises a low bandwidth radar device configured to monitor a field of view relative to the vehicle.

6. The method of claim 5, wherein said field of view comprises a front view relative to the vehicle.

7. The method of claim 5, wherein said field of view comprises a side view relative to the vehicle.

8. The method of claim 1, wherein compressive sensing including generating a matrix comprising the temporal projection, the Fourier transform, and the integral term configured to analyze the reflected waveform comprises employing compressive sensing to determine a measurement matrix Φ

applied to the reflected waveform, wherein the measurement matrix Φ

is represented by the following relationship;

Φ

=[0 I 0]*[F]*[It]

wherein [0 I 0] is a temporal projection matrix,

[F] is a Fourier transform matrix, and

[It] is an integral term.

9. The method of claim 8, wherein said measurement matrix Φ

applied to the reflected waveform is determined in a derivative space.

10. The method of claim 1, wherein identifying leading and trailing edges of the remote object comprises employing an Ll norm minimization procedure including finding a minimum of the reflected waveform () employing linear programming executing in accordance with the following relationship:

11. A method for remote object sensing on-board a vehicle employing a low-resolution radar imaging system, comprising:

operating an analog-to-digital (A/D) converter at a sampling rate proportional to a compressibility of sensed objects to generate a digitized form of a linear frequency modulation (LFM) waveform generated by the low-resolution radar imaging system and reflected from a remote object;

within a signal processor;

employing compressive sensing to analyze the digitized form of the LFM waveform generated by the low-resolution radar imaging system and reflected from the remote object, said compressive sensing including determining a measurement matrix for the remote object in a derivative space based upon a temporal projection which is predetermined in an off-line environment, a Fourier transform, and an integral term; and

identifying leading and trailing edges of the remote object by employing a norm minimization procedure to reconstruct a range profile based upon the measurement matrix for the remote object in the derivative space;

wherein employing a norm minimization procedure includes finding a minimum of the reflected waveform employing linear programming; and

providing an estimate of an actual location of the remote object based on the identified leading and trailing edges of the remote object.

12. The method of claim 11, wherein the norm minimization procedure comprises an Ll norm minimization procedure.

13. The method of claim 11, wherein determining the measurement matrix for the remote object comprises determining a measurement matrix Φ

applied to the reflected LFM waveform wherein the measurement matrix Φ

is represented by the following relationship;

Φ

=[0 I 0]*[F]*[It]

wherein [0 I 0] is a temporal projection matrix,

[F] is a Fourier transform matrix, and

[It] is an integral term.

14. The method of claim 11, wherein identifying leading and trailing edges of the remote object comprises employing an Ll norm minimization procedure including finding a minimum of the reflected waveform () employing linear programming executing in accordance with the following relationship: