System and method for relative localization

• US 9,134,403 B1
• Filed: 02/20/2013
• Issued: 09/15/2015
• Est. Priority Date: 02/20/2013
• Status: Expired due to Fees

• Current Assignee: the united states of america as represented by the secretary of the navy
• Original Assignee: the united states of america as represented by the secretary of the navy
• Inventors: Anderson, Roger J.
• Primary Examiner(s): BYTHROW, PETER M
• Application Number:
  US13/771,909
• Time in Patent Office: 937 Days
• Field of Search: 342/107, 342/113, 342/118, 342/146, 342147-158
• US Class Current: 1/1
• CPC Class Codes: G01S 1/02 using radio waves G01S19/00 takes precedence
• CPC Class Codes: G01S 1/08 Systems for determining direction or position line
• CPC Class Codes: G01S 1/20 using a comparison of transit time of synchronised signals transmitted from non-directional antennas or antenna systems spaced apart, i.e. path-difference systems
• CPC Class Codes: G01S 3/00 Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received position-fixing by co-ordinating a plurality of determinations of direction or position lines G01S5/00
• CPC Class Codes: G01S 3/02 using radio waves
• CPC Class Codes: G01S 5/08 Position of single direction-finder fixed by determining direction of a plurality of spaced sources of known location
• CPC Class Codes: G01S 5/16 using electromagnetic waves other than radio waves
• CPC Class Codes: G01S 5/163 Determination of attitude using inertial means G01C9/00; control of attitude G05D1/49

Abstract

Localization systems and methods for unambiguously determining the range, bearing, and relative heading of a neighboring object relative to a reference point are provided. The systems and methods utilize a triangulation-based approach, wherein the range and heading information is based on measurements of angles between a reference coordinate system superposed on the reference point to a minimum of three target points on the neighboring object. The target points can include a minimum of three uniquely discernible beacons mounted to the neighboring object. A sensor capable of detecting the beacons is mounted at the reference point. The range and heading of the neighboring object can be calculated by an analysis of the geometries of the beacons and the reference point.

Claims

1. A method for localization of a first target, comprising:

sensing at a reference point a relative position of each of at least three beacons, said beacons having a predetermined geometric relationship on said first target;

determining a bearing angle for each of said beacons relative to said reference point;

determining a configuration of said beacons based on said relative position;

calculating a range from each of said beacons to said reference point based on said predetermined geometric relationship, said bearing angle for each of said beacons and said configuration; and

determining a heading of said first target relative to said reference point based on said range from each of said beacons and said configuration.

2. The method of claim 1, wherein calculating a range further comprises calculating an angle between a line, r_R, from said reference point, O, to a rightmost one of said beacons, R, and a line, λ

_R, from a center one of said beacons, C, to R.

3. The method of claim 2, wherein calculating an angle further comprises numerically analyzing an expression for said angle, α

_R, wherein;

λ

_L sin(π

+β

_L+β

_R−

θ

_LR−

α

_R)sin(θ

_RC)=λ

_R sin(θ

_LC)sin(α

_R),

when said configuration is a first configuration having a line, r_C, from said point O to C that intersects a line, λ

_C, between a leftmost one of said beacons, L, and R;

λ

_L sin(π

−

β

_L−

β

_R−

θ

_LR−

α

_R)sin(θ

_RC)=λ

_R sin(θ

_LC)sin(α

_R),

when said configuration is a second configuration wherein said line r_C does not intersect said line λ

_C, and wherein;

λ

_L is a line from L to C;

β

_L is an angle formed between said line λ

_L and said line λ

_C;

β

_R is an angle formed between said line λ

_R and said line λ

_C;

θ

_LR is an absolute value of a difference between a bearing of said line r_R and a bearing of a line, r_L, from said point O to L;

θ

_RC is an absolute value of a difference between said bearing of said line r_R and a bearing of said line r_C; and

θ

_LC is an absolute value of a difference between said bearing of said line r_L and said bearing of said line r_C.

4. The method of claim 3, wherein calculating a range further comprises solving expressions for said line r_L, said line r_C and said line r_R, wherein, for said first configuration:

5. The method of claim 1, further comprising emitting radiation from each of said beacons at differing wavelengths to enable identification.

6. The method of claim 1, further comprising pulsing each of said beacons at differing frequencies to enable identification.

7. The method of claim 1, wherein numerically analyzing comprises application of at least one of Newton'"'"'s method, a method of bisection, a genetic algorithm and an optimization algorithm.

8. The method of claim 1, wherein calculating a range further comprises analyzing expressions for a range, r_L, between said reference point, O, and a leftmost one of said beacons, L, a range, r_C, between said point O and a center one of said beacons, C, and a range, r_R, between said point O and a rightmost one of said beacons, R, wherein:

λ

_L²=r_L²+r_C²−

2r_Lr_C cos(θ

_LC),

λ

_R²=r_R²+r_C²−

2r_Rr_C cos(θ

_RC)

and

λ

_C²=r_L²+r_R²−

2r_Lr_R cos(θ

_LR),

in which

λ

_L is a line from L to C;

λ

_R is a line from C to R;

λ

_C is a line from L to R;

θ

_LC is an absolute value of a difference between a bearing of said line r_L and a bearing of said line r_C;

θ

_RC is an absolute value of a difference between a bearing of said line r_R and said bearing of said line r_C; and

θ

_LR is an absolute value of a difference between said bearing of said line r_R and said bearing of said line r_L.

9. The method of claim 8, wherein analyzing comprises application of at least one of Newton'"'"'s method, a method of bisection, a genetic algorithm and an optimization algorithm.

10. The method of claim 1, further comprising timing emissions from said at least three beacons to correspond with a predetermined schedule.

11. The method of claim 10, further comprising localizing additional targets, wherein said timing differs for each of said additional targets and said first target according to said schedule.

12. A target localization system, comprising:

a set of at least three beacons, said set being located on said target in a predetermined geometric relationship; and

a sensor located a distance from said target, said sensor attuned to receive emissions from each of said beacons.

13. The system of claim 12, further comprising:

a processor connected to said sensor; and

processor readable medium disposed on said processor and containing instructions for;

determining a bearing angle for each of said beacons relative to said sensor; and

calculating a range from each of said beacons to said sensor based on said predetermined geometric relationship and said bearing angle for each of said beacons.

14. The system of claim 13, wherein said instructions further comprise instructions for:

determining a configuration of said beacons based on said bearing angle for each of said beacons; and

determining a heading of said target relative to said sensor based on said range from each of said beacons and said configuration.

15. The system of claim 14, further comprising a controller connected to said beacons, said controller pulsing each of said beacons at differing frequencies to enable identification of each of said beacons by said sensor.

16. The system of claim 14, further comprising a controller connected to said beacons, said controller differing wavelengths of said emissions from each of said beacons to enable identification of each of said beacons by said sensor.