Method for determining future position boundary for a moving object from location estimates

• US 9,273,965 B2
• Filed: 02/03/2014
• Issued: 03/01/2016
• Est. Priority Date: 02/03/2014
• Status: Active Grant

• Current Assignee: Raytheon Company (Rtx Corporation)
• Original Assignee: Raytheon Company (Rtx Corporation)
• Inventors: Cody, Mac Allen, Kruesi, Heidi Jean, Cole, Robert James, Wright, Richard Matthew
• Primary Examiner(s): Cheung, Calvin
• Assistant Examiner(s): INGRAM, THOMAS P
• Application Number:
  US14/171,649
• Publication Number:
  US 20150219459A1
• Time in Patent Office: 757 Days
• US Class Current: 1/1
• CPC Class Codes: G01S 13/723 by using numerical data
• CPC Class Codes: G01S 13/878 Combination of several spaced transmitters or receivers of known location for determining the position of a transponder or a reflector G01S13/874 takes precedence
• CPC Class Codes: G01S 15/66 Sonar tracking systems
• CPC Class Codes: G01S 15/876 Combination of several spaced transmitters or receivers of known location for determining the position of a transponder or a reflector G01S15/872 takes precedence
• CPC Class Codes: G01S 2013/466 by Trilateration, i.e. two antennas or two sensors determine separately the distance to a target, whereby with the knowledge of the baseline length, i.e. the distance between the antennas or sensors, the position data of the target is determined
• CPC Class Codes: G01S 2013/468 by Triangulation, i.e. two antennas or two sensors determine separately the bearing, direction or angle to a target, whereby with the knowledge of the baseline length, the position data of the target is determined
• CPC Class Codes: G01S 2015/465 by Trilateration, i.e. two transducers determine separately the distance to a target, whereby with the knowledge of the baseline length, i.e. the distance between the transducers, the position data of the target is determined
• CPC Class Codes: G06T 2207/20076 Probabilistic image processing

Abstract

A method for estimating a boundary for a future location of a moving object includes: receiving location information about two previous locations of the moving object represented by a first and a second elliptical error probabilities (EEPs); representing each of the EEPs as a conic section via an implicit quadratic equation; defining four tangent lines from the implicit quadratic equation, each tangent line being tangent to both of the EEPs; determining two transverse tangent lines from the four tangent lines; forming a cone in a direction from the first EEP to the second EEP from the two transverse tangent lines; and estimating the boundary of the future location of the moving object as a first side of the cone formed by a first transverse tangent line and a second side of the cone formed by a second transverse tangent line, of the two transverse tangent lines.

Claims

1. A computer implemented method for estimating a boundary for a future location of a moving object, the method comprising:

receiving, by a receiver, location information about two previous locations of the moving object represented by a first and a second elliptical error probabilities (EEPs);

converting the parameters of each of the first and the second EEPs to parameters of a quadratic form to represent said each of the first and the second EEPs as a conic section via an implicit quadratic equation;

computing four tangent lines from the implicit quadratic equation, each tangent line being tangent to both of the first and the second EEPs;

determining two transverse tangent lines from the four tangent lines to provide a maximum angle formed by a vector passing from the first EEP to the second EEP;

constructing a cone in a direction from the first EEP to the second EEP from the two transverse tangent lines; and

estimating the boundary of the future location of the moving object as a first side of the cone formed by a first transverse tangent line and a second side of the cone formed by a second transverse tangent line, of the two transverse tangent lines.

2. The method of claim 1, further comprising superimposing the cone over a map to display the future location of the moving object over the map.

3. The method of claim 1, wherein each EEP includes a mean location in the form of a two dimensional vector in latitude and longitude, and a covariance matrix.

4. The method of claim 1, wherein representing each of the EEPs as a conic section via an implicit quadratic equation comprises converting parameters of the EEP to parameters of a quadratic form.

5. The method of claim 1, wherein determining two transverse tangent lines comprises representing each of the four tangent lines by a line segment;

and determining line crossing of each tangent line with respect to the other three tangent lines by determining whether each tangent point of a tangent line falls on opposite sides of the line said each tangent line crosses.

6. The method of claim 1, wherein the two traverse tangent lines between the two EEPs provide the maximum angle formed by a vector passing from the first EEP to the second EEP.

7. The method of claim 1, wherein forming a cone comprises constructing a cone whose vertex corresponds to the point of intersection of the two traverse tangent lines and whose sides are the traverse tangent line segments contacting the second EEP.

8. A non-transitory tangible computer storage medium having stored therein computer instructions, the computer instructions when executed by one or more computers perform the following process for estimating a boundary for a future location of a moving object, for which location information about two previous locations of the moving object represented by a first and a second elliptical error probabilities (EEPs) is received:

representing each of the first and the second EEPs as a conic section via an implicit quadratic equation;

defining four tangent lines from the implicit quadratic equation, each tangent line being tangent to both of the first and the second EEPs;

determining two transverse tangent lines from the four tangent lines;

forming a cone in a direction from the first EEP to the second EEP from the two transverse tangent lines; and

estimating the boundary of the future location of the moving object as a first side of the cone formed by a first transverse tangent line and a second side of the cone formed by a second transverse tangent line, of the two transverse tangent lines.

9. The non-transitory tangible computer storage medium of claim 8, further comprising computer instructions when executed by one or more computers to perform superimposing the cone over a map to display the future location of the moving object on the map.

10. The non-transitory tangible computer storage medium of claim 8, wherein each EEP includes a mean location in the form of a two dimensional vector in latitude and longitude, and a covariance matrix.

11. The non-transitory tangible computer storage medium of claim 8, wherein representing each of the EEPs as a conic section via an implicit quadratic equation comprises converting parameters of the EEP to parameters of a quadratic form.

12. The non-transitory tangible computer storage medium of claim 8, wherein determining two transverse tangent lines comprises representing each of the four tangent lines by a line segment;

and determining line crossing of each tangent line with respect to the other three tangent lines by determining whether each tangent point of a tangent line falls on opposite sides of the line said each tangent line crosses.

13. The non-transitory tangible computer storage medium of claim 8, wherein the two traverse tangent lines between the two EEPs provide the maximum angle formed by a vector passing from the first EEP to the second EEP.

14. The non-transitory tangible computer storage medium of claim 8, wherein forming a cone comprises constructing a cone whose vertex corresponds to the point of intersection of the two traverse tangent lines and whose sides are the traverse tangent line segments contacting the second EEP.