Systems and methods for efficient targeting
A system for determining the physical path of an object can map several candidate paths to a suitable path space that can be explored using a convex optimization technique. The optimization technique may take advantage of the typical sparsity of the path space and can identify a likely physical path using a function of sensor observation as constraints. A track of an object can also be determined using a track model and a convex optimization technique.
1. A method for analyzing motions of objects, the method comprising performing by a processor the steps of:
(a1) representing as a first path point in a path space a first expected path of motion of a first point scatterer in a physical space, the first expected path in the physical space comprising a plurality of locations in the physical space;
(b1) generating a first steering vector based on a first plurality of phase shifts at a receiving antenna, the first plurality of phase shifts corresponding to an association between the first point scatterer and the first path point;
(c1) computing a first field by manipulating a plurality of antenna observations using the first steering vector; and
(d1) determining, based on an intensity of the field, whether the first point scatterer traveled along the first expected path.
2. The method of claim 1 , wherein:
the path space comprises a parametric space; and
at least one parameter of the parametric space is selected from the group consisting of: a position, a linear velocity, and an angular velocity.
3. The method of claim 1 , wherein the representation of the first path point in the path space comprises one of:
a three dimensional position vector;
a six dimensional vector comprising a three dimensional position vector and a three dimensional velocity vector; and
a vector comprising a six dimensional vector representing rigid body motion and a position vector.
4. The method of claim 1 , wherein:
the receiving antenna comprises N E elements, each element being associated with up to N F frequencies and up to N T pulses forming a single dwell; and
each one of the first plurality of phase shifts is associated with an antenna element, one of the N F frequencies, and one pulse.
5. The method of claim 4 , wherein a number of the plurality of antenna observations is less than N E *N F *N T .
6. The method of claim 4 , wherein the first expected path of motion of the first point scatterer in the physical space corresponds to a single dwell of the antenna, the single dwell corresponding to N E elements, N F frequencies, and N T pulses.
7. The method of claim 1 , further comprising:
(a2) representing as a second path point in the path space a second expected path of motion of the first point scatterer in the physical space, the second expected path in the physical space comprising another plurality of locations in the physical space;
(b2) generating a second steering vector based on a second plurality of phase shifts at the receiving antenna, the second plurality of phase shifts corresponding to an association between the first point scatterer and the second path point;
(c2) computing a second field by manipulating the plurality of antenna observations using the second steering vector; and
(d2) determining, based on an intensity of the first field and the second field, whether the first point scatterer traveled along the first expected path or the second expected path.
8. The method of claim 1 , further comprising:
(a2) representing as a second path point in the path space a second expected path of motion of a second point scatterer in the physical space, the second expected path in the physical space comprising another plurality of locations in the physical space;
(b2) generating a second steering vector based on a second plurality of phase shifts at the receiving antenna, the second plurality of phase shifts corresponding to an association between the second point scatterer and the second path point;
(c2) computing a second field by manipulating the plurality of antenna observations using the second steering vector;
(d2) determining, based on an intensity of the second field, whether the second point scatterer traveled along the second expected path;
(e) determining via a comparison of the first and second path points whether a rigid body is associated with the first and second point scatters; and
(f) determining whether the rigid body traveled along a path in the physical space associated with at least one of the first and second expected paths.
9. A method for analyzing attributes of objects, the method comprising performing by a processor the steps of:
(a) representing as a distribution of path points in a path space expected paths of motion of a point scatterer in a physical space, each expected path in the physical space comprising a plurality of locations in the physical space;
(b) generating a distribution of steering vectors based on a plurality of phase shifts at a receiving antenna, the plurality of phase shifts corresponding to an association between the point scatterer and the distribution of path points;
(c) computing a field-intensity distribution based on, at least in part, a plurality of antenna observations and the distribution of steering vectors; and
(d) determining, based on the field-intensity distribution, a path of a first point scatterer in the physical space.
10. The method of claim 9 , wherein computing the field-intensity distribution comprises applying adaptive weights to at least one of: (i) one or more of the plurality of antenna observations, and (ii) the distribution of steering vectors, the adaptive weights being selected to minimize interference from an interfering point scatterer in the physical space.
11. The method of claim 9 , wherein:
computing the field-intensity distribution comprises:
partitioning the path space into first-level regions;
computing the field intensity for each first-level region;
selecting a first-level region having maximum field intensity;
partitioning path space in the selected region into second-level regions;
computing the field intensity for each second-level region; and
selecting a second-level region having maximum field intensity; and
determining the path in the physical space comprises
selecting a representative path point within the selected second-level region; and
identifying a path in the physical space that corresponds to the representative path point.
12. The method of claim 9 , further comprising determining, based on the field-intensity distribution, a path of a second point scatterer in the physical space.
13. The method of claim 12 , further comprising:
determining via a comparison of the paths of the first and second point scatterers that a rigid body is associated with the first and second point scatterers.
14. The method of claim 13 , further comprising:
determining the path of the rigid body in the physical space based on at least one of the path of the first point scatterer and the path of the second point scatterer.
15. The method of claim 13 , further comprising:
determining an attribute of the rigid body based on at least one of the path of the first point scatterer and the path of the second point scatterer.
16. The method of claim 15 , wherein the attribute of the rigid body is selected from the group consisting of a range, a velocity, and an angular velocity.