Positioning system with a sparse antenna array

1. A positioning system, comprising:

an antenna array with a plurality of transmit elements including at least two transmit elements separated by a spacing more than a half wavelength and configured to transmit at least one set of electromagnetic pulses substantially simultaneously,

wherein each of the at least two transmit elements is configured to transmit one pulse in the set of pulses, each pulse having a respective carrier signal frequency, and the wavelength corresponds to an average of respective carrier signal frequencies of transmitted pulses from the at least two transmit elements, such that the antenna array transmits the electromagnetic pulses in a spatial pattern with grating lobes having an associated resolvable angular resolution;

a receiver configured to receive a return signal over a period of time, the return signal including at least a first return pulse and a second return pulse from an object within a detection area of the system, wherein the first return pulse corresponds to the transmitted pulse from one transmit element and the second return pulse corresponds to the transmitted pulse from the other transmit element; and

a detector configured to process the return signal so as to isolate the first return pulse and the second return pulse and thereby determine a position of the object in relation to the system,

wherein the detector includes angular resolution logic for determining the resolvable angular resolution of the grating lobes in accordance with the spacing between the at least two transmit elements and directional resolution logic for determining a direction of the object in accordance with a difference in arrival times of the first return pulse and the second return pulse at the receiver, including determining a grating lobe in the spatial pattern corresponding to the return signal.

2. The system of claim 1 , wherein the pulse from each of the at least two transmit elements is encoded differently.

3. The system of claim 1 , wherein the pulse from each of the at least two transmit elements has a different carrier signal phase.

4. The system of claim 1 , wherein the pulse from each of the at least two transmit elements has a different carrier signal frequency.

5. The system of claim 1 , wherein the transmit elements are omni-directional.

6. The system of claim 1 , wherein the transmitted pulse from each of the at least two transmit elements has a polarization and the receiver preferentially receives return signals having the polarization.

7. The system of claim 6 , wherein the polarization is selected from the group consisting of linear polarization, elliptical polarization, fight-hand elliptical polarization, left-hand elliptical polarization, fight-hand circular polarization and left-hand circular polarization.

8. The system of claim 1 , wherein the object is a passive reflector.

9. The system of claim 1 , wherein the object is an active landmark.

10. The system of claim 1 , farther comprising a third transmit element that is non-collinear with the first two transmit elements, wherein the third transmit element is configured to transmit a pulse having a respective carrier signal frequency.

11. The system of claim 10 , further comprising a fourth transmit element that is not co-planar with other transmit elements, wherein the fourth transmit element is configured to transmit a pulse having a respective carrier signal frequency.

12. The system of claim 1 ,

wherein the object is a landmark; and

wherein the receiver is part of the antenna array.

13. The system of claim 1 ,

wherein the object is a landmark;

wherein the receiver is part of the antenna array; and

wherein the position of the object in relation to the system is determined with resolution of better than 1 cm.