1. A method comprising:
a) providing at least four phase-coherent synthetic aperture radar (SAR) platforms;
b) transmitting a radar waveform from one of the at least four SAR platforms;
c) receiving scattered energy waveform by the at least four SAR platforms, the scattered energy comprising a superposition of a plurality of point scatters in range, cross-range, and height convolved with the radar waveform;
d) generating a plurality of complex two dimensional (2-D) SAR images by forming a complex 2-D SAR image at each SAR platform based on the scattered energy received at each SAR platform, each complex 2-D SAR image comprising a plurality of pixels, each pixel comprising a magnitude and a phase;
e) co-registering the plurality of complex 2-D SAR images to generate a discretized 3-D space comprising a plurality of 3-D voxels, each 3-D voxel comprising a range bound, a cross-range bound, and a height bound;
f) calculating three differential paired phase functions for each 3-D voxel of the plurality of 3-D voxels;
g) calculating a plurality of sub-voxel positions;
h) for each sub-voxel position calculation, determining whether a point scatter of the plurality of point scatters falls within a single 3-D voxel of the plurality of 3-D voxels;
i) reporting a range, a cross-range, and a height of the point scatter, based on the range bound, cross-range bound, and height bound of the single 3-D voxel of the plurality of 3-D voxels, if the calculated position of the point scatter falls within the single 3-D voxel of the plurality of 3-D voxels;
j) reporting a non-compliant scatter, if the calculated position of the point scatter of the plurality of point scatters does not fall within the single 3-D voxel; and
k) repeating steps i) through j) until a 3-D image with sub-voxel position is generated.
2. The method according to claim 1, wherein the at least four SAR platforms comprise a tetrahedral arrangement.
3. The method according to claim 1, wherein the at least four SAR platforms are time-coherent.
4. The method according to claim 1, wherein calculating a plurality of sub-voxel positions comprising one of inverting the three differential paired phase functions and using numerical optimization to minimize quadratic error functions.
5. The method according to claim 1, further comprising:
reducing sub-pixel position error in a presence of at least one of phase bias and platform flight perturbations by dilation of a constellation geometry of the four SAR platforms.
6. A method comprising:
a) providing at least four phase-coherent synthetic aperture radar (SAR) platforms;
b) generating a two-dimensional (2-D) SAR image for each SAR platform of the at least four phase-coherent synthetic aperture radar (SAR) platforms; and
c) generating a three-dimensional (3-D) SAR image by co-registering the generated 2-D SAR images, the 3-D SAR image comprising sub-voxel position,
wherein the 3-D image comprises a plurality of voxels, wherein said generating a three-dimensional (3-D) SAR image comprises calculating a plurality of sub-voxel positions by one of using numerical optimization to minimize quadratic error functions and inverting three differential paired phase functions calculated for each voxel of the plurality of voxels.
7. An apparatus comprising:
at least four non-coplanar, phase-coherent synthetic aperture radar (SAR) platforms, each SAR platform of said SAR platforms comprising a corresponding phase-synchronized local oscillator cohered to a common reference clock, a first SAR platform of said SAR platforms operable to transmit a radar waveform, and said SAR platforms operable to receive scattered energy waveforms resulting from the radar waveform and operable to generate two-dimensional (2-D) SAR images based on the received scattered energy waveforms; and
a synchronizing processor operable to communicate with said SAR platforms and operable to synchronize a plurality of SAR transmission and receiving intervals for said SAR platforms,
an image-coregistration processor operable to receive at least four 2-D SAR images from said SAR platforms, and operable to generate a 3-D SAR image having 3-D voxel positions by coregistering the 2-D SAR images; and
a sub-voxel position processor operable to calculate sub-voxel positions of single point scatters from differential phase measurements on a given voxel across said SAR platforms.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A method for efficient processing of product returns from a first facility to a second facility in connection with an electronic registration (ER) system comprising a computer including a processor, the method comprising:
receiving, by the computer and at the first facility, unique identifying information for each product for which return authorization is sought;
transmitting, by the computer, for each product for which return authorization is sought, the unique identifying information to a general database for a determination as to whether applicable return criteria are met based on information stored in the general database;
obtaining, by the computer and the processor of the ER system, a return authorization from the general database for products that qualify for return in response to determinations that applicable return criteria are met; and
enabling the products that qualify for return to be shipped, along with an identification of the return authorization, to the second facility to obtain credit for the returned products,
wherein the general database is located at a location remote from the first facility, and wherein the transmitting is accomplished via electronic communication with the remote location.
2. The method of claim 1, wherein the unique identifying information is entered by scanning a bar code for the product.
3. The method of claim 1, wherein the location remote from the first facility is a manufacturer facility for processing product returns.
4. The method of claim 3, wherein the general database includes a product registration database comprising information received concerning purchased products including date of purchase, and further wherein the general database includes the applicable return criteria for the products.
5. The method of claim 3, wherein the return authorization is a return authorization number, and further comprising applying the return authorization number to a shipping package prior to causing the products that qualify for return to be shipped.
6. The method of claim 1, wherein the first and second facilities are retailer and manufacturer facilities, respectively.
7. A method for pre-authorizing product returns from a first facility to a second facility using an electronic registration (ER) system comprising a computer including a processor, the method comprising:
receiving, from the first facility, unique identifying information for each product for which return authorization is sought;
evaluating, by the computer and the processor of the ER system and for each product for which return authorization is sought, the unique identifying information to determine whether applicable return criteria are met, the applicable return criteria being determined in connection with a product registration database and depending on whether the product has been physically received;
for products that qualify for return, creating a return authorization code and forwarding the return authorization code to the first facility using the computer and the processor of the ER system,
wherein return authorization codes are to accompany the products that qualify for return when the products are returned to the second facility.
8. The method of claim 7, wherein the unique identifying information includes a universal product code and a product serial number, and wherein the evaluating includes accessing the product registration database to verify that the identified product complies with return criteria.
9. The method of claim 7, wherein the receiving obtains the unique identifying information by way of electronic communication.
10. The method of claim 7, wherein the first and second facilities are retailer and manufacturer facilities, respectively.
11. A method of reducing unauthorized returns of purchased products from a first facility to a second facility, the method comprising:
(a) maintaining a product information database remote from the first facility, the database including information for each purchased product as well as return criteria for purchased products;
(b) receiving unique product identification information from the first facility at a host system having access to said product information database, wherein the unique product identification information uniquely identifies a product for which a return is sought;
(c) using the host system to access the product information database to identify applicable return criteria for the product based on the unique product identification information;
(d) determining, by a computer processor, whether the product qualifies for return based on the identified applicable return criteria;
(e) transmitting, by the computer processor, to the first facility a return qualification message that indicates whether the product qualifies for return;
(f) determining whether the product has been physically returned to the first facility; and
(g) indicating that the product should be accepted for return at the second facility if the return qualification message indicates that the product qualifies for return and if the product has been returned to the first facility.
12. The method of claim 11, further comprising repeating (b) through (d) for a plurality of products for which return is sought, and performing (e) so that the return qualification message covers a batch of products.
13. The method of claim 12, wherein the products are to be shipped to and accepted for return, in a batch, at the second facility if the return qualification message so indicates and has been returned to the first facility.
14. The method of claim 11, wherein the first and second facilities are retailer and manufacturer facilities, respectively.
15. The method of claim 14, wherein the manufacturer facility is a manufacturer facility for processing product returns.
16. The method of claim 14, wherein the retailer’s facility is a retailer’s central facility for processing product returns received from the retailer’s retail outlets.
17. The method of claim 11, wherein the product information database stores information for a plurality of purchased products of different types.
18. The method of claim 17, wherein different return criteria are defined for the different types.
19. The method of claim 11, wherein different return criteria are defined for products manufactured by different manufacturers andor for products sold by different retailers.