# US 10,371,813 B2 · Systems and methods for using time of flight measurements for imaging target objects > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 10,371,813 B2 - Document ID: US10371813B2 - Status: Granted - Kind: B2 - Application number: 14/896,375 - Filed: 2014-08-13 - Published: 2016-06-02 - Granted: 2019-08-06 - Earliest claimed: 2013-08-13 - Assignees: Duke University - Applicants: Duke University - Inventors: Orges Furxhi; Ruoyu Zhu; David J. Brady; Daniel Marks - Web page: https://patentgrep.com/patent/US10371813B2 ## CPC - G01S 13/89: for mapping or imaging - G01S 7/352: {Receivers} - G01S 13/003: {Bistatic radar systems; Multistatic radar systems} - G01S 13/34: using transmission of continuous, frequency-modulated waves while heterodyning the received signal, or a signal derived therefrom, with a locally-generated signal related to the contemporaneously transmitted signal - G01S 13/87: Combinations of radar systems, e.g. primary radar and secondary radar - G01S: RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES ## Abstract An imaging system as disclosed can include multiple bistatic radar sensors configured to transmit electromagnetic waves towards a surface of a target object and configured to measure the electromagnetic waves reflected from the surface of the target object. The imaging system includes a computing device that determines time of flight estimates based on the measured waves. The computing device can draw, within an image model for the target object, multiple candidate surface portions of the surface of the target object based on the TOF estimates and predetermined positions of the bistatic radar sensors. Further, the computing device can assign weights to the candidate surface portions. The computing device can determine points where the candidate surface portions meet with a predetermined probability based on the weights. The computing device is configured to define an estimated surface of the target object in the image model based on the determined points. ## Claims ### Claim 1 An imaging system comprising: a plurality of bistatic radar sensors configured to transmit electromagnetic waves towards a surface of a target object and to measure the electromagnetic waves reflected from the surface of the target object; and a computing device comprising at least one processor and memory configured to: determine time of flight (TOF) estimates based on the measured electromagnetic waves; draw, within an image model for the target object, a plurality of candidate surface portions of the surface of the target object based on the TOF estimates and predetermined positions of the bistatic radar sensors; assign weights to each of the candidate surface portions; determine points in the image model where the candidate surface portions meet with a predetermined probability based on the weights; and define an estimated surface of the target object in the image model based on the determined points, wherein the computing device, for assigning the weights to each of the candidate surface portions, is configured to: place a plurality of test ellipses in the image model, each test ellipse being tangent to a different portion of the candidate surface portions; calculate TOFs from predetermined positions of the bistatic radar sensors; and determine distances between the calculated TOFs and the determined TOF estimates, wherein the weights are assigned based on the determined distances, higher weights being assigned to closer distances. ### Claim 2 (depends on 1) The imaging system of claim 1, wherein the computing device is configured to use the estimated surface to display an image of the target object. ### Claim 3 (depends on 1) The imaging system of claim 1, wherein the bistatic sensors are positioned in a predetermined orientation and distance with respect to each other. ### Claim 4 (depends on 1) The imaging system of claim 1, wherein the bistatic sensors are positioned one of with regular spacing, with Golomb ruler spacing, with random spacing, on a plane facing the target object, and around the target object. ### Claim 5 (depends on 1) The imaging system of claim 1, wherein the bistatic radar sensors are configured to operate in a Frequency Modulated Continuous Wave (FMCW) mode to sweep the electromagnetic wave across a predetermined bandwidth. ### Claim 6 (depends on 1) The imaging system of claim 1, wherein the candidate surface portions are one of a portion of an ellipse and a portion of an ellipsoid. ### Claim 7 (depends on 1) The imaging system of claim 1, wherein the computing device is configured to smooth the determined points for defining the estimate surface of the target object. ### Claim 8 (depends on 1) The imaging system of claim 1, wherein the image model is one of a two-dimensional image model and a three-dimensional image model. ### Claim 9 (depends on 1) The imaging system of claim 1, wherein the computing device is configured to determine a reflectivity of the surface of the target object based on the estimated surface and the measured electromagnetic waves. ### Claim 10 (depends on 1) The imaging system of claim 1, wherein the test ellipse is a circle. ### Claim 11 (depends on 1) The imaging system of claim 1, further comprising a display configured to display a representation of the estimated surface of the target object. ### Claim 12 A method comprising: transmitting electromagnetic waves towards a surface of a target object; measuring the electromagnetic waves reflected from the surface of the target object; determining time of flight (TOF) estimates based on the measured electromagnetic waves; drawing, within an image model for the target object, a plurality of candidate surface portions of the surface of the target object based on the TOF estimates and predetermined positions of the bistatic radar sensors; assigning weights to each of the candidate surface portions; determining points in the image model where the candidate surface portions meet with a predetermined probability based on the weights; and defining an estimated surface of the target object in the image model based on the determined points; placing a plurality of test ellipses in the image model, each test ellipse being tangent to a different portion of the candidate surface portions; calculating TOFs from predetermined positions of bistatic radar sensors; and determining distances between the calculated TOFs and the determined TOF estimates, wherein the weights are assigned based on the determined distances, higher weights being assigned to closer distances. ### Claim 13 (depends on 12) The method of claim 12, further comprising using the estimated surface to display an image of the target object. ### Claim 14 (depends on 12) The method of claim 12, wherein transmitting electromagnetic waves and measuring the electromagnetic waves comprises using a plurality of bistatic sensors positioned in a predetermined orientation and distance with respect to each other. ### Claim 15 (depends on 14) The method of claim 14, wherein the bistatic sensors are positioned one of with regular spacing, with Golomb ruler spacing, with random spacing, on a plane facing the target object, and around the target object. ### Claim 16 (depends on 14) The method of claim 14, wherein the bistatic radar sensors are configured to operate in a Frequency Modulated Continuous Wave (FMCW) mode to sweep the electromagnetic wave across a predetermined bandwidth. ### Claim 17 (depends on 12) The method of claim 12, wherein the candidate surface portions are one of a portion of an ellipse and a portion of an ellipsoid. ### Claim 18 (depends on 12) The method of claim 12, further comprising smoothing the determined points for defining the estimate surface of the target object. ### Claim 19 (depends on 12) The method of claim 12, wherein the image model is one of a two-dimensional image model and a three-dimensional image model. ### Claim 20 (depends on 12) The method of claim 12, wherein transmitting electromagnetic waves and measuring the electromagnetic waves comprises using a plurality of bistatic sensors, and wherein the method further comprises determining a reflectivity of the surface of the target object based on the estimated surface and the measured electromagnetic waves. ### Claim 21 (depends on 12) The method of claim 12, wherein transmitting electromagnetic waves and measuring the electromagnetic waves comprises using a plurality of bistatic sensors, and wherein the plurality of bistatic radar sensors comprise a plurality of transmitter and receiver pairs, wherein the method comprises, for each transmitter and receiver pair: determining a TOF estimate; drawing, within the image model, a candidate ellipse for the surface of the target object based on the TOF estimate and the predetermined position of the transmitter and receiver pair; and assigning weights to the candidate ellipse; and wherein the computing device is configured to: determining points in the image model where the candidate ellipses meet with a predetermined probability based on the weights; and defining an estimated surface of the target object in the image model based on the determined points where the candidate ellipses meet with the predetermined probability. ### Claim 22 (depends on 12) The method of claim 12, wherein the test ellipse is a circle. ### Claim 23 (depends on 12) The method of claim 12, further comprising displaying a representation of the estimated surface of the target object.