# US 12,223,847 B2 · Spatio-temporal track density shaping > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 12,223,847 B2 - Document ID: US12223847B2 - Status: Granted - Kind: B2 - Application number: 17/677,663 - Filed: 2022-02-22 - Published: 2023-08-24 - Granted: 2025-02-11 - Earliest claimed: 2022-02-22 - Assignees: Raytheon Company - Applicants: Raytheon Company - Inventors: Thomas Frewen; Hala Mostafa; Michael D. Dubois; Stephen K. Freitag - Web page: https://patentgrep.com/patent/US12223847B2 ## CPC - G08G 5/56: for two or more aircraft - G06F 18/2148: {characterised by the process organisation or structure, e.g. boosting cascade} - G06N 20/00: Machine learning - G08G 5/22: located on the ground - G08G 5/26: Transmission of traffic-related information between aircraft and ground stations - G08G 5/727: {from a ground station} - G08G: TRAFFIC CONTROL SYSTEMS (guiding railway traffic, ensuring the safety of railway traffic B61L; arrangement of road signs or traffic signals E01F9/00; radar or analogous systems, sonar systems, lidar systems specially adapted for traffic control G01S13/91, G01S15/88, G01S17/88; {radar or analogous systems, sonar systems, lidar systems specially adapted for anti-collision purposes G01S13/93, G01S15/93, G01S17/93}) - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) - G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS ## Abstract A system includes a first dataset of vehicle trajectories including individual vehicle tracks forming a first track density, a desired vehicle track density profile, a spatio-temporal coverage metric, and a track model including Heaviside functions encoding track time origins and durations for the individual vehicle tracks and including locations for the plurality of individual vehicle tracks. Approximations of the Heaviside functions are minimized as a function of the spatio-temporal coverage metric. The first dataset of vehicle trajectories is manipulated to satisfy the desired vehicle track density profile through minimizing an approximation of the Heaviside functions. Each individual vehicle track in the first dataset of vehicle trajectories is shifted as a result of the optimization, thereby generating a second dataset of vehicle trajectories having a second track density. ## Claims ### Claim 1 A process comprising: receiving into a computer processor a first dataset of vehicle trajectories comprising a plurality of individual vehicle tracks forming a first track density; receiving into the computer processor a vehicle track density profile; receiving into the computer processor a target spatio-temporal coverage metric that is an indication of a user-specified vehicle track density profile; receiving into the computer processor a track model comprising a plurality of Heaviside functions encoding track time origins and durations for the plurality of individual vehicle tracks and comprising locations for the plurality of individual vehicle tracks; minimizing an approximation of the Heaviside functions as a function of the target spatio-temporal coverage metric; optimizing the first dataset of vehicle trajectories as a function of the vehicle track density profile and the minimized approximation of the Heaviside functions; reshaping each individual vehicle track start time and start location in the first dataset of vehicle trajectories as a function of the optimizing, thereby generating a second dataset of vehicle trajectories having a second track density; and training a vehicle resources machine learning algorithm using the second dataset of vehicle trajectories. ### Claim 2 (depends on 1) The process of claim 1, wherein the optimizing comprises a minimization of a deviation from a predetermined value of the target spatio-temporal metric. ### Claim 3 (depends on 1) The process of claim 1, wherein the optimizing comprises a sequential least-squares optimizing. ### Claim 4 (depends on 1) The process of claim 1, wherein the first dataset of vehicle trajectories comprises one or more of a real track dataset and a synthetic track dataset. ### Claim 5 (depends on 1) The process of claim 1, wherein the vehicle track density profile comprises one or more of a spatial profile and temporal profile. ### Claim 6 (depends on 1) The process of claim 1, wherein the vehicle track density profile comprises track identifications, track start times, track durations, and track coordinates. ### Claim 7 (depends on 1) The process of claim 1, wherein the vehicle track density profile comprises a plurality of Heaviside functions comprising track start times, track durations, and track coordinates. ### Claim 8 (depends on 1) The process of claim 1, wherein the vehicle resources comprise one or more of a vehicle traffic control system, a radar resource management system, and a sensor. ### Claim 9 (depends on 1) The process of claim 1, wherein the vehicle trajectories comprise aircraft trajectories, the individual vehicle tracks comprise individual aircraft tracks, the vehicle track density profile comprises an aircraft track density profile, and wherein the vehicle resources machine learning algorithm comprises an aircraft resources machine learning algorithm. ### Claim 10 A non-transitory machine-readable medium comprising instructions that when executed by a processor executes a process comprising: receiving into a computer processor a first dataset of vehicle trajectories comprising a plurality of individual vehicle tracks forming a first track density; receiving into the computer processor a vehicle track density profile; receiving into the computer processor a target spatio-temporal coverage metric that is an indication of a user-specified vehicle track density profile; receiving into the computer processor a track model comprising a plurality of Heaviside functions encoding track time origins and durations for the plurality of individual vehicle tracks and comprising locations for the plurality of individual vehicle tracks; minimizing an approximation of the Heaviside functions as a function of the target spatio-temporal coverage metric; optimizing the first dataset of vehicle trajectories as a function of the vehicle track density profile and the minimized approximation of the Heaviside functions; reshaping each individual vehicle track start time and start location in the first dataset of vehicle trajectories as a function of the optimizing, thereby generating a second dataset of vehicle trajectories having a second track density; and training a vehicle resources machine learning algorithm using the second dataset of vehicle trajectories. ### Claim 11 (depends on 10) The non-transitory machine-readable medium of claim 10, wherein the optimizing comprises a minimization of a deviation from a predetermined value of the target spatio-temporal metric. ### Claim 12 (depends on 10) The non-transitory machine-readable medium of claim 10, wherein the first dataset of vehicle trajectories comprises one or more of a real track dataset and a synthetic track dataset. ### Claim 13 (depends on 10) The non-transitory machine-readable medium of claim 10, wherein the vehicle track density profile comprises one or more of a spatial profile and a temporal profile. ### Claim 14 (depends on 10) The non-transitory machine-readable medium of claim 10, wherein the vehicle track density profile comprises track identifications, track start times, track durations, and track coordinates. ### Claim 15 (depends on 10) The non-transitory machine-readable medium of claim 10, wherein the vehicle track density profile comprises a plurality of Heaviside functions comprising track start times, track durations, and track coordinates. ### Claim 16 (depends on 10) The non-transitory machine-readable medium of claim 10, wherein the vehicle trajectories comprise aircraft trajectories, the individual vehicle tracks comprise individual aircraft tracks, the vehicle track density profile comprises an aircraft track density profile, and wherein the vehicle resources machine learning algorithm comprises an aircraft resources machine learning algorithm. ### Claim 17 A system comprising: a computer processor; and a computer memory coupled to the computer processor; wherein the computer processor and the computer memory are operable for: receiving into the computer processor a first dataset of vehicle trajectories comprising a plurality of individual vehicle tracks forming a first track density; receiving into the computer processor a vehicle track density profile; receiving into the computer processor a target spatio-temporal coverage metric that is an indication of a user-specified vehicle track density profile: receiving into the computer processor a track model comprising a plurality of Heaviside functions encoding track time origins and durations for the plurality of individual vehicle tracks and comprising locations for the plurality of individual vehicle tracks; minimizing an approximation of the Heaviside functions as a function of the target spatio-temporal coverage metric; optimizing the first dataset of vehicle trajectories as a function of the vehicle track density profile and the minimized approximation of the Heaviside functions; reshaping each individual vehicle track start time and start location in the first dataset of vehicle trajectories as a function of the optimizing, thereby generating a second dataset of vehicle trajectories having a second track density; and training a vehicle resources machine learning algorithm using the second dataset of vehicle trajectories.