US5848377A
Expired / Lapsed
US
⏱️ 0.0 years remaining
Wong's angles to determine trajectories of objects
Assignee: Individual
•
Filing: 1993-08-29
•
Granted: 1998-12-08
•
Expires: 2013-08-29
Abstract
Abstract A set of three geometric anagles is initiated to track the trajectories of moving objects. The objects to be tracked include but not limit to: satellites, space shuttles, airplanes, missiles moving in aerospace; submarines, ships, fish groups and other moving objects in hydrospace; cars, trucks, trains, human-beings and anmals moving on lands; planet motions in the solar system; particle motions in a controlled experiment in our national labories; contaminants, and hazardous materials in a variety of environmental conditions. All these objects can be detected and monitored by means of various sensing technologies which include seismic, acoustic, electro-magnetic, thermal, chemical, electro-optical and infrared. Mapping and monitoring systems could be deployed in unattended arrays or aboard ground, air, or maritime vehicles.
Inventors
- 👤 Po Kee Wong
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-31 22:48
CPC Classifications
G; G01; G01S; G01S19/00; G01S19/38; G01S19/39; G01S19/42; G01S5/00; G01S5/02; G01S5/04
Claims Analysis
Total Claims: 12
Claim 1
Independent Claim
215 words
A process of locating a moving object relative to earth, comprising the steps of: sensing the object through electro-magnetic or electro-optical means; selecting three ground stations on earth, each ground station having unique coordinates, relative to the earth's center, of altitude, longitude and latitude; processing, by three-dimensional coordinate geometry, distances (a) between the three ground stations and (b) between the center and each of the three ground stations; calculating Wong's angles for each of the ground stations to the sensed object; obtain, by trigonometry, a range from the moving object to each of the ground stations, the range being defined in terms of the Wong's angles and of the distances; obtain a position vector defined by the Wong's angles and the distances; specifying an altitude of the moving object by taking a difference between the position vector and the earth's radius; defining, by Newton's gravitational law, a gravitational acceleration of the moving object in terms of the Wong's angles; determining object velocity by taking a first derivative of position vector with respect to time; determining object acceleration by taking a second derivative of the position vector with respect to time; predicting object trajectory in terms of a trajectory solid angle; and locating the object at a predetermined time following the step of sensing the object.
Claim 2
Dependent Claim
215 words
A process of locating a moving object relative to earth, comprising the steps of: sensing the object through electro-magnetic or electro-optical means; selecting three ground stations on earth, each ground station having unique coordinates, relative to the earth's center, of altitude, longitude and latitude; processing, by three-dimensional coordinate geometry, distances (a) between the three ground stations and (b) between the center and each of the three ground stations; calculating Wong's angles for each of the ground stations to the sensed object; obtain, by trigonometry, a range from the moving object to each of the ground stations, the range being defined in terms of the Wong's angles and of the distances; obtain a position vector defined by the Wong's angles and the distances; specifying an altitude of the moving object by taking a difference between the position vector and the earth's radius; defining, by Newton's gravitational law, a gravitational acceleration of the moving object in terms of the Wong's angles; determining object velocity by taking a first derivative of position vector with respect to time; determining object acceleration by taking a second derivative of the position vector with respect to time; predicting object trajectory in terms of a trajectory solid angle; and locating the object at a predetermined time following the step of sensing the object.
Claim 3
Dependent Claim
66 words
A method according to claim 1, wherein the step of selecting three ground stations comprises assigning Cartesian coordinate positions as points A(x A , y A , z A ), B(x B , y B , z B ), and C(x C , y C , z C ), where A,B and C represent Cartesian coordinate (x,y,z) positions for the stations relative to the earth's center.
Claim 4
Dependent Claim
37 words
A method according to claim 2, wherein the step of determining distances between the center and each of the ground stations comprises calculating ##EQU10## for points A,B and C, as earth's center is located at point 0,0,0.
Claim 5
Dependent Claim
20 words
A method according to claim 3, wherein the step of determining distances between the three ground stations comprises calculating. ##EQU11##
Claim 6
Dependent Claim
99 words
A method according to claim 1, wherein the step of determining the Wong's angles comprises defining a triangular base for the ground stations as points A(x A , y A , z A ), B(x B , y B , z B ), and C(x C , y C , z C ), where A,B and C represent Cartesian coordinate (x,y,z) positions for the stations relative to the earth's center, and determining angles α, β and γ as ∠PAB, ∠PBA, and ∠PBC, respectively, where P represents a Cartesian coordinate position of the moving object relative to the earth's center.
Claim 7
Dependent Claim
37 words
A method according to claim 5, wherein the step of determining a range comprises calculating ##EQU12## where c defines distance between stations at A and B, and where a defines distance between stations at B and C.
Claim 8
Dependent Claim
17 words
A method according to claim 6, wherein the step of determining a position vector comprises calculating ##EQU13##
Claim 9
Dependent Claim
14 words
A method according to claim 1, wherein the moving object comprises a GPS satellite.
Claim 10
Dependent Claim
14 words
A method according to claim 1, wherein the ground stations are GPS ground stations.
Claim 11
Independent Claim
218 words
A method of locating a GPS satellite relative to earth, comprising the steps of: sensing the satellite through electro-magnetic or electro-optical means; selecting three GPS ground stations on earth, each ground station having unique coordinates, relative to the earth's center, of altitude, longitude and latitude; processing, by three-dimensional coordinate geometry, distances (a) between the three GPS ground stations and (b) between the center and each of the three ground stations; calculating Wong's angles for each of the GPS ground stations to the satellite; obtain, by trigonometry, a range from the satellite to each of the ground stations, the range being defined in terms of the Wong's angles and of the distances; obtain a position vector defined by the Wong's angles and the distances; determining an altitude of the satellite by taking a difference between the position vector and the earth's radius; defining, by Newton's gravitational law, a gravitational acceleration of the satellite in terms of the Wong's angles; determining satellite velocity by taking a first derivative of the position vector with respect to time; determining satellite acceleration by taking a second derivative of the position vector with respect to time; predicting the trajectory of the satellite in terms of a trajectory solid angle; and locating the satellite at a predetermined time following the step of sensing the satellite.
Claim 12
Independent Claim
218 words
A method of locating a GPS satellite relative to earth, comprising the steps of: sensing the satellite through electro-magnetic or electro-optical means; selecting three GPS ground stations on earth, each ground station having unique coordinates, relative to the earth's center, of altitude, longitude and latitude; processing, by three-dimensional coordinate geometry, distances (a) between the three GPS ground stations and (b) between the center and each of the three ground stations; calculating Wong's angles for each of the GPS ground stations to the satellite; obtain, by trigonometry, a range from the satellite to each of the ground stations, the range being defined in terms of the Wong's angles and of the distances; obtain a position vector defined by the Wong's angles and the distances; determining an altitude of the satellite by taking a difference between the position vector and the earth's radius; defining, by Newton's gravitational law, a gravitational acceleration of the satellite in terms of the Wong's angles; determining satellite velocity by taking a first derivative of the position vector with respect to time; determining satellite acceleration by taking a second derivative of the position vector with respect to time; predicting the trajectory of the satellite in terms of a trajectory solid angle; and locating the satellite at a predetermined time following the step of sensing the satellite.
References Cited (Backward Citations)
No citation records indexed.
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 2001-12-07 | 2002-06-08 | 2002-12-08 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 2005-12-07 | 2006-06-08 | 2006-12-08 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 2009-12-07 | 2010-06-08 | 2010-12-08 | $7700.00 | Window Closed / Lapsed |