Passive ranging through global positioning system
First Claim
1. A method for determining the distance from a target to an observation station, using four GPS satellites as radiation sources, and a GPS receiver at the observation station to form a bistatic radar system, wherein an angle of arrival (AOA) of the target to the observation station has been measured first, said method comprising:
- measuring the respective delay times, t1to, t2to, t3to and t4to, of signals travelling from the four satellites to the target and then to the observation station, the signals having been scattered by the target; and
calculating the position of the target, using the following four equations which represent simultaneous nonlinear equations;
space="preserve" listing-type="equation">(x.sub.t- x.sub.1).sup.2 +(y.sub.t- y.sub.1).sup.2 +(z.sub.t- z.sub.1).sup.2 +(x.sub.t- x.sub.o).sup.2
space="preserve" listing-type="equation"> +(y.sub.t- y.sub.o).sup.2 +(z.sub.t- z.sub.o).sup.2 =Ct.sub.1to
space="preserve" listing-type="equation">(x.sub.t- x.sub.2).sup.2 +(y.sub.t- y.sub.2).sup.2 +(z.sub.t- z.sub.2).sup.2 +(x.sub.t- x.sub.o).sup.2
space="preserve" listing-type="equation"> +(y.sub.t- y.sub.o).sup.2 +(z.sub.t- z.sub.o).sup.2 =Ct.sub.2to
space="preserve" listing-type="equation">(x.sub.t- x.sub.3).sup.2 +(y.sub.t- y.sub.3).sup.2 +(z.sub.t- z.sub.3).sup.2 +(x.sub.t- x.sub.o).sup.2
space="preserve" listing-type="equation"> +(y.sub.t- y.sub.o).sup.2 +(z.sub.t- z.sub.o).sup.2 =Ct.sub.3to
space="preserve" listing-type="equation">(x.sub.t- x.sub.4).sup.2 +(y.sub.t- y.sub.4).sup.2 +(z.sub.t- z.sub.4).sup.2 +(x.sub.t- x.sub.o).sup.2
space="preserve" listing-type="equation"> +(y.sub.t- y.sub.o).sup.2 +(z.sub.t- z.sub.o).sup.2 =Ct.sub.4towhere C is the speed of light, (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) and (x4, y4, z4) are respective positions of the four satellites, (xt, yt, zt) is the position of the target, and (xo, yo, zo) is the position of the observation station, wherein traces of the position of the target form ellipsoidal surfaces with respect to the positions of the satellites and the position of the observation station, and a point where the ellipsoidal surfaces intercept represents the position of the target.
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Accused Products
Abstract
To passively measure the range to a target, GPS signals which are scattered by the target are used to determine the distance from the target to an observation station whose position Po is determined by a GPS technique. If the delay time from the reflected signal of the target can be measured, the position Pt of the target can be calculated. Four simultaneous nonlinear equations from the four satellites can be written as
(x.sub.t -x.sub.i).sup.2 +(y.sub.t -y.sub.i).sup.2 +(z.sub.t
-zi)2
+(x.sub.t -x.sub.o).sup.2 +(y.sub.t -y.sub.o).sup.2 +(z.sub.t
-zo)2 =Ctito
where i=1, 2, 3, 4 represent the four satellites having positions, Pi, C is the speed of light, tito is the time for the satellite signal travelling from the ith satellite to Pt then to Po. The trace of Pt forms ellipsoidal surfaces with respect to Pi and Po. The point where the ellipsoidal surfaces intercept represents the position of the target. If only the distance between the target and observation station is of interest, this distance can be estimated easily. The distances from the target and the observation station to the satellite are about 20,000 km, whereas the distance Rot between the target and observation station is probably less than 100 km. Therefore the distance can be estimated as
R.sub.ot ≅(C(t.sub.ito -t.sub.io)
where tio is the time for the satellite signal to travel from satellite i to the observation point which is already known from the conventional GPS approach. In the above equation, only the reflection from one satellite is required.
50 Citations
3 Claims
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1. A method for determining the distance from a target to an observation station, using four GPS satellites as radiation sources, and a GPS receiver at the observation station to form a bistatic radar system, wherein an angle of arrival (AOA) of the target to the observation station has been measured first, said method comprising:
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measuring the respective delay times, t1to, t2to, t3to and t4to, of signals travelling from the four satellites to the target and then to the observation station, the signals having been scattered by the target; and calculating the position of the target, using the following four equations which represent simultaneous nonlinear equations;
space="preserve" listing-type="equation">(x.sub.t- x.sub.1).sup.2 +(y.sub.t- y.sub.1).sup.2 +(z.sub.t- z.sub.1).sup.2 +(x.sub.t- x.sub.o).sup.2
space="preserve" listing-type="equation"> +(y.sub.t- y.sub.o).sup.2 +(z.sub.t- z.sub.o).sup.2 =Ct.sub.1to
space="preserve" listing-type="equation">(x.sub.t- x.sub.2).sup.2 +(y.sub.t- y.sub.2).sup.2 +(z.sub.t- z.sub.2).sup.2 +(x.sub.t- x.sub.o).sup.2
space="preserve" listing-type="equation"> +(y.sub.t- y.sub.o).sup.2 +(z.sub.t- z.sub.o).sup.2 =Ct.sub.2to
space="preserve" listing-type="equation">(x.sub.t- x.sub.3).sup.2 +(y.sub.t- y.sub.3).sup.2 +(z.sub.t- z.sub.3).sup.2 +(x.sub.t- x.sub.o).sup.2
space="preserve" listing-type="equation"> +(y.sub.t- y.sub.o).sup.2 +(z.sub.t- z.sub.o).sup.2 =Ct.sub.3to
space="preserve" listing-type="equation">(x.sub.t- x.sub.4).sup.2 +(y.sub.t- y.sub.4).sup.2 +(z.sub.t- z.sub.4).sup.2 +(x.sub.t- x.sub.o).sup.2
space="preserve" listing-type="equation"> +(y.sub.t- y.sub.o).sup.2 +(z.sub.t- z.sub.o).sup.2 =Ct.sub.4towhere C is the speed of light, (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) and (x4, y4, z4) are respective positions of the four satellites, (xt, yt, zt) is the position of the target, and (xo, yo, zo) is the position of the observation station, wherein traces of the position of the target form ellipsoidal surfaces with respect to the positions of the satellites and the position of the observation station, and a point where the ellipsoidal surfaces intercept represents the position of the target. - View Dependent Claims (2, 3)
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Specification
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- Resources
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Current AssigneeUnited States Of America As Represented By The Secretary Of The Air Force
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Original AssigneeUnited States Of America As Represented By The Secretary Of The Air Force
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InventorsTsui, James B. Y., Shaw, Rudy L.
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Primary Examiner(s)Hellner, Mark
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Application NumberUS07/879,016Time in Patent Office286 DaysField of Search342/13, 342/125, 342/126, 342/357, 342/453US Class Current342/357.61CPC Class CodesG01S 11/02 using radio waves G01S19/00...G01S 13/003 Bistatic radar systems; Mul...G01S 19/18 Military applicationsG01S 19/22 Multipath-related issuesG01S 19/39 the satellite radio beacon ...G01S 5/12 by co-ordinating position l...
