Source: http://www.google.nl/patents/US20050215269
Timestamp: 2017-12-14 22:29:14
Document Index: 584110615

Matched Legal Cases: ['art 2005', 'art 2008', 'art 2013', 'art 2005', 'art 2013', 'art 2008', 'art 2008', 'art 2016']

Patent US20050215269 - Navigation system - Google Patenten
The present invention relates to a method of determining the location of a target. The method includes initializing a set of base stations to determine their location relative to each other. At the target, the time of arrival of at least one signal from each of the plurality of base stations Is measured....http://www.google.nl/patents/US20050215269?utm_source=gb-gplus-sharePatent US20050215269 - Navigation system
Publicatienummer US20050215269 A1
Aanvraagnummer US 11/059,911
Aanvraagdatum 17 feb 2005
Ook gepubliceerd als CA2554417A1, CA2554417C, EP1721186A1, US7403783, US7983694, US8010133, US20080103696, US20080167051, WO2005081012A1
Publicatienummer 059911, 11059911, US 2005/0215269 A1, US 2005/215269 A1, US 20050215269 A1, US 20050215269A1, US 2005215269 A1, US 2005215269A1, US-A1-20050215269, US-A1-2005215269, US2005/0215269A1, US2005/215269A1, US20050215269 A1, US20050215269A1, US2005215269 A1, US2005215269A1
Uitvinders Ka Cheok, G. Smid
Patentcitaties (48), Verwijzingen naar dit patent (44), Classificaties (21), Juridische gebeurtenissen (9)
US 20050215269 A1
initializing a plurality of base stations to determine their relative location to each other;
measuring, at the target, the time of arrival of at least one signal from each of the plurality of base stations;
calculating directly the location of the target relative to the plurality of base stations using a closed solution, where the plurality of base stations is at three when a time of arrival technique is used and wherein the plurality of base stations is at least four when a time difference of arrival technique is used.
5. The method of claim 1, further comprising initializing the base stations to determine their global geographic location.
7. The method of claim 1, wherein the measuring and calculating steps are repeated at least 200 times a sec.
13. The method of claim 1, wherein the measuring step comprises oversampling the received signal between about 0.3 and about 30 giga-samples/sec.
14. The method of claim 1, wherein the measuring step comprises oversampling with a digital sampler or an analog-to-digital converter.
15. The method of claim 1 wherein the calculating step yields a location of the target with a resolution between about 0.01 and about 1.0 meter.
16. The method of claim 1 wherein the calculating step yields a location of the target with an accuracy between about 0.01 and about 1.0 meter.
17. A system for determining the location of a receiver, comprising:
at least three base stations and at least one target for a TOA technique and at least four base stations and a target for a TDOA technique,
each base station comprising at least one GHF UWB transmitter,
wherein at least one base station and the target are mobile and wherein the target is capable of calculating its location using a closed form solution based.
18. The system of claim 17, wherein the target is an unmanned ground vehicle comprising a mine sweeper.
19. The system of claim 17, wherein the target is an unmanned aerial vehicle comprising an aerial drone.
20. The system of claim 17, wherein the target is an unmanned sea vehicle.
TOA Range Measurement. To begin initializing the network, BS1 will broadcast a UWB signal transmission to BS2, BS3 & BS4. Upon receiving the signal, each base station waits for a predetermined time delay and replies with its own UWB signal transmission that identifies with the base station. BS1 will clock the time-of-arrivals for the each of the replies from BS2, BS3 & BS4 and record the total time-of-flight T121, T131 & T141. As an a example, the total time-of-flight T121 comprises: time-of-flight T12 for the first signal transmission to go from BS1 to BS2; the delay TD2 at BS2; and T21(=T12), the time-of-flight for the reply transmission to go from BS2 to BS1. That is, T121, =T12+TD2+T21. Therefore the time of flight between BS1 & BS2 is T 12 = ( T 121 - T D2 ) 2
In general, the TOA timing is given by T i j = ( T iji - T Dj ) 2 ( 1 )
Local Coordinate Frame. The information obtained through the signal transmissions above may be utilized to determine location of the base stations on a local coordinate system. For convenience, a local Cartesian coordinate system is utilized, although other coordinate system may be appropriate: Let [ x 1 y 1 z 1 ] , [ x 2 y 2 z 2 ] , [ x 3 y 3 z 3 ] & [ x 4 y 4 z 4 ]
l 23 2=(l12 −x 3)2 +y 3 2 (3)
l 32 2=( x 3 −x 4)2+(y 3 −y 4)2 +z 4 2 (3)
From this relationship, the desired coordinates is thus given by x 3 = l 12 2 + l 13 2 - l 23 2 2 l 12 y 3 = ( l 13 2 - x 3 2 ) 1 / 2 x 4 = l 12 2 + l 14 2 - l 24 2 2 l 12 y 4 = ( x 3 - x 4 ) 2 + y 3 2 + l 14 2 - x 4 2 2 y 3 z 4 = ( l 34 2 - ( x 3 - x 4 ) 2 - ( y 3 - y 4 ) 2 ) 1 / 2 ( 4 )
Coordinates of additional BS's. The result is readily extended to additional BSi, i=5, 6, . . . ,N, where N is the total number of base stations. The distances e l1i, l2i & l3i from BSi to BS1, BS2 & BS3 would be calculated on the TOA measurement technique already described above. By induction from equation (4), the coordinates of BSi would then be given by x i = l 12 2 + l 1 i 2 - l 2 i 2 2 l 12 y i = ( x 3 - x i ) 2 + y 3 2 + l 1 i 2 - x i 2 2 y 3 i = 5 , 6 , … , N z i = ( l 3 i 2 - ( x 3 - x i ) 2 - ( y 3 - y i ) 2 ) 1 / 2 ( 5 )
Kinematics. Global geographical locations of the base stations are related to the relative locations by a translation and rotation kinematic relationship as follows: [ x i G y i G z i G ] = [ d x d y d z ] + [ e 11 e 12 e 13 e 21 e 22 e 23 e 31 e 32 e 33 ] [ x i y i z i ] where x i G , y i G & G z i ( 6 )
denote geographical coordinates, dx, dy & dz are the translation parameters, eij, i=1,2,3, j=1,2,3 represent the rotation transformation parameters and xi, yi & zi are the relative coordinates determined earlier. The geographical coordinates Gxi, Gyi & Gzi correspond to what is generally known as longitude, latitude and height of a location, whereas xi, yi, & zi, are the local relative coordinates obtained using the methods of UWB RAC & TOA measurements.
GPS data. The translation and rotation parameters may preferably be determined by placing GPS receivers on three of the base stations, although only a single GPS receiver is required. For explanation purposes, suppose that GPS antennas are installed as close as possible to the transceivers of BS1, BS2 & BS3. The global geographical coordinates of these base stations may be accurately determined by using precision GPS, or by calculating statistical mean of less precise GPS data when they are stationary. They would be denoted by [ x 1 G y 1 G z 1 G ] , [ x 2 G y 2 G z 2 G ] & [ x 3 G y 3 G z 3 G ] .
Translation parameters. It is readily seen that the translation parameters simply equate to the GPS coordinates of BS1, which is the origin of the local coordinate frame; i.e., [ d x d y d z ] = [ x 1 G y 1 G z 1 G ] ( 7 )
Rotational parameters. The rotation transformation parameters must satisfy [ x 2 G y 2 G z 2 G ] = [ d x d y d z ] + [ e 11 e 12 e 13 e 21 e 22 e 23 e 31 e 32 e 33 ] [ l 12 0 0 ] ( 8 ) [ x 3 G y 3 G z 3 G ] = [ d x d y d z ] + [ e 11 e 12 e 13 e 21 e 22 e 23 e 31 e 32 e 33 ] [ x 3 y 3 0 ] ( 9 ) and [ e 11 e 12 e 13 e 21 e 22 e 23 e 31 e 32 e 33 ] [ e 11 e 21 e 31 e 12 e 22 e 32 e 13 e 23 e 33 ] = [ 1 0 0 0 1 0 0 0 1 ] ( 10 )
e 11(G x 2 −d x)/l l2
e 23=(1−e 21 2 −e 32 2)1/2
e 33=(1−e 31 2 −e 32 2)1/2
Local BS coordinates. Determining the location of the target may also be accomplished through the use of a TOA technique. The coordinate locations [ x 1 y 1 z 1 ] , [ x 2 y 2 z 2 ] , … , [ x N y N z N ]
Local TU coordinates. Let [ x y z ]
r 1 2=(x−x 1)2+(y−y 1)2+(z−z 1)2
r 2 2=(x−x 2)2+(y−y 2)2+(z−z 2)2
r N 2=(x−x N)2+(y−y N)2+(z−z N)2 (12)
r 1 2 =x 2−2xx 1 +x 1 2 +y 2−2yy 1 +y 1 2 +z 2−2zz 1+z1 2
r 2 2 ×x 2−2xx 2 +x 2 2 +y 2−2yy 2 +y 2 2 +z 2−2zz 2 +z 2 2
r N 2 =x 2−2xx N +x N 2 +y 2−2yy N +y N 2 +z 2−2zz N +z N 2 (13)
Closed-form TOA method for TU location. Manipulating the expanded equations, it can be shown that the coordinates of the target is given by [ x y z ] = 1 2 [ ( x 2 - x 1 ) ( y 2 - y 1 ) ( z 2 - z 1 ) ( x 3 - x 2 ) ( y 3 - y 2 ) ( z 3 - z 2 ) ⋮ ⋮ ⋮ ( x 1 - x N ) ( y 1 - y N ) ( z 1 - z N ) ] # [ ( x 2 2 - x 1 2 ) + ( y 2 2 - y 1 2 ) + ( z 2 2 - z 1 2 ) - ( r 2 2 - r 1 2 ) ( x 3 2 - x 2 2 ) + ( y 3 2 - y 2 2 ) + ( z 3 2 - z 2 2 ) - ( r 3 2 - r 2 2 ) ⋮ ( x 1 2 - x N 2 ) + ( y 1 2 - y N 2 ) + ( z 1 2 - z N 2 ) - ( r 1 2 - r N 2 ) ] ( 14 )
Necessary condition. For N=3, the pseudo-inverse is the standard matrix inverse, i.e., [ ]#=[ ]−1, For N>3, the pseudo-inverse is defined [ ]#=([ ]T[ ])−1[ ]T, where [ ]T denotes the matrix transpose. From the necessary condition of algebra, a solution for x, y & z exists only for cases where N≧3 and all the BS's are located at distinct locations. Therefore, the minimum number of base stations required to determine the location x, y & z of the target is 3. In practice, at least 4 base stations are desirable.
TDOA Method. Alternatively, determining the location of the target may also be accomplished through the use of a TDOA technique. Use of the TDOA technique is preferred, particularly when increased security is desired because the target need only have the capability to receive signals. By not transmitting signals, the target cannot reveal its location. In the TDOA method, the [ x 1 y 1 z 1 ] , [ x 2 y 2 z 2 ] , … , [ x N y N z N ]
coordinates of base stations locations are known and [ x y z ]
TDOA Location Problem. The TDOA problem is to compute x, y & z from knowing the coordinates [ x 1 y 1 z 1 ] , [ x 2 y 2 z 2 ] , … , [ x N y N z N ]
C(T 1 −T 0)=r 1
C(T 2 −T 0)=l 12 +CT D2 +r 2
C(T N −T 0)=l IN +CT DN +r N (15)
where C is the speed of light at a given temperature. The unknown variables in the above equation are T0, r1, r2, . . . ,rN.
Δri,1 =r i −r 1, i=2, . . . ,N (16)
⊕r i,1 =C(T i −T 1 −T Di)−l 1i, i=2, . . . ,N (17)
Δr i,1 r 1 =r i r 1−r1 2 (19)
Next note that following combination of Δri,1 2 & Δri,1r1 eliminates the cross term rir1: Δ r i , 1 2 + 2 Δ r i , 1 r 1 = r i 2 - r 1 2 = ( x - x i ) 2 + ( y - y i ) 2 + ( z - z i ) 2 - ( x - x 1 ) 2 + ( y - y 1 ) 2 + ( z - z 1 ) 2 = x 2 - 2 x x i + x i 2 + y 2 - 2 y y i + y i 2 + z 2 - 2 z z i + z i 2 - ( x 2 - 2 x x 1 + x 1 2 + y 2 - 2 y y 1 + y 1 2 + z 2 - 2 z z 1 + z 1 2 ) = x i 2 + y i 2 + z i 2 - ( x 1 2 + y 1 2 + z 1 2 ) - 2 ( x i - x 1 ) x - 2 ( y i - y 1 ) y - 2 ( z i - z 1 ) z ( 20 )
Δr i,1 2+2Δr i,1 r 1 =h i 2 −h 1 2−2Δx i,1 x−2Δy i,1 y−2Δz i,1 z (21)
hi 2=xi 2+yi 2+yi 2
Δxi,1=xi−x1
Δyi,1=yi−y1
Δzi,1=zi−z1
Linear relationships. The above manipulation results in a set of algebraic equations which is linear in x, y & z and r1. Matrices may be used to solve these linear equations. [ Δ x 2 , 1 Δ y 2 , 1 Δ z 2 , 1 Δ x 3 , 1 Δ y 3 , 1 Δ z 3 , 1 ⋮ ⋮ ⋮ Δ x N , 1 Δ y N , 1 Δ z N , 1 ] [ x y z ] = 1 2 [ h 2 2 - h 1 2 - Δ r 2 , 1 2 h 3 2 - h 1 2 - Δ r 3 , 1 2 ⋮ h N 2 - h 1 2 - Δ r N , 1 2 ] + [ - Δ r 2 , 1 - Δ r 3 , 1 ⋮ - Δ r N , 1 ] r 1 ( 22 )
Least squared error (LSE) estimate {want to avoid this phrase} of x, y & z The location x, y & z of the target is expressed in terms of r1 as: [ x y z ] = [ Δ x 2 , 1 Δ y 2 , 1 Δ z 2 , 1 Δ x 3 , 1 Δ y 3 , 1 Δ z 3 , 1 ⋮ ⋮ ⋮ Δ x N , 1 Δ y N , 1 Δ z N , 1 ] # [ - Δ r 2 , 1 - Δ r 3 , 1 ⋮ - Δ r N , 1 ] r 1 + ( 23 ) 1 2 [ Δ x 2 , 1 Δ y 2 , 1 Δ z 2 , 1 Δ x 3 , 1 Δ y 3 , 1 Δ z 3 , 1 ⋮ ⋮ ⋮ Δ x N , 1 Δ y N , 1 Δ z N , 1 ] # [ h 2 2 - h 1 2 - Δ r 2 , 1 2 h 3 2 - h 1 2 - Δ r 3 , 1 2 ⋮ h N 2 - h 1 2 - Δ r N , 1 2 ] = [ a x r 1 + b x a y r 1 + b y a z r 1 + b z ] where : [ a x a y a z ] = [ Δ x 2 , 1 Δ y 2 , 1 Δ z 2 , 1 Δ x 3 , 1 Δ y 3 , 1 Δ z 3 , 1 ⋮ ⋮ ⋮ Δ x N , 1 Δ y N , 1 Δ z N , 1 ] # [ - Δ r 2 , 1 - Δ r 3 , 1 ⋮ - Δ r N , 1 ] [ b x b y b z ] = 1 2 [ Δ x 2 , 1 Δ y 2 , 1 Δ z 2 , 1 Δ x 3 , 1 Δ y 3 , 1 Δ z 3 , 1 ⋮ ⋮ ⋮ Δ x N , 1 Δ y N , 1 Δ z N , 1 ] # [ h 2 2 - h 1 2 - Δ r 2 , 1 2 h 3 2 - h 1 2 - Δ r 3 , 1 2 ⋮ h N 2 - h 1 2 - Δ r N , 1 2 ]
Manipulation to quadratic form (Second key simplification). Expand the Euclidean distance relationship to yield another expression relating x, y & z and r1. r 1 2 = ( x - x 1 ) 2 + ( y - y 1 ) 2 + ( z - z 1 ) 2 = x 2 + y 2 + z 2 + x 1 2 + y 1 2 + z 1 2 - 2 x x 1 - 2 y y 1 - 2 z z 1 ( 24 )
b=−2(ax(x1−bx)+ay(y1−by)+az(z1−bz))
c=(x1−bx)2+(y1−b y)2+(z1−bz)2
The quadratic polynomial yields two answers for r1. r 1 = - b ± b 2 - 4 a c 2 a ( 28 )
Calculation of x, y & z. Selecting the positive answer for r1 and compute the location of target as: [ x y z ] = [ a x a y a z ] r 1 + [ b x b y b z ] ( 29 )
Ranging & Positioning Errors. Accuracy in the measurement of ranges depends on several factors including hardware clock & delays, transmission model, etc. Each measured range can be expressed as the sum of its true range and its measurement error, i.e., r1+Δr 1, i=1, . . . , N. The position of the target can also be similarly expressed as x+Δx, y+Δy & z+Δz, where Δx, Δy & Δz are the calculation errors. It follows from the least squares estimate formula (14) that the calculation errors are related to the measurements errors as [ Δ x Δ y Δ z ] = [ ( x 2 - x 1 ) ( y 2 - y 1 ) ( z 2 - z 1 ) ( x 3 - x 2 ) ( y 3 - y 2 ) ( z 3 - z 2 ) ⋮ ⋮ ⋮ ( x 1 - x N ) ( y 1 - y N ) ( z 1 - z N ) ] # [ r 1 - r 2 ⋯ 0 0 r 2 - r 3 ⋮ ⋮ ⋮ ⋰ - r 1 0 ⋯ r N ] ︸ C [ Δ r 1 Δ r 2 ⋮ Δ r N ] = C [ Δ r 1 Δ r 2 ⋮ Δ r N ] ( 30 )
Positioning accuracy. Assuming the average measurement errors are zero, the covariance of the measurement errors can be expressed as Q r = average of { [ Δ r 1 Δ r 2 ⋮ Δ r N ] [ Δ r 1 Δ r 2 ⋯ Δ r N ] } ( 31 )
The covariance of the errors in calculation of the position x, y & z, is similarly defined as Q r = average of { [ Δ x Δ y Δ z ] [ Δ x Δ y Δ z ] } ( 32 )
Formula (33) defines the resolution or accuracy in the calculation of the position in terms of covariance Qx. The standard deviations of the resolution is given by |{square root}{square root over (Qx)}|, which is the square root of the covariance. The variance depends on the matrix C, which relies on the locations of base stations (xi's, yi's & zi's) and their ranges (ri's) to the target. That is, positioning accuracy depends on the configuration of BS's location and the current position of the target. As discussed above, by placing one base station or the target out of the plane of the remaining base stations, the accuracy can be increased.
Illustration of Ranging & Positioning Accuracy. In practice, UWB RAC equipment will be tested and calibrated via experiments and correlating it with known measurements. Therefore well calibrated equipment can be as accurate in calibration as its ranging resolution. Referring to a prior example, a 350 Mbits/s chiprate UWB signal could be over-sampled at a rate of 1.75 Gbits/s (five times the chiprate), so that the PN correlation yield a ranging resolution of about 0.1713 meter. For example, the resolution can be treated as the standard deviation; and its covariance would be 0.02934 m2. Since each UWB RAC receivers are independent, the ranging covariance Qr becomes a diagonal matrix with 0.02934 as elements. The positioning accuracy is then reflected in the positioning covariance Qx=C Qr CT, where C depends xi's, yi's & zi's and ri's. For example, let the {xi, yi, zi} of the BSi, i=1, . . . , 5, be located at ad hoc network coordinates of {0, 0, 0}, {1000, 0, 0}, {1000, 1000, 0}, {0 1000, 1000} & {1000, 1000, 1000}, with the coordinates represents meters from the origin. Let the target be located at {400 500 600}, such that {ri} is {877.50}, {984.89} {984.89}, {754.98} & {877.50}. Then the position error covariance results in Q x = CQ r C T = [ 0.0226 - 0.0142 0.0142 - 0.0142 0.0569 - 0.0427 0.0142 - 0.04270 0.0511 ]
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Classificatie in de VS 455/456.1, 455/456.5
Internationale classificatie G01S5/06, G01S5/08, G01S5/10, H04W64/00, G01S19/25, G01S5/02, G01S5/14
Coöperatieve classificatie G01S5/06, G01S5/0289, H04W64/00, G01S5/08, G01S5/10, G01S5/14, G01S5/0284
Europese classificatie G01S5/02R, G01S5/08, G01S5/06, G01S5/02R1, H04W64/00
Owner name: ARMY, US GOVERNMENT REPRESENTED BY THE SECRETARY O
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3 okt 2006 AS Assignment
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:CHEOK, KA C.;SMID, G. EDZKO;REEL/FRAME:018341/0133
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