Use of an altitude sensor to augment availability of GPS location fixes
First Claim
1. A method for determination of location coordinates of a selected three-dimensional location of a user on or adjacent to the Earth'"'"'s surface, the method comprising the steps of:
- receiving Global Positioning System (GPS) signals from at least three GPS satellites, numbered i=1, 2, . . . , and measuring the pseudoranges ρ
i from satellite number i to a selected user location;
representing the pseudorange ρ
i at a selected measurement time t=tk as a sum
space="preserve" listing-type="equation">ρ
.sub.i (t.sub.k)=r.sub.i +b+e.sub.i,
space="preserve" listing-type="equation">r.sub.i =r.sub.i (t.sub.k)={(x.sub.i (t.sub.k)-x(t.sub.k)).sup.2 +(y.sub.i (t.sub.k)-y(t.sub.k)).sup.2 +(z.sub.i (t.sub.k)-z(t.sub.k)).sup.2 }.sup.1/2,where (xi,yi,zi) are the known, time varying location coordinates of the ith satellite in a selected first coordinate system, (x,y,z) are the true location coordinates of the user, to be determined, in the selected first coordinate system, b is an unknown user clock bias, and ei represents other unknown measurement errors for satellite i, at the measurement time t=tk ;
providing a nominal location solution set (xn,yn,zn) of known location coordinates in the selected first coordinate system that provide a nominal estimate of location solutions for the pseudorange equations for the three satellites, and defining
space="preserve" listing-type="equation">r.sub.i,n (t.sub.k)={(x.sub.i (t.sub.k)-x.sub.n).sup.2 +(y.sub.i (t.sub.k)-y.sub.n).sup.2 +(z.sub.i (t.sub.k)-z.sub.n).sup.2 }.sup.1/2,
space="preserve" listing-type="equation">ρ
.sub.i,n (t.sub.k)=r.sub.i,n (t.sub.k)+e.sub.i '"'"' (i=1,2,3)where ei '"'"' is an estimate of the variable ei ;
computing pseudorange increments δ
ρ
i,n =ρ
i -ρ
i,n, for the three satellites numbered i=1, 2, 3;
selecting a triple of location coordinates (x4, y4, z4)=(0,0,0) for a fictitious fourth satellite, numbered i=4, in the selected first coordinate system, where the distance from the fourth satellite location to the nominal solution location (xn,yn,zn) is
space="preserve" listing-type="equation">r.sub.4,n =r.sub.n ={(x.sub.n).sup.2 +(y.sub.n).sup.2 +(z.sub.n).sup.2 }.sup.1/2 ;
providing a selected mean sea level surface Sms1 that represents the average mean sea level of the Earth;
providing a selected ellipsoidal surface Sell that approximates the surface of the Earth;
representing the scalar length
space="preserve" listing-type="equation">r={(x'"'"'.sup.2 +y'"'"'.sup.2 +z'"'"'.sup.2 }.sup.1/2of a vector r extending from the fourth satellite location to a location with coordinates (x'"'"',y'"'"',z'"'"'), where an extension of the vector r intersects the surface Sell and thereby defines a vector rell (x'"'"',y'"'"',z'"'"') from the fourth satellite to this intersection point, as a sum of the length rs (x'"'"',y'"'"',z'"'"') of the vector rell plus the signed altitude Aell of the user with respect to the selected ellipsoidal surface,
space="preserve" listing-type="equation">r=r.sub.s +A.sub.ell ;
providing an altitude sensor having an altimeter reading zalt (t) as an estimate of an elevation coordinate Ams1 (t) of the user above the mean sea level surface at a selected time t, where zalt (t) is a sum of terms including the elevation coordinate Ams1 (t), plus a bias term B(t) arising from altitude sensor measurement error, plus a sensor noise error term Q(t) that has approximately zero mean;
providing a reference elevation coordinate zref (t) as a sum including the elevation coordinate Ams1 (t) plus an error term G(t) that has approximately zero mean in the reference elevation coordinate at a selected calibration time t=tcal, where zref (tcal) is determined using at least one of (i) the altitude Ams1 obtained from a GPS location solution, computed using at least four satellites with no altitude constraints at one or more selected times t=tcal, and (ii) an independently determined, accurate value of Ams1 (tcal);
computing an estimated altitude Aest (t) of the elevation coordinate Ams1 (t), from which the sensor bias has been removed, for a selected interval of times t>
tcal as a difference Aest (t)=zalt (t)-C(tcal), where C(tcal)=zalt (tcal)-zref (tcal);
providing a selected second coordinate system that is expressed in latitude, longitude and altitude coordinates, (lat,lon,alt), where the altitude coordinate is Aell ;
determining the latitude, longitude and altitude coordinates (latn, lonn, altn) that correspond to the nominal solution location coordinate values (xn,yn,zn) in the selected second coordinate system;
determining a signed distance Δ
MSL(latn,lonn)=Ams1 -Aell of the selected ellipsoidal surface above the mean sea level surface at a location whose latitude and longitude coordinates in the selected second coordinate system are (latn, lonn), from a look-up table that provides the signed difference between the height of the selected ellipsoid surface and the mean sea level surface at a location with latitude and longitude coordinates (lat,lon) and arbitrary altitude in the selected second coordinate system for a location with selected location coordinates in the selected first coordinate system;
expressing the length rs (xn,yn,zn) of the vector rell (xn,yn,zn) as a sum ##EQU11## calculating a distance r4 from the fourth satellite to a location at the altitude Aest by the relationr4 =rs (xn,yn,zn)+(Aest -Δ
MSL(xn,yn,zn)), using the estimated altitude Aest, and forming a difference
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Abstract
Methods for GPS-assisted determination of location coordinates of a mobile user or selected position on or adjacent to the Earth'"'"'s surface with improved accuracy. Elevation readings from an altimeter or barometer are integrated with readings of the GPS-determined elevation coordinate for that location, using Kalman filter techniques, minimum least square techniques, or comparison of certain statistically defined parameters associated with the altimeter and GPS variables, such as the standard deviation of the expected errors in these variables. The resulting elevation coordinate may be a statistical blend or filtered blend of the altimeter value and a GPS-determined value for the elevation coordinate; or this resulting elevation coordinate can be chosen to be one or the other of these values, based upon comparison of time varying statistical parameters corresponding to the altimeter and the GPS.
179 Citations
25 Claims
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1. A method for determination of location coordinates of a selected three-dimensional location of a user on or adjacent to the Earth'"'"'s surface, the method comprising the steps of:
-
receiving Global Positioning System (GPS) signals from at least three GPS satellites, numbered i=1, 2, . . . , and measuring the pseudoranges ρ
i from satellite number i to a selected user location;representing the pseudorange ρ
i at a selected measurement time t=tk as a sum
space="preserve" listing-type="equation">ρ
.sub.i (t.sub.k)=r.sub.i +b+e.sub.i,
space="preserve" listing-type="equation">r.sub.i =r.sub.i (t.sub.k)={(x.sub.i (t.sub.k)-x(t.sub.k)).sup.2 +(y.sub.i (t.sub.k)-y(t.sub.k)).sup.2 +(z.sub.i (t.sub.k)-z(t.sub.k)).sup.2 }.sup.1/2,where (xi,yi,zi) are the known, time varying location coordinates of the ith satellite in a selected first coordinate system, (x,y,z) are the true location coordinates of the user, to be determined, in the selected first coordinate system, b is an unknown user clock bias, and ei represents other unknown measurement errors for satellite i, at the measurement time t=tk ; providing a nominal location solution set (xn,yn,zn) of known location coordinates in the selected first coordinate system that provide a nominal estimate of location solutions for the pseudorange equations for the three satellites, and defining
space="preserve" listing-type="equation">r.sub.i,n (t.sub.k)={(x.sub.i (t.sub.k)-x.sub.n).sup.2 +(y.sub.i (t.sub.k)-y.sub.n).sup.2 +(z.sub.i (t.sub.k)-z.sub.n).sup.2 }.sup.1/2,
space="preserve" listing-type="equation">ρ
.sub.i,n (t.sub.k)=r.sub.i,n (t.sub.k)+e.sub.i '"'"' (i=1,2,3)where ei '"'"' is an estimate of the variable ei ; computing pseudorange increments δ
ρ
i,n =ρ
i -ρ
i,n, for the three satellites numbered i=1, 2, 3;selecting a triple of location coordinates (x4, y4, z4)=(0,0,0) for a fictitious fourth satellite, numbered i=4, in the selected first coordinate system, where the distance from the fourth satellite location to the nominal solution location (xn,yn,zn) is
space="preserve" listing-type="equation">r.sub.4,n =r.sub.n ={(x.sub.n).sup.2 +(y.sub.n).sup.2 +(z.sub.n).sup.2 }.sup.1/2 ;providing a selected mean sea level surface Sms1 that represents the average mean sea level of the Earth; providing a selected ellipsoidal surface Sell that approximates the surface of the Earth; representing the scalar length
space="preserve" listing-type="equation">r={(x'"'"'.sup.2 +y'"'"'.sup.2 +z'"'"'.sup.2 }.sup.1/2of a vector r extending from the fourth satellite location to a location with coordinates (x'"'"',y'"'"',z'"'"'), where an extension of the vector r intersects the surface Sell and thereby defines a vector rell (x'"'"',y'"'"',z'"'"') from the fourth satellite to this intersection point, as a sum of the length rs (x'"'"',y'"'"',z'"'"') of the vector rell plus the signed altitude Aell of the user with respect to the selected ellipsoidal surface,
space="preserve" listing-type="equation">r=r.sub.s +A.sub.ell ;providing an altitude sensor having an altimeter reading zalt (t) as an estimate of an elevation coordinate Ams1 (t) of the user above the mean sea level surface at a selected time t, where zalt (t) is a sum of terms including the elevation coordinate Ams1 (t), plus a bias term B(t) arising from altitude sensor measurement error, plus a sensor noise error term Q(t) that has approximately zero mean; providing a reference elevation coordinate zref (t) as a sum including the elevation coordinate Ams1 (t) plus an error term G(t) that has approximately zero mean in the reference elevation coordinate at a selected calibration time t=tcal, where zref (tcal) is determined using at least one of (i) the altitude Ams1 obtained from a GPS location solution, computed using at least four satellites with no altitude constraints at one or more selected times t=tcal, and (ii) an independently determined, accurate value of Ams1 (tcal); computing an estimated altitude Aest (t) of the elevation coordinate Ams1 (t), from which the sensor bias has been removed, for a selected interval of times t>
tcal as a difference Aest (t)=zalt (t)-C(tcal), where C(tcal)=zalt (tcal)-zref (tcal);providing a selected second coordinate system that is expressed in latitude, longitude and altitude coordinates, (lat,lon,alt), where the altitude coordinate is Aell ; determining the latitude, longitude and altitude coordinates (latn, lonn, altn) that correspond to the nominal solution location coordinate values (xn,yn,zn) in the selected second coordinate system; determining a signed distance Δ
MSL(latn,lonn)=Ams1 -Aell of the selected ellipsoidal surface above the mean sea level surface at a location whose latitude and longitude coordinates in the selected second coordinate system are (latn, lonn), from a look-up table that provides the signed difference between the height of the selected ellipsoid surface and the mean sea level surface at a location with latitude and longitude coordinates (lat,lon) and arbitrary altitude in the selected second coordinate system for a location with selected location coordinates in the selected first coordinate system;expressing the length rs (xn,yn,zn) of the vector rell (xn,yn,zn) as a sum ##EQU11## calculating a distance r4 from the fourth satellite to a location at the altitude Aest by the relation r4 =rs (xn,yn,zn)+(Aest -Δ
MSL(xn,yn,zn)), using the estimated altitude Aest, and forming a difference - View Dependent Claims (3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 16, 17, 19)
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2. δ
- ρ
4. n =r4 -r4,n ;forming a 4×
4 matrix H having entries Hik (i=1, 2, 3, 4;
k=1, 2, 3,
4) defined by Hi1 =(xn -xi)/ri,n, Hi2 =(yn -yi)/ri,n, Hi3 =(zn -zi)/ri,n for i=1, 2, 3, H41 =(xn)/r4,n, H42 =(yn)/r4,n, H43 =(zn)/r4,n, H14 =H24 =H34 =1, and H44 =0, and computing an inverse matrix H-1 =G with entries Gik ;computing estimated location coordinate values (xp,yp,zp) for the unknown location coordinates (x,y,z), defined by ##EQU12## using the estimated location coordinate values (xp,yp,zp) to determine and display, by visually perceptible means or audibly perceptible means, an estimated present location of the user.
- ρ
-
8. A method for determination of location coordinates of a selected three-dimensional location of a user on or adjacent to the Earth'"'"'s surface, the method comprising the steps of:
-
receiving Global Positioning System (GPS) signals from at least three GPS satellites, numbered i=1, 2, 3, . . . , N-1 (N-1≧
3) and measuring the pseudoranges ρ
i from satellite number i to a selected user location;representing the pseudorange ρ
i at a selected measurement time t=tk as a sum
space="preserve" listing-type="equation">ρ
.sub.i (t.sub.k)=r.sub.i +b+e.sub.i,
space="preserve" listing-type="equation">r.sub.i =r.sub.i (t.sub.k)={(x.sub.i (t.sub.k)-x(t.sub.k)).sup.2 +(y.sub.i (t.sub.k)-y(t.sub.k)).sup.2 +(z.sub.i (t.sub.k)-z(t.sub.k)).sup.2 }.sup.1/2,where (xi,yi,zi) are the known, time varying location coordinates of the ith satellite in a selected first coordinate system, (x,y,z) are the true location coordinates of the user, to be determined, in the selected first coordinate system, b is an unknown user clock bias, and ei represents other unknown measurement errors for satellite i, at the measurement time t=tk ; providing a nominal location solution set (xn,yn,zn) of known location coordinates in the selected first coordinate system that provide a nominal estimate of location solutions for the pseudorange equations for the three satellites, and defining
space="preserve" listing-type="equation">r.sub.i,n (t.sub.k)={(x.sub.i (t.sub.k)-x.sub.n).sup.2 +(y.sub.i (t.sub.k)-y.sub.n).sup.2 +(z.sub.i (t.sub.k)-z.sub.n).sup.2 }.sup.1/2,
space="preserve" listing-type="equation">ρ
.sub.i,n (t.sub.k)=r.sub.i,n (t.sub.k)+e.sub.i '"'"' (i =1,2,3, . . . , N-1),where ei '"'"' is an estimate of the variable ei ; computing pseudorange increments δ
ρ
i,n =ρ
i -ρ
i,n, for the N-1 satellites numbered i=1, 2, . . . , N-1;selecting a triple of location coordinates (xN,yN,zN)=(0,0,0) for a fictitious Nth satellite, numbered i=N, in the selected first coordinate system, where the distance from the fourth satellite location to the nominal solution location (xn,yn,zn) is
space="preserve" listing-type="equation">r.sub.N,n =r.sub.n ={(x.sub.n).sup.2 +(y.sub.n).sup.2 +(z.sub.n).sup.2 }.sup.1/2 ;providing a selected mean sea level surface Sms1 that represents the average mean sea level of the Earth; providing a selected ellipsoid surface Sell that approximates the surface of the Earth; representing the scalar length
space="preserve" listing-type="equation">r={x'"'"'.sup.2 +y'"'"'.sup.2 +z'"'"'.sup.2 }.sup.1/2of a vector r extending from the fourth satellite location to a location with coordinates (x'"'"',y'"'"',z'"'"'), where an extension of the vector r intersects the surface Sell and thereby defines a vector rell (x'"'"',y'"'"',z'"'"') from the fourth satellite to this intersection point, as a sum of the length rs (x'"'"',y'"'"',z'"'"') of the vector rell plus the signed altitude Aell of the user with respect to the selected ellipsoidal surface,
space="preserve" listing-type="equation">r=r.sub.s +A.sub.ell ;providing an altitude sensor having an altimeter reading zalt (t) as an estimate of an elevation coordinate Ams1 (t) of the user above the mean sea level surface at a selected time t, where zalt (t) is a sum of terms including the elevation coordinate Ams1 (t.sub.), plus a bias term B(t) arising from altitude sensor measurement error, plus a sensor noise error term Q(t) that has approximately zero mean; providing a reference elevation coordinate zref (t) as a sum including the elevation coordinate Ams1 (t) plus an error term G(t) that has approximately zero mean in the reference elevation coordinate at a selected calibration time t=tcal, where zref (tcal) is determined using at least one of (i) the altitude Ams1 obtained from a GPS location solution, computed using at least four satellites with no altitude constraints at one or more selected times t=tcal, and (ii) an independently determined, accurate value of Ams1 (tcal); computing an estimated altitude Aest (t) of the elevation coordinate Ams1 (t), from which the sensor bias has been removed, for a selected interval of times t>
tcal as a difference Aest (t)=zalt (t)-C(tcal), where C(tcal)=zalt (tcal)-zref (tcal);providing a selected second coordinate system that is expressed in latitude, longitude and altitude coordinates, (lat,lon,alt), where the altitude coordinate is Aell ; determining the latitude, longitude and altitude coordinates (latn, lonn, altn) that correspond to the nominal solution location coordinate values (xn,yn,zn) in the selected second coordinate system; determining a signed distance Δ
MSL(latn,lonn)=Ams1 -Aell of the selected ellipsoidal surface above the mean sea level surface at a location whose latitude and longitude coordinates in the selected second coordinate system are (latn, lonn), from a look-up table that provides the signed difference between the height of the selected ellipsoid surface and the mean sea level surface at a location with latitude and longitude coordinates (lat,lon) and arbitrary altitude in the selected second coordinate system for a location with selected location coordinates in the selected first coordinate system;expressing the length rs (xn,yn,zn) of the vector rell (xn,yn,zn) as a sum ##EQU13## calculating a distance rN from the Nth satellite to a location at the altitude Aest by the relation
space="preserve" listing-type="equation">r.sub.N =r.sub.s (x.sub.n,y.sub.n,z.sub.n)+(A.sub.est -Δ
MSL(x.sub.n,y.sub.n,z.sub.n)),using the estimated altitude Aest, and forming a difference
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-
9. δ
- ρ
4. n =rN -rN,n ;forming an N×
4 matrix H having entries Hik (i=1, 2, 3, . . . , N;
k=1, 2, 3,
4) defined by Hi1 =(xn -xi)/ri,n, Hi2 =(yn -yi)/ri,n, Hi3 =(zn -zi)/ri,n for i=1, 2, 3, . . . N-1, HN1 =(xn)/rN,n, HN2 =(yn)/rN,n, HN3 =(zn)/rN,n, HN4 =0, H14 =H24 =H34 = . . . =HN-1,4 =1, and computing a 4×
N matrix (Htr H)-1 Htr =G with entries Gik ;computing estimated location coordinate values (xp,yp,zp) for the unknown location coordinates (x,y,z), defined by ##EQU14## using the estimated location coordinate values (xp,yp,zp) to determine and display, by visually perceptible means or audibly perceptible means, an estimated present location of the user.
- ρ
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15. A method for determination of location coordinates of a selected position on or adjacent to the Earth'"'"'s surface with improved accuracy, the method comprising the steps of:
-
using a Global Positioning System (GPS) to determine the location coordinates (xgps, ygps, zgps) of a selected location on or adjacent the Earth'"'"'s surface, for GPS signals received from a group of GPS satellites numbered i=1, 2, . . . , N (N≧
3), where the coordinate zgps =zgps (t) is an estimate of the true elevation or vertical coordinate A(t) of the selected location relative to a fixed vertical location at a selected time t;providing an altimeter reading zalt (t) that is an estimate of the elevation coordinate A(t) of the selected location relative to the fixed vertical location at a selected time t; computing statistically determined estimates σ
gps (t) and σ
alt (t) of the standard deviations of the variables zgps (t) and zalt (t), respectively, for at least one selected time t;defining an estimate Aest (t) of the elevation coordinate A(t) of the selected position to be equal to zgps (t) if the standard deviations σ
gps (t) and σ
alt (t) satisfy a selected first criterion, and defining Aest (t) to be equal to zalt (t) if the standard deviations σ
gps (t) and σ
alt (t) satisfy a selected second criterion, and defining Aest (t) to be equal to a value that lies between the value zgps (t) and the value zalt (t) if the standard deviations σ
gps (t) and σ
alt (t) satisfy neither the first criterion nor the second criterion, where the first criterion is σ
gps (t)<
σ
alt (t)+Δ
z1, and the second criterion is σ
gps (t)>
σ
alt (t)+Δ
z2, where Δ
z1 and Δ
z2 are selected real numbers that may be positive, negative or zero, with Δ
z1 ≦
Δ
z2 ; andcalibrating the altimeter reading aalt against an accurate value for zalt at least once at a selected time t=tcal subsequent to a time at which an altimeter reading is initially taken.
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18. A method for determination of location coordinates of a selected position on or adjacent to the Earth'"'"'s surface with improved accuracy, the method comprising the steps of:
-
using a Global Positioning System (GPS) to determine the location coordinates (xgps, ygps, zgps) of a selected location on or adjacent to the Earth'"'"'s surface, where the coordinate zgps =zgps (t) represents the true elevation or vertical coordinate A(t) of the selected location relative to a fixed elevation at a selected time t; providing an altimeter having an altimeter reading zalt (t) that is an estimate of the elevation coordinate A(t) of the selected location at a selected time t; computing a statistically determined estimate σ
gps (t) of the standard deviation of the variable zgps (t) for at least one selected time by the following steps;computing the vertical dilution of precision VDOP(t) and the satellite pseudorange ρ
i (t) for each satellite number i in the satellite configuration used to determine the GPS location coordinates (xgps, ygps, zgps);forming the product maxi [VDOP(t).ρ
i (t)]=ε
V (t) representing a statistical error variable for the pseudorange variables; anddefining said standard deviation σ
gps (t) to be the standard deviation σ
.sub.ε
V (t) for the error variable ε
V (t);computing a statistically determined estimate σ
alt (t) of the standard deviations of the variable zalt (t) for the selected time t; andestimating the elevation coordinate A(t) of the selected location by an estimated value Aest given by
space="preserve" listing-type="equation">A.sub.est (t)=w(t)z.sub.gps (t)+(1-w(t))z.sub.gps (t),where w(t) is a weight function that tends monotonically toward the value 1 over a selected time interval, if the standard deviations σ
gps (t) and σ
alt (t) associated with the variables zgps (t) and zalt (t) satisfy a selected first criterion, and that tends monotonically toward the value 0 if the standard deviations σ
gps (t) and σ
alt (t) satisfy a selected second criterion. - View Dependent Claims (21)
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20. A method for determination of location coordinates of a selected position on or adjacent to the Earth'"'"'s surface with improved accuracy, the method comprising the steps of:
-
using a Global Positioning System (GPS) to determine the location coordinates (xgps, ygps, zgps) of a selected location on or adjacent the Earth'"'"'s surface, for GPS signals received from a group of GPS satellites numbered i=1, 2, . . . , N (N≧
3), where the coordinate zgps =zgps (t) is an estimate of the true elevation or vertical coordinate A(t) of the selected location relative to a fixed vertical location at a selected time t;providing an altimeter reading zalt (t) that is an estimate of the elevation coordinate A(t) of the selected location relative to the fixed vertical location at a selected time t; computing a statistically determined estimate σ
gps (t) of the standard deviation of the variable zgps (t) for at least one selected time by the following steps;computing the vertical dilution of precision VDOP(t) and the satellite pseudorange ρ
i (t) for each satellite number i in the satellite configuration used to determine the GPS location coordinates (xgps, ygps, zgps);forming the product maxi [VDOP(t).ρ
i (t)]=ε
V (t) representing a statistical error variable for the pseudorange variables; anddefining said standard deviation σ
gps (t) to be the standard deviation σ
.sub.ε
V (t) for the error variable ε
V (t);computing a statistically determined estimate σ
alt (t) of the standard deviations of the variable zalt (t) for the selected time t; andinterpreting an estimate Aest (t) of the elevation coordinate A(t) of the selected position to be equal to zgps (t) if the standard deviations σ
gps (t) and σ
alt (t) satisfy a selected first criterion, and defining Aest (t) to be equal to zalt (t) if the standard deviations σ
gps (t) and σ
alt (t) satisfy a selected second criterion. - View Dependent Claims (23, 24)
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22. A method for determination of location coordinates of a selected position on or adjacent to the Earth'"'"'s surface with improved accuracy, the method comprising the steps of:
-
using a Global Positioning System (GPS) to determine the location coordinates (xgps, ygps, zgps) of a selected location on or adjacent to the Earth'"'"'s surface, where the coordinate zgps =zgps (t) represents the true elevation or vertical coordinate A(t) of the selected location relative to a fixed elevation at a selected time t; providing an altimeter having an altimeter reading zalt (t) that is an estimate of the elevation coordinate A(t) of the selected location at a selected time t; computing statistically determined standard deviations σ
gps (t) and σ
alt (t) of the variables zgps (t) and zalt (t), respectively, for at least one selected time t;estimating the elevation coordinate A(t) of the selected location by an estimated value Aest given by
space="preserve" listing-type="equation">A.sub.est (t)=w(t)z.sub.gps (t)+(1-w(t))z.sub.gps (t),where w(t) is a weight function that tends monotonically toward the value 1 over a selected time interval, if the standard deviations σ
gps (t) and σ
alt (t) associated with the variables zgps (t) and zalt (t) satisfy a selected first criterion, and that tends monotonically toward the value 0 if the standard deviations σ
gps (t) and σ
alt (t) satisfy a selected second criterion, where the first criterion is σ
gps (t)<
σ
alt (t)+Δ
z1, and the second criterion is σ
gps (t)>
σ
alt (t)+Δ
z2, where Δ
z1 and Δ
z2 are selected real numbers that may be positive, negative or zero, with Δ
z1 <
Δ
z2 ; andcalibrating the altimeter reading zalt against an accurate value for zalt at least once at a selected time t=tcal subsequent to a time at which an altimeter reading is initially taken.
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25. A method for determination of location coordinates of a selected position on or adjacent to the Earth'"'"'s surface with improved accuracy, the method comprising the steps of:
-
using a Global Positioning System (GPS) to determine the location coordinates (xgps, ygps, zgps) of a selected location on or adjacent the Earth'"'"'s surface, for GPS signals received from a group of GPS satellites numbered i=1, 2, . . . , N (N≧
3), where the coordinate zgps =zgps (t) is an estimate of the true elevation or vertical coordinate A(t) of the selected location relative to a fixed vertical location at a selected time t;providing an altimeter having an altimeter reading zalt (t) that is an estimate of the elevation coordinate A(t) of the selected location relative to the fixed vertical location at a selected time t; computing statistically determined estimates σ
gps (t) and σ
alt (t) of the standard deviations of the variables zgps (t) and zalt (t), respectively, for at least one selected time t; anddefining the elevation coordinate A(t) of the selected location to be a linear combination of the values zgps (t) and zalt (t), defined by
space="preserve" listing-type="equation">z(t)=K.sub.1 z.sub.gps (t)+K.sub.2 z.sub.alt (t),
space="preserve" listing-type="equation">K.sub.1 =c.sub.1 (σ
.sub.gps (t)).sup.p /[c.sub.1 (σ
.sub.gps (t)).sup.p +c.sub.2 (σ
.sub.alt (t)).sup.q ],
space="preserve" listing-type="equation">K.sub.2 =c.sub.2 (σ
.sub.alt (t)).sup.q /[c.sub.1 (σ
.sub.gps (t)).sup.p +c.sub.2 (σ
.sub.alt (t)).sup.q ]=1-K.sub.1,where C1, C2, p and q are selected positive constants.
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Specification