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Use of an altitude sensor to augment availability of GPS location fixes

  • US 5,646,857 A
  • Filed: 03/31/1995
  • Issued: 07/08/1997
  • Est. Priority Date: 03/31/1995
  • Status: Expired due to Fees
First Claim
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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

    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

    MSL(xn,yn,zn)), using the estimated altitude Aest, and forming a difference

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