Obtenir ECEF XYZ étant donné les coordonnées de départ, la distance, l'azimut et l'altitude

Question

Je n'arrive pas à trouver quoi que ce soit sur la conversion de RAE en XYZ. Si je suis sur un ellipsoïde WGS84, à la position -742507, -5462738, 3196706 et que je détecte un objet à une distance de 30 km, un azimut de 310 et un angle d'élévation de 18 degrés, comment puis-je le convertir en ECEF? Coordonnées XYZ?

Merci.

Answer 1

Il semble qu'il n'y ait pas de processus simple pour ce faire. La meilleure méthode que j'ai trouvée est de convertir des coordonnées RAE en coordonnées SEZ, puis des coordonnées SEZ aux coordonnées ECR. Voici un code C# I modifié à C++ pour y parvenir:

void main() { 
    // NOTE: distances are in meters, while angles are in degrees 
    double siteECR[] = { -763997.48, -5458565.87, 3196706.0 }; 
    double objRAE[] = { 30000.0, 310.0, 18.0 }; 
    double objECR[] = { 0.0, 0.0, 0.0 }; 

    // Should return ~[-764142.7629, -5458517.683, 3217218.18] in objECR 
    RAEtoECR(siteECR, objRAE, objECR); 
} 

/************************************************************************************************************************/ 
/* Converts a Range, Azimuth, Elevation location to a Latitude, Longitude, Altitude location   */ 
/* siteLLA - array holding the Latitude, Longitude, and Altitude of the site location in degrees and meters  */ 
/* rae  - array holding the Range, Azimuth, and Elevation, in degrees, of the object viewed from the site location */ 
/* objECR - destination array to hold the ECR X, Y, Z location in meters    */ 
/************************************************************************************************************************/ 
void RAEtoECR(double siteECR[], double rae[], double objECR[]) { 
    double tempSEZ[] = { 0.0, 0.0, 0.0 }; 
    double siteLLA[] = { 0.0, 0.0, 0.0 }; 

    ECRtoLLA(siteECR, siteLLA); 
    RAEtoSEZ(siteLLA, objRAE, tempSEZ); 
    SEZtoECR(siteLLA, tempSEZ, objECR); 
} 

/************************************************************************************************************************/ 
/* Converts a Range, Azimuth, Elevation location to a South, East, Zenith location   */ 
/* siteLLA - array holding the Latitude, Longitude, and Altitude of the site location in degrees and meters */ 
/* rae  - array holding the Range, Azimuth, and Elevation, in degrees, of the object viewed from the site location */ 
/* sez  - destination array to hold the South, East, and Zenith coordinates of the object being viewed in meters */ 
/************************************************************************************************************************/ 
void RAEtoSEZ(double siteLLA[], double rae[], double sez[]) { 
    double range, azimuth, elevation; 
    range = rae[0]; 
    azimuth = rae[1]; 
    elevation = rae[2]; 

    // Compute needed math 
    double slat = sin(Deg2Rad(siteLLA[0])); 
    double slon = sin(Deg2Rad(siteLLA[1])); 
    double clat = cos(Deg2Rad(siteLLA[0])); 
    double clon = cos(Deg2Rad(siteLLA[1])); 

    // Convert to radians 
    azimuth = DEG2RAD(azimuth); 
    elevation = DEG2RAD(elevation); 

    // Convert 
    sez[0] = -range * cos(elevation) * cos(azimuth); 
    sez[1] = range * cos(elevation) * sin(azimuth); 
    sez[2] = range * sin(elevation); 
} 

/************************************************************************************************************************/ 
/* Converts a South, East, Zenith location to an ECR X, Y, Z location    */ 
/* siteLLA - array holding the Latitude, Longitude, and Altitude of the site location in degrees and meters  */ 
/* sez  - array holding the South, East, and Zenith coordinates of the object being viewed in meters  */ 
/* ecr  - destination array to hold the ECR X, Y, Z location in meters    */ 
/************************************************************************************************************************/ 
void SEZtoECR(double siteLLA[], double sez[], double ecr[]) { 
    // Convert siteLLA to XYZ 
    double[] siteXYZ = { 0.0, 0.0, 0.0 }; 
    LLAtoECR(siteLLA, siteXYZ); 

    double south, east, zenith; 
    south = sez[0]; 
    east = sez[1]; 
    zenith = sez[2]; 

    // Compute needed math 
    double slat = sin(Deg2Rad(siteLLA[0])); 
    double slon = sin(Deg2Rad(siteLLA[1])); 
    double clat = cos(Deg2Rad(siteLLA[0])); 
    double clon = cos(Deg2Rad(siteLLA[1])); 

    // Convert 
    ecr[0] = (slat * clon * south) + (-slon * east) + (clat * clon * zenith) + siteXYZ[0]; 
    ecr[1] = (slat * slon * south) + (clon * east) + (clat * slon * zenith) + siteXYZ[1]; 
    ecr[2] = (-clat *  south) + (slat * zenith) + siteXYZ[2]; 
} 

Answer 2

Vous pouvez utiliser les fonctions Matlab sph2cart.m

Ou

http://computitos.files.wordpress.com/2008/03/cartesian_spherical_transformation.pdf

Assurez-vous que votre l'0degree dans votre projet est le même que math 0degree.

• navy utilise 0 degré nord.

Answer 3

La réponse de lumberjack est superbe. Ici, il est en javascript au cas où quelqu'un en a besoin:

main(); 

function main() { 
    // NOTE: distances are in meters, while angles are in degrees 

    var siteECR = { 
     X: -763997.48, 
     Y: -5458565.87, 
     Z: 3196706.0 
    }; 

    var siteLLA = { 
     Latitude: 30.28011211999193, 
     Longitude: -97.96753350982041, 
     Altitude: -1033.8619585652073 
    }; 

    var objRAE = { 
     Range: 30000.0, 
     Azimuth: 310.0, 
     Elevation: 18.0 
    } 

    var objECR = { X: 0, Y: 0, Z: 0 } 

    // Should return ~[-764142.7629, -5458517.683, 3217218.18] in objECR 
    RAEtoECR(siteECR, siteLLA, objRAE, objECR); 

    console.log(objECR); 
} 

/************************************************************************************************************************/ 
/* Converts a Range, Azimuth, Elevation location to a Latitude, Longitude, Altitude location   */ 
/* siteLLA - array holding the Latitude, Longitude, and Altitude of the site location in degrees and meters  */ 
/* rae  - array holding the Range, Azimuth, and Elevation, in degrees, of the object viewed from the site location */ 
/* objECR - destination array to hold the ECR X, Y, Z location in meters    */ 
/************************************************************************************************************************/ 
function RAEtoECR(siteECR, siteLLA, rae, objECR) { 
    var tempSEZ = { South: 0, East: 0, Zenith: 0 }; 

    //ECRtoLLA(siteECR, siteLLA); 
    RAEtoSEZ(siteLLA, rae, tempSEZ); 
    SEZtoECR(siteECR, siteLLA, tempSEZ, objECR); 
} 

function toRadians(angle) { 
    return angle * (Math.PI/180); 
} 

/************************************************************************************************************************/ 
/* Converts a Range, Azimuth, Elevation location to a South, East, Zenith location   */ 
/* siteLLA - array holding the Latitude, Longitude, and Altitude of the site location in degrees and meters */ 
/* rae  - array holding the Range, Azimuth, and Elevation, in degrees, of the object viewed from the site location */ 
/* sez  - destination array to hold the South, East, and Zenith coordinates of the object being viewed in meters */ 
/************************************************************************************************************************/ 
function RAEtoSEZ(siteLLA, rae, sez) { 
    var range = rae.Range; 
    var azimuth = rae.Azimuth; 
    var elevation = rae.Elevation; 

    // Compute needed math 
    var slat = Math.sin(toRadians(siteLLA.Latitude)); 
    var slon = Math.sin(toRadians(siteLLA.Longitude)); 
    var clat = Math.cos(toRadians(siteLLA.Latitude)); 
    var clon = Math.cos(toRadians(siteLLA.Longitude)); 

    // Convert to radians 
    azimuth = toRadians(azimuth); 
    elevation = toRadians(elevation); 

    // Convert 
    sez.South = -range * Math.cos(elevation) * Math.cos(azimuth); 
    sez.East = range * Math.cos(elevation) * Math.sin(azimuth); 
    sez.Zenith = range * Math.sin(elevation); 
} 

/************************************************************************************************************************/ 
/* Converts a South, East, Zenith location to an ECR X, Y, Z location    */ 
/* siteLLA - array holding the Latitude, Longitude, and Altitude of the site location in degrees and meters  */ 
/* sez  - array holding the South, East, and Zenith coordinates of the object being viewed in meters  */ 
/* ecr  - destination array to hold the ECR X, Y, Z location in meters    */ 
/************************************************************************************************************************/ 
function SEZtoECR(siteXYZ, siteLLA, sez, ecr) { 

    var south = sez.South; 
    var east = sez.East; 
    var zenith = sez.Zenith; 

    // Compute needed math 
    var slat = Math.sin(toRadians(siteLLA.Latitude)); 
    var slon = Math.sin(toRadians(siteLLA.Longitude)); 
    var clat = Math.cos(toRadians(siteLLA.Latitude)); 
    var clon = Math.cos(toRadians(siteLLA.Longitude)); 

    // Convert 
    ecr.X = (slat * clon * south) + (-slon * east) + (clat * clon * zenith) + siteXYZ.X; 
    ecr.Y = (slat * slon * south) + (clon * east) + (clat * slon * zenith) + siteXYZ.Y; 
    ecr.Z = (-clat *  south) + (slat * zenith) + siteXYZ.Z; 
}