高度を持つ2つのGPS座標の間の垂直方向の関係を計算する

Question

アンテナトラッカーを構築する予定です。私は、GPSのA地点から標高とGPS地点Bから高度を取得し、傾斜を取得する必要があります。

これは、例えばポイントです：

latA = 39.099912 
lonA = -94.581213 
altA = 273.543 
latB = 38.627089 
lonB = -90.200203 
altB = 1380.245 

私はすでに水平ベアリング式を持っているし、それは私に97.89138167122422

を与えます。これは、コードです：

function toRadian(num) { 
    return num * (Math.PI/180); 
} 

function toDegree(num) { 
    return num * (180/Math.PI); 
} 

function getHorizontalBearing(fromLat, fromLon, toLat, toLon) { 
    fromLat = toRadian(fromLat); 
    fromLon = toRadian(fromLon); 
    toLat = toRadian(toLat); 
    toLon = toRadian(toLon); 

    let dLon = toLon - fromLon; 
    let x = Math.tan(toLat/2 + Math.PI/4); 
    let y = Math.tan(fromLat/2 + Math.PI/4); 
    let dPhi = Math.log(x/y); 
    if (Math.abs(dLon) > Math.PI) { 
     if (dLon > 0.0) { 
      dLon = -(2 * Math.PI - dLon); 
     } else { 
      dLon = (2 * Math.PI + dLon); 
     } 
    } 

    return (toDegree(Math.atan2(dLon, dPhi)) + 360) % 360; 
} 

let n = getHorizontalBearing(39.099912, -94.581213, 38.627089, -90.200203); 
console.info(n); 

しかし、私傾斜角を見つける方法を知らない。誰でも私を助けることができますか？

Answer 1

私は周りを検索した後に答えを得たと思います。

これは完全なコードです。これが間違っていると思われる場合は、私を修正してください。

function toRadian(num) { 
    return num * (Math.PI/180); 
} 

function toDegree(num) { 
    return num * (180/Math.PI); 
} 

// North is 0 degree, South is 180 degree 
function getHorizontalBearing(fromLat, fromLon, toLat, toLon, currentBearing) { 
    fromLat = toRadian(fromLat); 
    fromLon = toRadian(fromLon); 
    toLat = toRadian(toLat); 
    toLon = toRadian(toLon); 

    let dLon = toLon - fromLon; 
    let x = Math.tan(toLat/2 + Math.PI/4); 
    let y = Math.tan(fromLat/2 + Math.PI/4); 
    let dPhi = Math.log(x/y); 
    if (Math.abs(dLon) > Math.PI) { 
     if (dLon > 0.0) { 
      dLon = -(2 * Math.PI - dLon); 
     } else { 
      dLon = (2 * Math.PI + dLon); 
     } 
    } 

    let targetBearing = (toDegree(Math.atan2(dLon, dPhi)) + 360) % 360; 
    return targetBearing - currentBearing; 
} 

// Horizon is 0 degree, Up is 90 degree 
function getVerticalBearing(fromLat, fromLon, fromAlt, toLat, toLon, toAlt, currentElevation) { 
    fromLat = toRadian(fromLat); 
    fromLon = toRadian(fromLon); 
    toLat = toRadian(toLat); 
    toLon = toRadian(toLon); 

    let fromECEF = getECEF(fromLat, fromLon, fromAlt); 
    let toECEF = getECEF(toLat, toLon, toAlt); 
    let deltaECEF = getDeltaECEF(fromECEF, toECEF); 

    let d = (fromECEF[0] * deltaECEF[0] + fromECEF[1] * deltaECEF[1] + fromECEF[2] * deltaECEF[2]); 
    let a = ((fromECEF[0] * fromECEF[0]) + (fromECEF[1] * fromECEF[1]) + (fromECEF[2] * fromECEF[2])); 
    let b = ((deltaECEF[0] * deltaECEF[0]) + (deltaECEF[2] * deltaECEF[2]) + (deltaECEF[2] * deltaECEF[2])); 
    let elevation = toDegree(Math.acos(d/Math.sqrt(a * b))); 
    elevation = 90 - elevation; 

    return elevation - currentElevation; 
} 

function getDeltaECEF(from, to) { 
    let X = to[0] - from[0]; 
    let Y = to[1] - from[1]; 
    let Z = to[2] - from[2]; 

    return [X, Y, Z]; 
} 

function getECEF(lat, lon, alt) { 
    let radius = 6378137; 
    let flatteningDenom = 298.257223563; 
    let flattening = 0.003352811; 
    let polarRadius = 6356752.312106893; 

    let asqr = radius * radius; 
    let bsqr = polarRadius * polarRadius; 
    let e = Math.sqrt((asqr-bsqr)/asqr); 
    // let eprime = Math.sqrt((asqr-bsqr)/bsqr); 

    let N = getN(radius, e, lat); 
    let ratio = (bsqr/asqr); 

    let X = (N + alt) * Math.cos(lat) * Math.cos(lon); 
    let Y = (N + alt) * Math.cos(lat) * Math.sin(lon); 
    let Z = (ratio * N + alt) * Math.sin(lat); 

    return [X, Y, Z]; 
} 

function getN(a, e, latitude) { 
    let sinlatitude = Math.sin(latitude); 
    let denom = Math.sqrt(1 - e * e * sinlatitude * sinlatitude); 
    return a/denom; 
} 

let n = getHorizontalBearing(39.099912, -94.581213, 39.099912, -94.588032, 0.00); 
console.info("Horizontal bearing:\t", n); 

let m = getVerticalBearing(39.099912, -94.581213, 273.543, 39.099912, -94.588032, 873.543, 0.0); 
console.info("Vertical bearing:\t", m);