ios - IOS 外部 GPS 数据的 WGS84 Geoid Height Altitude Offset

Question

对于我正在编写的应用程序，我们将 IOS 设备与外部传感器连接，该传感器通过本地 wifi 网络输出 GPS 数据。该数据以关于高度的“原始”格式出现。一般来说，所有 GPS 高度都需要根据当前位置应用与 WGS84 大地水准面高度相关的校正因子。

例如，在以下地理控制点 ( http://www.ngs.noaa.gov/cgi-bin/ds_mark.prl?PidBox=HV9830 ) 中，它位于纬度 38 56 36.77159 和经度 077 01 08.34929

HV9830* NAD 83(2011) POSITION- 38 56 36.77159(N) 077 01 08.34929(W)   ADJUSTED  
HV9830* NAD 83(2011) ELLIP HT-    42.624 (meters)        (06/27/12)   ADJUSTED
HV9830* NAD 83(2011) EPOCH   -  2010.00
HV9830* NAVD 88 ORTHO HEIGHT -    74.7    (meters)     245.    (feet) VERTCON   
HV9830  ______________________________________________________________________
HV9830  GEOID HEIGHT    -        -32.02  (meters)                     GEOID12A
HV9830  NAD 83(2011) X  -  1,115,795.966 (meters)                     COMP
HV9830  NAD 83(2011) Y  - -4,840,360.447 (meters)                     COMP
HV9830  NAD 83(2011) Z  -  3,987,471.457 (meters)                     COMP
HV9830  LAPLACE CORR    -         -2.38  (seconds)                    DEFLEC12A

您可以看到大地水准面高度为-32 米。因此，鉴于这一点附近的原始 GPS 读数，人们必须应用 -32 米的校正才能计算出正确的高度。 (注意:校正为负数，因此您实际上会减去负数，从而将读数向上移动 32 米)。

与 Android 不同，据我们了解，关于 coreLocation，此 GeoidHeight 信息由 IOS 在内部自动计算。我们遇到困难的地方是我们正在使用带有传感器的本地 wifi 网络，该传感器计算未校正的 GPS 并收集外部传感器数据以及 GPS 的 coreLocation 读数。我想知道是否有人知道有大地水准面信息的库 (C/Objective-C)，当我从我们的传感器包中读取原始 GPS 信号时，它可以帮助我即时进行这些计算。

感谢您的帮助。

旁注:请不要建议我查看以下帖子: Get altitude by longitude and latitude in Android 这是一个很好的解决方案，但我们没有实时互联网连接，因此我们无法向 Goole 或 USGS 进行实时查询。

Answer 1

我在这里解决了我的问题。我所做的是创建一个 Fortran 代码的 c 实现的 ObjectiveC 实现来完成我需要的事情。原始 c 可以在这里找到:http://sourceforge.net/projects/egm96-f477-c/

您需要从 Source Forge 下载项目才能访问此代码所需的输入文件:CORCOEF 和 EGM96

我的 objective-c 实现如下:

大地水准面计算器.h

#import <Foundation/Foundation.h>

@interface GeoidCalculator : NSObject
+ (GeoidCalculator *)instance;


-(double) getHeightFromLat:(double)lat    andLon:(double)lon;
-(double) getCurrentHeightOffset;
-(void) updatePositionWithLatitude:(double)lat andLongitude:(double)lon;

@end

大地水准面计算器.m

#import "GeoidCalculator.h"
#import <stdio.h>
#import <math.h>


#define l_value    (65341)
#define _361    (361)

@implementation GeoidCalculator

static int nmax;

static double currentHeight;

static double cc[l_value+ 1], cs[l_value+ 1], hc[l_value+ 1], hs[l_value+ 1],
        p[l_value+ 1], sinml[_361+ 1], cosml[_361+ 1], rleg[_361+ 1];

+ (GeoidCalculator *)instance {
    static GeoidCalculator *_instance = nil;

    @synchronized (self) {
        if (_instance == nil) {
            _instance = [[self alloc] init];
            init_arrays();
            currentHeight = -9999;
        }
    }

    return _instance;
}


- (double)getHeightFromLat:(double)lat andLon:(double)lon {
    [self updatePositionWithLatitude:lat andLongitude:lon];
    return [self getCurrentHeightOffset];
}


- (double)getCurrentHeightOffset {
    return currentHeight;
}

- (void)updatePositionWithLatitude:(double)lat andLongitude:(double)lon {
    const double rad = 180 / M_PI;
    double flat, flon, u;
    flat = lat; flon = lon;

    /*compute the geocentric latitude,geocentric radius,normal gravity*/
    u = undulation(flat / rad, flon / rad, nmax, nmax + 1);

    /*u is the geoid undulation from the egm96 potential coefficient model
       including the height anomaly to geoid undulation correction term
       and a correction term to have the undulations refer to the
       wgs84 ellipsoid. the geoid undulation unit is meters.*/
    currentHeight = u;
}


double hundu(unsigned nmax, double p[l_value+ 1],
        double hc[l_value+ 1], double hs[l_value+ 1],
        double sinml[_361+ 1], double cosml[_361+ 1], double gr, double re,
        double cc[l_value+ 1], double cs[l_value+ 1]) {/*constants for wgs84(g873);gm in units of m**3/s**2*/
    const double gm = .3986004418e15, ae = 6378137.;
    double arn, ar, ac, a, b, sum, sumc, sum2, tempc, temp;
    int k, n, m;
    ar = ae / re;
    arn = ar;
    ac = a = b = 0;
    k = 3;
    for (n = 2; n <= nmax; n++) {
        arn *= ar;
        k++;
        sum = p[k] * hc[k];
        sumc = p[k] * cc[k];
        sum2 = 0;
        for (m = 1; m <= n; m++) {
            k++;
            tempc = cc[k] * cosml[m] + cs[k] * sinml[m];
            temp = hc[k] * cosml[m] + hs[k] * sinml[m];
            sumc += p[k] * tempc;
            sum += p[k] * temp;
        }
        ac += sumc;
        a += sum * arn;
    }
    ac += cc[1] + p[2] * cc[2] + p[3] * (cc[3] * cosml[1] + cs[3] * sinml[1]);
/*add haco=ac/100 to convert height anomaly on the ellipsoid to the undulation
add -0.53m to make undulation refer to the wgs84 ellipsoid.*/
    return a * gm / (gr * re) + ac / 100 - .53;
}

void dscml(double rlon, unsigned nmax, double sinml[_361+ 1], double cosml[_361+ 1]) {
    double a, b;
    int m;
    a = sin(rlon);
    b = cos(rlon);
    sinml[1] = a;
    cosml[1] = b;
    sinml[2] = 2 * b * a;
    cosml[2] = 2 * b * b - 1;
    for (m = 3; m <= nmax; m++) {
        sinml[m] = 2 * b * sinml[m - 1] - sinml[m - 2];
        cosml[m] = 2 * b * cosml[m - 1] - cosml[m - 2];
    }
}

void dhcsin(unsigned nmax, double hc[l_value+ 1], double hs[l_value+ 1]) {


    // potential coefficient file
    //f_12 = fopen("EGM96", "rb");
    NSString* path2 = [[NSBundle mainBundle] pathForResource:@"EGM96" ofType:@""];
    FILE* f_12 = fopen(path2.UTF8String, "rb");
    if (f_12 == NULL) {
        NSLog([path2 stringByAppendingString:@" not found"]);
    }



    int n, m;
    double j2, j4, j6, j8, j10, c, s, ec, es;
/*the even degree zonal coefficients given below were computed for the
 wgs84(g873) system of constants and are identical to those values
 used in the NIMA gridding procedure. computed using subroutine
 grs written by N.K. PAVLIS*/
    j2 = 0.108262982131e-2;
    j4 = -.237091120053e-05;
    j6 = 0.608346498882e-8;
    j8 = -0.142681087920e-10;
    j10 = 0.121439275882e-13;
    m = ((nmax + 1) * (nmax + 2)) / 2;
    for (n = 1; n <= m; n++)hc[n] = hs[n] = 0;
    while (6 == fscanf(f_12, "%i %i %lf %lf %lf %lf", &n, &m, &c, &s, &ec, &es)) {
        if (n > nmax)continue;
        n = (n * (n + 1)) / 2 + m + 1;
        hc[n] = c;
        hs[n] = s;
    }
    hc[4] += j2 / sqrt(5);
    hc[11] += j4 / 3;
    hc[22] += j6 / sqrt(13);
    hc[37] += j8 / sqrt(17);
    hc[56] += j10 / sqrt(21);


    fclose(f_12);

}

void legfdn(unsigned m, double theta, double rleg[_361+ 1], unsigned nmx)
/*this subroutine computes  all normalized legendre function
in "rleg". order is always
m, and colatitude is always theta  (radians). maximum deg
is  nmx. all calculations in double precision.
ir  must be set to zero before the first call to this sub.
the dimensions of arrays  rleg must be at least equal to  nmx+1.
Original programmer :Oscar L. Colombo, Dept. of Geodetic Science
the Ohio State University, August 1980
ineiev: I removed the derivatives, for they are never computed here*/
{
    static double drts[1301], dirt[1301], cothet, sithet, rlnn[_361+ 1];
    static int ir;
    int nmx1 = nmx + 1, nmx2p = 2 * nmx + 1, m1 = m + 1, m2 = m + 2, m3 = m + 3, n, n1, n2;
    if (!ir) {
        ir = 1;
        for (n = 1; n <= nmx2p; n++) {
            drts[n] = sqrt(n);
            dirt[n] = 1 / drts[n];
        }
    }
    cothet = cos(theta);
    sithet = sin(theta);
    /*compute the legendre functions*/
    rlnn[1] = 1;
    rlnn[2] = sithet * drts[3];
    for (n1 = 3; n1 <= m1; n1++) {
        n = n1 - 1;
        n2 = 2 * n;
        rlnn[n1] = drts[n2 + 1] * dirt[n2] * sithet * rlnn[n];
    }
    switch (m) {
        case 1:
            rleg[2] = rlnn[2];
            rleg[3] = drts[5] * cothet * rleg[2];
            break;
        case 0:
            rleg[1] = 1;
            rleg[2] = cothet * drts[3];
            break;
    }
    rleg[m1] = rlnn[m1];
    if (m2 <= nmx1) {
        rleg[m2] = drts[m1 * 2 + 1] * cothet * rleg[m1];
        if (m3 <= nmx1)
            for (n1 = m3; n1 <= nmx1; n1++) {
                n = n1 - 1;
                if ((!m && n < 2) || (m == 1 && n < 3))continue;
                n2 = 2 * n;
                rleg[n1] = drts[n2 + 1] * dirt[n + m] * dirt[n - m] *
                        (drts[n2 - 1] * cothet * rleg[n1 - 1] - drts[n + m - 1] * drts[n - m - 1] * dirt[n2 - 3] * rleg[n1 - 2]);
            }
    }
}

void radgra(double lat, double lon, double *rlat, double *gr, double *re)
/*this subroutine computes geocentric distance to the point,
the geocentric latitude,and
an approximate value of normal gravity at the point based
the constants of the wgs84(g873) system are used*/
{
    const double a = 6378137., e2 = .00669437999013, geqt = 9.7803253359, k = .00193185265246;
    double n, t1 = sin(lat) * sin(lat), t2, x, y, z;
    n = a / sqrt(1 - e2 * t1);
    t2 = n * cos(lat);
    x = t2 * cos(lon);
    y = t2 * sin(lon);
    z = (n * (1 - e2)) * sin(lat);
    *re = sqrt(x * x + y * y + z * z);/*compute the geocentric radius*/
    *rlat = atan(z / sqrt(x * x + y * y));/*compute the geocentric latitude*/
    *gr = geqt * (1 + k * t1) / sqrt(1 - e2 * t1);/*compute normal gravity:units are m/sec**2*/
}


double undulation(double lat, double lon, int nmax, int k) {
    double rlat, gr, re;
    int i, j, m;
    radgra(lat, lon, &rlat, &gr, &re);
    rlat = M_PI / 2 - rlat;
    for (j = 1; j <= k; j++) {
        m = j - 1;
        legfdn(m, rlat, rleg, nmax);
        for (i = j; i <= k; i++)p[(i - 1) * i / 2 + m + 1] = rleg[i];
    }
    dscml(lon, nmax, sinml, cosml);
    return hundu(nmax, p, hc, hs, sinml, cosml, gr, re, cc, cs);
}

void init_arrays(void) {
    int ig, i, n, m;
    double t1, t2;






    NSString* path1 = [[NSBundle mainBundle] pathForResource:@"CORCOEF" ofType:@""];


    //correction coefficient file:  modified with 'sed -e"s/D/e/g"' to be read with fscanf
    FILE* f_1 = fopen([path1 cStringUsingEncoding:1], "rb");
    if (f_1 == NULL) {
        NSLog([path1 stringByAppendingString:@" not found"]);
    }


    nmax = 360;
    for (i = 1; i <= l_value; i++)cc[i] = cs[i] = 0;

    while (4 == fscanf(f_1, "%i %i %lg %lg", &n, &m, &t1, &t2)) {
        ig = (n * (n + 1)) / 2 + m + 1;
        cc[ig] = t1;
        cs[ig] = t2;
    }
/*the correction coefficients are now read in*/
/*the potential coefficients are now read in and the reference
 even degree zonal harmonic coefficients removed to degree 6*/
    dhcsin(nmax, hc, hs);
    fclose(f_1);
}


@end

我已经针对大地水准面高度计算器 (http://www.unavco.org/community_science/science-support/geoid/geoid.html) 进行了一些有限的测试，看起来一切都匹配

更新 iOS8 或更高版本

从 IOS8 开始，此代码可能无法正常工作。您可能需要更改包的加载方式:

[[NSBundle mainBundle] pathForResource:@"EGM96"ofType:@""];

在此处进行一些谷歌搜索或添加评论。