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      1 /*
      2  * Copyright (C) 2009 The Android Open Source Project
      3  *
      4  * Licensed under the Apache License, Version 2.0 (the "License");
      5  * you may not use this file except in compliance with the License.
      6  * You may obtain a copy of the License at
      7  *
      8  *      http://www.apache.org/licenses/LICENSE-2.0
      9  *
     10  * Unless required by applicable law or agreed to in writing, software
     11  * distributed under the License is distributed on an "AS IS" BASIS,
     12  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     13  * See the License for the specific language governing permissions and
     14  * limitations under the License.
     15  */
     16 
     17 package android.hardware;
     18 
     19 import java.util.GregorianCalendar;
     20 
     21 /**
     22  * Estimates magnetic field at a given point on
     23  * Earth, and in particular, to compute the magnetic declination from true
     24  * north.
     25  *
     26  * <p>This uses the World Magnetic Model produced by the United States National
     27  * Geospatial-Intelligence Agency.  More details about the model can be found at
     28  * <a href="http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml">http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml</a>.
     29  * This class currently uses WMM-2010 which is valid until 2015, but should
     30  * produce acceptable results for several years after that. Future versions of
     31  * Android may use a newer version of the model.
     32  */
     33 public class GeomagneticField {
     34     // The magnetic field at a given point, in nonoteslas in geodetic
     35     // coordinates.
     36     private float mX;
     37     private float mY;
     38     private float mZ;
     39 
     40     // Geocentric coordinates -- set by computeGeocentricCoordinates.
     41     private float mGcLatitudeRad;
     42     private float mGcLongitudeRad;
     43     private float mGcRadiusKm;
     44 
     45     // Constants from WGS84 (the coordinate system used by GPS)
     46     static private final float EARTH_SEMI_MAJOR_AXIS_KM = 6378.137f;
     47     static private final float EARTH_SEMI_MINOR_AXIS_KM = 6356.7523142f;
     48     static private final float EARTH_REFERENCE_RADIUS_KM = 6371.2f;
     49 
     50     // These coefficients and the formulae used below are from:
     51     // NOAA Technical Report: The US/UK World Magnetic Model for 2010-2015
     52     static private final float[][] G_COEFF = new float[][] {
     53         { 0.0f },
     54         { -29496.6f, -1586.3f },
     55         { -2396.6f, 3026.1f, 1668.6f },
     56         { 1340.1f, -2326.2f, 1231.9f, 634.0f },
     57         { 912.6f, 808.9f, 166.7f, -357.1f, 89.4f },
     58         { -230.9f, 357.2f, 200.3f, -141.1f, -163.0f, -7.8f },
     59         { 72.8f, 68.6f, 76.0f, -141.4f, -22.8f, 13.2f, -77.9f },
     60         { 80.5f, -75.1f, -4.7f, 45.3f, 13.9f, 10.4f, 1.7f, 4.9f },
     61         { 24.4f, 8.1f, -14.5f, -5.6f, -19.3f, 11.5f, 10.9f, -14.1f, -3.7f },
     62         { 5.4f, 9.4f, 3.4f, -5.2f, 3.1f, -12.4f, -0.7f, 8.4f, -8.5f, -10.1f },
     63         { -2.0f, -6.3f, 0.9f, -1.1f, -0.2f, 2.5f, -0.3f, 2.2f, 3.1f, -1.0f, -2.8f },
     64         { 3.0f, -1.5f, -2.1f, 1.7f, -0.5f, 0.5f, -0.8f, 0.4f, 1.8f, 0.1f, 0.7f, 3.8f },
     65         { -2.2f, -0.2f, 0.3f, 1.0f, -0.6f, 0.9f, -0.1f, 0.5f, -0.4f, -0.4f, 0.2f, -0.8f, 0.0f } };
     66 
     67     static private final float[][] H_COEFF = new float[][] {
     68         { 0.0f },
     69         { 0.0f, 4944.4f },
     70         { 0.0f, -2707.7f, -576.1f },
     71         { 0.0f, -160.2f, 251.9f, -536.6f },
     72         { 0.0f, 286.4f, -211.2f, 164.3f, -309.1f },
     73         { 0.0f, 44.6f, 188.9f, -118.2f, 0.0f, 100.9f },
     74         { 0.0f, -20.8f, 44.1f, 61.5f, -66.3f, 3.1f, 55.0f },
     75         { 0.0f, -57.9f, -21.1f, 6.5f, 24.9f, 7.0f, -27.7f, -3.3f },
     76         { 0.0f, 11.0f, -20.0f, 11.9f, -17.4f, 16.7f, 7.0f, -10.8f, 1.7f },
     77         { 0.0f, -20.5f, 11.5f, 12.8f, -7.2f, -7.4f, 8.0f, 2.1f, -6.1f, 7.0f },
     78         { 0.0f, 2.8f, -0.1f, 4.7f, 4.4f, -7.2f, -1.0f, -3.9f, -2.0f, -2.0f, -8.3f },
     79         { 0.0f, 0.2f, 1.7f, -0.6f, -1.8f, 0.9f, -0.4f, -2.5f, -1.3f, -2.1f, -1.9f, -1.8f },
     80         { 0.0f, -0.9f, 0.3f, 2.1f, -2.5f, 0.5f, 0.6f, 0.0f, 0.1f, 0.3f, -0.9f, -0.2f, 0.9f } };
     81 
     82     static private final float[][] DELTA_G = new float[][] {
     83         { 0.0f },
     84         { 11.6f, 16.5f },
     85         { -12.1f, -4.4f, 1.9f },
     86         { 0.4f, -4.1f, -2.9f, -7.7f },
     87         { -1.8f, 2.3f, -8.7f, 4.6f, -2.1f },
     88         { -1.0f, 0.6f, -1.8f, -1.0f, 0.9f, 1.0f },
     89         { -0.2f, -0.2f, -0.1f, 2.0f, -1.7f, -0.3f, 1.7f },
     90         { 0.1f, -0.1f, -0.6f, 1.3f, 0.4f, 0.3f, -0.7f, 0.6f },
     91         { -0.1f, 0.1f, -0.6f, 0.2f, -0.2f, 0.3f, 0.3f, -0.6f, 0.2f },
     92         { 0.0f, -0.1f, 0.0f, 0.3f, -0.4f, -0.3f, 0.1f, -0.1f, -0.4f, -0.2f },
     93         { 0.0f, 0.0f, -0.1f, 0.2f, 0.0f, -0.1f, -0.2f, 0.0f, -0.1f, -0.2f, -0.2f },
     94         { 0.0f, 0.0f, 0.0f, 0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.1f, 0.0f },
     95         { 0.0f, 0.0f, 0.1f, 0.1f, -0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.1f, 0.1f } };
     96 
     97     static private final float[][] DELTA_H = new float[][] {
     98         { 0.0f },
     99         { 0.0f, -25.9f },
    100         { 0.0f, -22.5f, -11.8f },
    101         { 0.0f, 7.3f, -3.9f, -2.6f },
    102         { 0.0f, 1.1f, 2.7f, 3.9f, -0.8f },
    103         { 0.0f, 0.4f, 1.8f, 1.2f, 4.0f, -0.6f },
    104         { 0.0f, -0.2f, -2.1f, -0.4f, -0.6f, 0.5f, 0.9f },
    105         { 0.0f, 0.7f, 0.3f, -0.1f, -0.1f, -0.8f, -0.3f, 0.3f },
    106         { 0.0f, -0.1f, 0.2f, 0.4f, 0.4f, 0.1f, -0.1f, 0.4f, 0.3f },
    107         { 0.0f, 0.0f, -0.2f, 0.0f, -0.1f, 0.1f, 0.0f, -0.2f, 0.3f, 0.2f },
    108         { 0.0f, 0.1f, -0.1f, 0.0f, -0.1f, -0.1f, 0.0f, -0.1f, -0.2f, 0.0f, -0.1f },
    109         { 0.0f, 0.0f, 0.1f, 0.0f, 0.1f, 0.0f, 0.1f, 0.0f, -0.1f, -0.1f, 0.0f, -0.1f },
    110         { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f } };
    111 
    112     static private final long BASE_TIME =
    113         new GregorianCalendar(2010, 1, 1).getTimeInMillis();
    114 
    115     // The ratio between the Gauss-normalized associated Legendre functions and
    116     // the Schmid quasi-normalized ones. Compute these once staticly since they
    117     // don't depend on input variables at all.
    118     static private final float[][] SCHMIDT_QUASI_NORM_FACTORS =
    119         computeSchmidtQuasiNormFactors(G_COEFF.length);
    120 
    121     /**
    122      * Estimate the magnetic field at a given point and time.
    123      *
    124      * @param gdLatitudeDeg
    125      *            Latitude in WGS84 geodetic coordinates -- positive is east.
    126      * @param gdLongitudeDeg
    127      *            Longitude in WGS84 geodetic coordinates -- positive is north.
    128      * @param altitudeMeters
    129      *            Altitude in WGS84 geodetic coordinates, in meters.
    130      * @param timeMillis
    131      *            Time at which to evaluate the declination, in milliseconds
    132      *            since January 1, 1970. (approximate is fine -- the declination
    133      *            changes very slowly).
    134      */
    135     public GeomagneticField(float gdLatitudeDeg,
    136                             float gdLongitudeDeg,
    137                             float altitudeMeters,
    138                             long timeMillis) {
    139         final int MAX_N = G_COEFF.length; // Maximum degree of the coefficients.
    140 
    141         // We don't handle the north and south poles correctly -- pretend that
    142         // we're not quite at them to avoid crashing.
    143         gdLatitudeDeg = Math.min(90.0f - 1e-5f,
    144                                  Math.max(-90.0f + 1e-5f, gdLatitudeDeg));
    145         computeGeocentricCoordinates(gdLatitudeDeg,
    146                                      gdLongitudeDeg,
    147                                      altitudeMeters);
    148 
    149         assert G_COEFF.length == H_COEFF.length;
    150 
    151         // Note: LegendreTable computes associated Legendre functions for
    152         // cos(theta).  We want the associated Legendre functions for
    153         // sin(latitude), which is the same as cos(PI/2 - latitude), except the
    154         // derivate will be negated.
    155         LegendreTable legendre =
    156             new LegendreTable(MAX_N - 1,
    157                               (float) (Math.PI / 2.0 - mGcLatitudeRad));
    158 
    159         // Compute a table of (EARTH_REFERENCE_RADIUS_KM / radius)^n for i in
    160         // 0..MAX_N-2 (this is much faster than calling Math.pow MAX_N+1 times).
    161         float[] relativeRadiusPower = new float[MAX_N + 2];
    162         relativeRadiusPower[0] = 1.0f;
    163         relativeRadiusPower[1] = EARTH_REFERENCE_RADIUS_KM / mGcRadiusKm;
    164         for (int i = 2; i < relativeRadiusPower.length; ++i) {
    165             relativeRadiusPower[i] = relativeRadiusPower[i - 1] *
    166                 relativeRadiusPower[1];
    167         }
    168 
    169         // Compute tables of sin(lon * m) and cos(lon * m) for m = 0..MAX_N --
    170         // this is much faster than calling Math.sin and Math.com MAX_N+1 times.
    171         float[] sinMLon = new float[MAX_N];
    172         float[] cosMLon = new float[MAX_N];
    173         sinMLon[0] = 0.0f;
    174         cosMLon[0] = 1.0f;
    175         sinMLon[1] = (float) Math.sin(mGcLongitudeRad);
    176         cosMLon[1] = (float) Math.cos(mGcLongitudeRad);
    177 
    178         for (int m = 2; m < MAX_N; ++m) {
    179             // Standard expansions for sin((m-x)*theta + x*theta) and
    180             // cos((m-x)*theta + x*theta).
    181             int x = m >> 1;
    182             sinMLon[m] = sinMLon[m-x] * cosMLon[x] + cosMLon[m-x] * sinMLon[x];
    183             cosMLon[m] = cosMLon[m-x] * cosMLon[x] - sinMLon[m-x] * sinMLon[x];
    184         }
    185 
    186         float inverseCosLatitude = 1.0f / (float) Math.cos(mGcLatitudeRad);
    187         float yearsSinceBase =
    188             (timeMillis - BASE_TIME) / (365f * 24f * 60f * 60f * 1000f);
    189 
    190         // We now compute the magnetic field strength given the geocentric
    191         // location. The magnetic field is the derivative of the potential
    192         // function defined by the model. See NOAA Technical Report: The US/UK
    193         // World Magnetic Model for 2010-2015 for the derivation.
    194         float gcX = 0.0f;  // Geocentric northwards component.
    195         float gcY = 0.0f;  // Geocentric eastwards component.
    196         float gcZ = 0.0f;  // Geocentric downwards component.
    197 
    198         for (int n = 1; n < MAX_N; n++) {
    199             for (int m = 0; m <= n; m++) {
    200                 // Adjust the coefficients for the current date.
    201                 float g = G_COEFF[n][m] + yearsSinceBase * DELTA_G[n][m];
    202                 float h = H_COEFF[n][m] + yearsSinceBase * DELTA_H[n][m];
    203 
    204                 // Negative derivative with respect to latitude, divided by
    205                 // radius.  This looks like the negation of the version in the
    206                 // NOAA Techincal report because that report used
    207                 // P_n^m(sin(theta)) and we use P_n^m(cos(90 - theta)), so the
    208                 // derivative with respect to theta is negated.
    209                 gcX += relativeRadiusPower[n+2]
    210                     * (g * cosMLon[m] + h * sinMLon[m])
    211                     * legendre.mPDeriv[n][m]
    212                     * SCHMIDT_QUASI_NORM_FACTORS[n][m];
    213 
    214                 // Negative derivative with respect to longitude, divided by
    215                 // radius.
    216                 gcY += relativeRadiusPower[n+2] * m
    217                     * (g * sinMLon[m] - h * cosMLon[m])
    218                     * legendre.mP[n][m]
    219                     * SCHMIDT_QUASI_NORM_FACTORS[n][m]
    220                     * inverseCosLatitude;
    221 
    222                 // Negative derivative with respect to radius.
    223                 gcZ -= (n + 1) * relativeRadiusPower[n+2]
    224                     * (g * cosMLon[m] + h * sinMLon[m])
    225                     * legendre.mP[n][m]
    226                     * SCHMIDT_QUASI_NORM_FACTORS[n][m];
    227             }
    228         }
    229 
    230         // Convert back to geodetic coordinates.  This is basically just a
    231         // rotation around the Y-axis by the difference in latitudes between the
    232         // geocentric frame and the geodetic frame.
    233         double latDiffRad = Math.toRadians(gdLatitudeDeg) - mGcLatitudeRad;
    234         mX = (float) (gcX * Math.cos(latDiffRad)
    235                       + gcZ * Math.sin(latDiffRad));
    236         mY = gcY;
    237         mZ = (float) (- gcX * Math.sin(latDiffRad)
    238                       + gcZ * Math.cos(latDiffRad));
    239     }
    240 
    241     /**
    242      * @return The X (northward) component of the magnetic field in nanoteslas.
    243      */
    244     public float getX() {
    245         return mX;
    246     }
    247 
    248     /**
    249      * @return The Y (eastward) component of the magnetic field in nanoteslas.
    250      */
    251     public float getY() {
    252         return mY;
    253     }
    254 
    255     /**
    256      * @return The Z (downward) component of the magnetic field in nanoteslas.
    257      */
    258     public float getZ() {
    259         return mZ;
    260     }
    261 
    262     /**
    263      * @return The declination of the horizontal component of the magnetic
    264      *         field from true north, in degrees (i.e. positive means the
    265      *         magnetic field is rotated east that much from true north).
    266      */
    267     public float getDeclination() {
    268         return (float) Math.toDegrees(Math.atan2(mY, mX));
    269     }
    270 
    271     /**
    272      * @return The inclination of the magnetic field in degrees -- positive
    273      *         means the magnetic field is rotated downwards.
    274      */
    275     public float getInclination() {
    276         return (float) Math.toDegrees(Math.atan2(mZ,
    277                                                  getHorizontalStrength()));
    278     }
    279 
    280     /**
    281      * @return  Horizontal component of the field strength in nonoteslas.
    282      */
    283     public float getHorizontalStrength() {
    284         return (float) Math.hypot(mX, mY);
    285     }
    286 
    287     /**
    288      * @return  Total field strength in nanoteslas.
    289      */
    290     public float getFieldStrength() {
    291         return (float) Math.sqrt(mX * mX + mY * mY + mZ * mZ);
    292     }
    293 
    294     /**
    295      * @param gdLatitudeDeg
    296      *            Latitude in WGS84 geodetic coordinates.
    297      * @param gdLongitudeDeg
    298      *            Longitude in WGS84 geodetic coordinates.
    299      * @param altitudeMeters
    300      *            Altitude above sea level in WGS84 geodetic coordinates.
    301      * @return Geocentric latitude (i.e. angle between closest point on the
    302      *         equator and this point, at the center of the earth.
    303      */
    304     private void computeGeocentricCoordinates(float gdLatitudeDeg,
    305                                               float gdLongitudeDeg,
    306                                               float altitudeMeters) {
    307         float altitudeKm = altitudeMeters / 1000.0f;
    308         float a2 = EARTH_SEMI_MAJOR_AXIS_KM * EARTH_SEMI_MAJOR_AXIS_KM;
    309         float b2 = EARTH_SEMI_MINOR_AXIS_KM * EARTH_SEMI_MINOR_AXIS_KM;
    310         double gdLatRad = Math.toRadians(gdLatitudeDeg);
    311         float clat = (float) Math.cos(gdLatRad);
    312         float slat = (float) Math.sin(gdLatRad);
    313         float tlat = slat / clat;
    314         float latRad =
    315             (float) Math.sqrt(a2 * clat * clat + b2 * slat * slat);
    316 
    317         mGcLatitudeRad = (float) Math.atan(tlat * (latRad * altitudeKm + b2)
    318                                            / (latRad * altitudeKm + a2));
    319 
    320         mGcLongitudeRad = (float) Math.toRadians(gdLongitudeDeg);
    321 
    322         float radSq = altitudeKm * altitudeKm
    323             + 2 * altitudeKm * (float) Math.sqrt(a2 * clat * clat +
    324                                                  b2 * slat * slat)
    325             + (a2 * a2 * clat * clat + b2 * b2 * slat * slat)
    326             / (a2 * clat * clat + b2 * slat * slat);
    327         mGcRadiusKm = (float) Math.sqrt(radSq);
    328     }
    329 
    330 
    331     /**
    332      * Utility class to compute a table of Gauss-normalized associated Legendre
    333      * functions P_n^m(cos(theta))
    334      */
    335     static private class LegendreTable {
    336         // These are the Gauss-normalized associated Legendre functions -- that
    337         // is, they are normal Legendre functions multiplied by
    338         // (n-m)!/(2n-1)!! (where (2n-1)!! = 1*3*5*...*2n-1)
    339         public final float[][] mP;
    340 
    341         // Derivative of mP, with respect to theta.
    342         public final float[][] mPDeriv;
    343 
    344         /**
    345          * @param maxN
    346          *            The maximum n- and m-values to support
    347          * @param thetaRad
    348          *            Returned functions will be Gauss-normalized
    349          *            P_n^m(cos(thetaRad)), with thetaRad in radians.
    350          */
    351         public LegendreTable(int maxN, float thetaRad) {
    352             // Compute the table of Gauss-normalized associated Legendre
    353             // functions using standard recursion relations. Also compute the
    354             // table of derivatives using the derivative of the recursion
    355             // relations.
    356             float cos = (float) Math.cos(thetaRad);
    357             float sin = (float) Math.sin(thetaRad);
    358 
    359             mP = new float[maxN + 1][];
    360             mPDeriv = new float[maxN + 1][];
    361             mP[0] = new float[] { 1.0f };
    362             mPDeriv[0] = new float[] { 0.0f };
    363             for (int n = 1; n <= maxN; n++) {
    364                 mP[n] = new float[n + 1];
    365                 mPDeriv[n] = new float[n + 1];
    366                 for (int m = 0; m <= n; m++) {
    367                     if (n == m) {
    368                         mP[n][m] = sin * mP[n - 1][m - 1];
    369                         mPDeriv[n][m] = cos * mP[n - 1][m - 1]
    370                             + sin * mPDeriv[n - 1][m - 1];
    371                     } else if (n == 1 || m == n - 1) {
    372                         mP[n][m] = cos * mP[n - 1][m];
    373                         mPDeriv[n][m] = -sin * mP[n - 1][m]
    374                             + cos * mPDeriv[n - 1][m];
    375                     } else {
    376                         assert n > 1 && m < n - 1;
    377                         float k = ((n - 1) * (n - 1) - m * m)
    378                             / (float) ((2 * n - 1) * (2 * n - 3));
    379                         mP[n][m] = cos * mP[n - 1][m] - k * mP[n - 2][m];
    380                         mPDeriv[n][m] = -sin * mP[n - 1][m]
    381                             + cos * mPDeriv[n - 1][m] - k * mPDeriv[n - 2][m];
    382                     }
    383                 }
    384             }
    385         }
    386     }
    387 
    388     /**
    389      * Compute the ration between the Gauss-normalized associated Legendre
    390      * functions and the Schmidt quasi-normalized version. This is equivalent to
    391      * sqrt((m==0?1:2)*(n-m)!/(n+m!))*(2n-1)!!/(n-m)!
    392      */
    393     private static float[][] computeSchmidtQuasiNormFactors(int maxN) {
    394         float[][] schmidtQuasiNorm = new float[maxN + 1][];
    395         schmidtQuasiNorm[0] = new float[] { 1.0f };
    396         for (int n = 1; n <= maxN; n++) {
    397             schmidtQuasiNorm[n] = new float[n + 1];
    398             schmidtQuasiNorm[n][0] =
    399                 schmidtQuasiNorm[n - 1][0] * (2 * n - 1) / (float) n;
    400             for (int m = 1; m <= n; m++) {
    401                 schmidtQuasiNorm[n][m] = schmidtQuasiNorm[n][m - 1]
    402                     * (float) Math.sqrt((n - m + 1) * (m == 1 ? 2 : 1)
    403                                 / (float) (n + m));
    404             }
    405         }
    406         return schmidtQuasiNorm;
    407     }
    408 }
    409