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authorThe Android Open Source Project <initial-contribution@android.com>2009-02-10 15:44:00 -0800
committerThe Android Open Source Project <initial-contribution@android.com>2009-02-10 15:44:00 -0800
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+/*
+ * Copyright (C) 2009 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package android.hardware;
+
+import java.util.GregorianCalendar;
+
+/**
+ * This class is used to estimated estimate magnetic field at a given point on
+ * Earth, and in particular, to compute the magnetic declination from true
+ * north.
+ *
+ * <p>This uses the World Magnetic Model produced by the United States National
+ * Geospatial-Intelligence Agency. More details about the model can be found at
+ * <a href="http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml">http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml</a>.
+ * This class currently uses WMM-2005 which is valid until 2010, but should
+ * produce acceptable results for several years after that.
+ */
+public class GeomagneticField {
+ // The magnetic field at a given point, in nonoteslas in geodetic
+ // coordinates.
+ private float mX;
+ private float mY;
+ private float mZ;
+
+ // Geocentric coordinates -- set by computeGeocentricCoordinates.
+ private float mGcLatitudeRad;
+ private float mGcLongitudeRad;
+ private float mGcRadiusKm;
+
+ // Constants from WGS84 (the coordinate system used by GPS)
+ static private final float EARTH_SEMI_MAJOR_AXIS_KM = 6378.137f;
+ static private final float EARTH_SEMI_MINOR_AXIS_KM = 6356.7523f;
+ static private final float EARTH_REFERENCE_RADIUS_KM = 6371.2f;
+
+ // These coefficients and the formulae used below are from:
+ // NOAA Technical Report: The US/UK World Magnetic Model for 2005-2010
+ static private final float[][] G_COEFF = new float[][] {
+ { 0f },
+ { -29556.8f, -1671.7f },
+ { -2340.6f, 3046.9f, 1657.0f },
+ { 1335.4f, -2305.1f, 1246.7f, 674.0f },
+ { 919.8f, 798.1f, 211.3f, -379.4f, 100.0f },
+ { -227.4f, 354.6f, 208.7f, -136.5f, -168.3f, -14.1f },
+ { 73.2f, 69.7f, 76.7f, -151.2f, -14.9f, 14.6f, -86.3f },
+ { 80.1f, -74.5f, -1.4f, 38.5f, 12.4f, 9.5f, 5.7f, 1.8f },
+ { 24.9f, 7.7f, -11.6f, -6.9f, -18.2f, 10.0f, 9.2f, -11.6f, -5.2f },
+ { 5.6f, 9.9f, 3.5f, -7.0f, 5.1f, -10.8f, -1.3f, 8.8f, -6.7f, -9.1f },
+ { -2.3f, -6.3f, 1.6f, -2.6f, 0.0f, 3.1f, 0.4f, 2.1f, 3.9f, -0.1f, -2.3f },
+ { 2.8f, -1.6f, -1.7f, 1.7f, -0.1f, 0.1f, -0.7f, 0.7f, 1.8f, 0.0f, 1.1f, 4.1f },
+ { -2.4f, -0.4f, 0.2f, 0.8f, -0.3f, 1.1f, -0.5f, 0.4f, -0.3f, -0.3f, -0.1f,
+ -0.3f, -0.1f } };
+
+ static private final float[][] H_COEFF = new float[][] {
+ { 0f },
+ { 0.0f, 5079.8f },
+ { 0.0f, -2594.7f, -516.7f },
+ { 0.0f, -199.9f, 269.3f, -524.2f },
+ { 0.0f, 281.5f, -226.0f, 145.8f, -304.7f },
+ { 0.0f, 42.4f, 179.8f, -123.0f, -19.5f, 103.6f },
+ { 0.0f, -20.3f, 54.7f, 63.6f, -63.4f, -0.1f, 50.4f },
+ { 0.0f, -61.5f, -22.4f, 7.2f, 25.4f, 11.0f, -26.4f, -5.1f },
+ { 0.0f, 11.2f, -21.0f, 9.6f, -19.8f, 16.1f, 7.7f, -12.9f, -0.2f },
+ { 0.0f, -20.1f, 12.9f, 12.6f, -6.7f, -8.1f, 8.0f, 2.9f, -7.9f, 6.0f },
+ { 0.0f, 2.4f, 0.2f, 4.4f, 4.8f, -6.5f, -1.1f, -3.4f, -0.8f, -2.3f, -7.9f },
+ { 0.0f, 0.3f, 1.2f, -0.8f, -2.5f, 0.9f, -0.6f, -2.7f, -0.9f, -1.3f, -2.0f, -1.2f },
+ { 0.0f, -0.4f, 0.3f, 2.4f, -2.6f, 0.6f, 0.3f, 0.0f, 0.0f, 0.3f, -0.9f, -0.4f,
+ 0.8f } };
+
+ static private final float[][] DELTA_G = new float[][] {
+ { 0f },
+ { 8.0f, 10.6f },
+ { -15.1f, -7.8f, -0.8f },
+ { 0.4f, -2.6f, -1.2f, -6.5f },
+ { -2.5f, 2.8f, -7.0f, 6.2f, -3.8f },
+ { -2.8f, 0.7f, -3.2f, -1.1f, 0.1f, -0.8f },
+ { -0.7f, 0.4f, -0.3f, 2.3f, -2.1f, -0.6f, 1.4f },
+ { 0.2f, -0.1f, -0.3f, 1.1f, 0.6f, 0.5f, -0.4f, 0.6f },
+ { 0.1f, 0.3f, -0.4f, 0.3f, -0.3f, 0.2f, 0.4f, -0.7f, 0.4f },
+ { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f },
+ { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f },
+ { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f },
+ { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f } };
+
+ static private final float[][] DELTA_H = new float[][] {
+ { 0f },
+ { 0.0f, -20.9f },
+ { 0.0f, -23.2f, -14.6f },
+ { 0.0f, 5.0f, -7.0f, -0.6f },
+ { 0.0f, 2.2f, 1.6f, 5.8f, 0.1f },
+ { 0.0f, 0.0f, 1.7f, 2.1f, 4.8f, -1.1f },
+ { 0.0f, -0.6f, -1.9f, -0.4f, -0.5f, -0.3f, 0.7f },
+ { 0.0f, 0.6f, 0.4f, 0.2f, 0.3f, -0.8f, -0.2f, 0.1f },
+ { 0.0f, -0.2f, 0.1f, 0.3f, 0.4f, 0.1f, -0.2f, 0.4f, 0.4f },
+ { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f },
+ { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f },
+ { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f },
+ { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f } };
+
+ static private final long BASE_TIME =
+ new GregorianCalendar(2005, 1, 1).getTimeInMillis();
+
+ // The ratio between the Gauss-normalized associated Legendre functions and
+ // the Schmid quasi-normalized ones. Compute these once staticly since they
+ // don't depend on input variables at all.
+ static private final float[][] SCHMIDT_QUASI_NORM_FACTORS =
+ computeSchmidtQuasiNormFactors(G_COEFF.length);
+
+ /**
+ * Estimate the magnetic field at a given point and time.
+ *
+ * @param gdLatitudeDeg
+ * Latitude in WGS84 geodetic coordinates -- positive is east.
+ * @param gdLongitudeDeg
+ * Longitude in WGS84 geodetic coordinates -- positive is north.
+ * @param altitudeMeters
+ * Altitude in WGS84 geodetic coordinates, in meters.
+ * @param timeMillis
+ * Time at which to evaluate the declination, in milliseconds
+ * since January 1, 1970. (approximate is fine -- the declination
+ * changes very slowly).
+ */
+ public GeomagneticField(float gdLatitudeDeg,
+ float gdLongitudeDeg,
+ float altitudeMeters,
+ long timeMillis) {
+ final int MAX_N = G_COEFF.length; // Maximum degree of the coefficients.
+
+ // We don't handle the north and south poles correctly -- pretend that
+ // we're not quite at them to avoid crashing.
+ gdLatitudeDeg = Math.min(90.0f - 1e-5f,
+ Math.max(-90.0f + 1e-5f, gdLatitudeDeg));
+ computeGeocentricCoordinates(gdLatitudeDeg,
+ gdLongitudeDeg,
+ altitudeMeters);
+
+ assert G_COEFF.length == H_COEFF.length;
+
+ // Note: LegendreTable computes associated Legendre functions for
+ // cos(theta). We want the associated Legendre functions for
+ // sin(latitude), which is the same as cos(PI/2 - latitude), except the
+ // derivate will be negated.
+ LegendreTable legendre =
+ new LegendreTable(MAX_N - 1,
+ (float) (Math.PI / 2.0 - mGcLatitudeRad));
+
+ // Compute a table of (EARTH_REFERENCE_RADIUS_KM / radius)^n for i in
+ // 0..MAX_N-2 (this is much faster than calling Math.pow MAX_N+1 times).
+ float[] relativeRadiusPower = new float[MAX_N + 2];
+ relativeRadiusPower[0] = 1.0f;
+ relativeRadiusPower[1] = EARTH_REFERENCE_RADIUS_KM / mGcRadiusKm;
+ for (int i = 2; i < relativeRadiusPower.length; ++i) {
+ relativeRadiusPower[i] = relativeRadiusPower[i - 1] *
+ relativeRadiusPower[1];
+ }
+
+ // Compute tables of sin(lon * m) and cos(lon * m) for m = 0..MAX_N --
+ // this is much faster than calling Math.sin and Math.com MAX_N+1 times.
+ float[] sinMLon = new float[MAX_N];
+ float[] cosMLon = new float[MAX_N];
+ sinMLon[0] = 0.0f;
+ cosMLon[0] = 1.0f;
+ sinMLon[1] = (float) Math.sin(mGcLongitudeRad);
+ cosMLon[1] = (float) Math.cos(mGcLongitudeRad);
+
+ for (int m = 2; m < MAX_N; ++m) {
+ // Standard expansions for sin((m-x)*theta + x*theta) and
+ // cos((m-x)*theta + x*theta).
+ int x = m >> 1;
+ sinMLon[m] = sinMLon[m-x] * cosMLon[x] + cosMLon[m-x] * sinMLon[x];
+ cosMLon[m] = cosMLon[m-x] * cosMLon[x] - sinMLon[m-x] * sinMLon[x];
+ }
+
+ float inverseCosLatitude = 1.0f / (float) Math.cos(mGcLatitudeRad);
+ float yearsSinceBase =
+ (timeMillis - BASE_TIME) / (365f * 24f * 60f * 60f * 1000f);
+
+ // We now compute the magnetic field strength given the geocentric
+ // location. The magnetic field is the derivative of the potential
+ // function defined by the model. See NOAA Technical Report: The US/UK
+ // World Magnetic Model for 2005-2010 for the derivation.
+ float gcX = 0.0f; // Geocentric northwards component.
+ float gcY = 0.0f; // Geocentric eastwards component.
+ float gcZ = 0.0f; // Geocentric downwards component.
+
+ for (int n = 1; n < MAX_N; n++) {
+ for (int m = 0; m <= n; m++) {
+ // Adjust the coefficients for the current date.
+ float g = G_COEFF[n][m] + yearsSinceBase * DELTA_G[n][m];
+ float h = H_COEFF[n][m] + yearsSinceBase * DELTA_H[n][m];
+
+ // Negative derivative with respect to latitude, divided by
+ // radius. This looks like the negation of the version in the
+ // NOAA Techincal report because that report used
+ // P_n^m(sin(theta)) and we use P_n^m(cos(90 - theta)), so the
+ // derivative with respect to theta is negated.
+ gcX += relativeRadiusPower[n+2]
+ * (g * cosMLon[m] + h * sinMLon[m])
+ * legendre.mPDeriv[n][m]
+ * SCHMIDT_QUASI_NORM_FACTORS[n][m];
+
+ // Negative derivative with respect to longitude, divided by
+ // radius.
+ gcY += relativeRadiusPower[n+2] * m
+ * (g * sinMLon[m] - h * cosMLon[m])
+ * legendre.mP[n][m]
+ * SCHMIDT_QUASI_NORM_FACTORS[n][m]
+ * inverseCosLatitude;
+
+ // Negative derivative with respect to radius.
+ gcZ -= (n + 1) * relativeRadiusPower[n+2]
+ * (g * cosMLon[m] + h * sinMLon[m])
+ * legendre.mP[n][m]
+ * SCHMIDT_QUASI_NORM_FACTORS[n][m];
+ }
+ }
+
+ // Convert back to geodetic coordinates. This is basically just a
+ // rotation around the Y-axis by the difference in latitudes between the
+ // geocentric frame and the geodetic frame.
+ double latDiffRad = Math.toRadians(gdLatitudeDeg) - mGcLatitudeRad;
+ mX = (float) (gcX * Math.cos(latDiffRad)
+ + gcZ * Math.sin(latDiffRad));
+ mY = gcY;
+ mZ = (float) (- gcX * Math.sin(latDiffRad)
+ + gcZ * Math.cos(latDiffRad));
+ }
+
+ /**
+ * @return The X (northward) component of the magnetic field in nanoteslas.
+ */
+ public float getX() {
+ return mX;
+ }
+
+ /**
+ * @return The Y (eastward) component of the magnetic field in nanoteslas.
+ */
+ public float getY() {
+ return mY;
+ }
+
+ /**
+ * @return The Z (downward) component of the magnetic field in nanoteslas.
+ */
+ public float getZ() {
+ return mZ;
+ }
+
+ /**
+ * @return The declination of the horizontal component of the magnetic
+ * field from true north, in degrees (i.e. positive means the
+ * magnetic field is rotated east that much from true north).
+ */
+ public float getDeclination() {
+ return (float) Math.toDegrees(Math.atan2(mY, mX));
+ }
+
+ /**
+ * @return The inclination of the magnetic field in degrees -- positive
+ * means the magnetic field is rotated downwards.
+ */
+ public float getInclination() {
+ return (float) Math.toDegrees(Math.atan2(mZ,
+ getHorizontalStrength()));
+ }
+
+ /**
+ * @return Horizontal component of the field strength in nonoteslas.
+ */
+ public float getHorizontalStrength() {
+ return (float) Math.sqrt(mX * mX + mY * mY);
+ }
+
+ /**
+ * @return Total field strength in nanoteslas.
+ */
+ public float getFieldStrength() {
+ return (float) Math.sqrt(mX * mX + mY * mY + mZ * mZ);
+ }
+
+ /**
+ * @param gdLatitudeDeg
+ * Latitude in WGS84 geodetic coordinates.
+ * @param gdLongitudeDeg
+ * Longitude in WGS84 geodetic coordinates.
+ * @param altitudeMeters
+ * Altitude above sea level in WGS84 geodetic coordinates.
+ * @return Geocentric latitude (i.e. angle between closest point on the
+ * equator and this point, at the center of the earth.
+ */
+ private void computeGeocentricCoordinates(float gdLatitudeDeg,
+ float gdLongitudeDeg,
+ float altitudeMeters) {
+ float altitudeKm = altitudeMeters / 1000.0f;
+ float a2 = EARTH_SEMI_MAJOR_AXIS_KM * EARTH_SEMI_MAJOR_AXIS_KM;
+ float b2 = EARTH_SEMI_MINOR_AXIS_KM * EARTH_SEMI_MINOR_AXIS_KM;
+ double gdLatRad = Math.toRadians(gdLatitudeDeg);
+ float clat = (float) Math.cos(gdLatRad);
+ float slat = (float) Math.sin(gdLatRad);
+ float tlat = slat / clat;
+ float latRad =
+ (float) Math.sqrt(a2 * clat * clat + b2 * slat * slat);
+
+ mGcLatitudeRad = (float) Math.atan(tlat * (latRad * altitudeKm + b2)
+ / (latRad * altitudeKm + a2));
+
+ mGcLongitudeRad = (float) Math.toRadians(gdLongitudeDeg);
+
+ float radSq = altitudeKm * altitudeKm
+ + 2 * altitudeKm * (float) Math.sqrt(a2 * clat * clat +
+ b2 * slat * slat)
+ + (a2 * a2 * clat * clat + b2 * b2 * slat * slat)
+ / (a2 * clat * clat + b2 * slat * slat);
+ mGcRadiusKm = (float) Math.sqrt(radSq);
+ }
+
+
+ /**
+ * Utility class to compute a table of Gauss-normalized associated Legendre
+ * functions P_n^m(cos(theta))
+ */
+ static private class LegendreTable {
+ // These are the Gauss-normalized associated Legendre functions -- that
+ // is, they are normal Legendre functions multiplied by
+ // (n-m)!/(2n-1)!! (where (2n-1)!! = 1*3*5*...*2n-1)
+ public final float[][] mP;
+
+ // Derivative of mP, with respect to theta.
+ public final float[][] mPDeriv;
+
+ /**
+ * @param maxN
+ * The maximum n- and m-values to support
+ * @param thetaRad
+ * Returned functions will be Gauss-normalized
+ * P_n^m(cos(thetaRad)), with thetaRad in radians.
+ */
+ public LegendreTable(int maxN, float thetaRad) {
+ // Compute the table of Gauss-normalized associated Legendre
+ // functions using standard recursion relations. Also compute the
+ // table of derivatives using the derivative of the recursion
+ // relations.
+ float cos = (float) Math.cos(thetaRad);
+ float sin = (float) Math.sin(thetaRad);
+
+ mP = new float[maxN + 1][];
+ mPDeriv = new float[maxN + 1][];
+ mP[0] = new float[] { 1.0f };
+ mPDeriv[0] = new float[] { 0.0f };
+ for (int n = 1; n <= maxN; n++) {
+ mP[n] = new float[n + 1];
+ mPDeriv[n] = new float[n + 1];
+ for (int m = 0; m <= n; m++) {
+ if (n == m) {
+ mP[n][m] = sin * mP[n - 1][m - 1];
+ mPDeriv[n][m] = cos * mP[n - 1][m - 1]
+ + sin * mPDeriv[n - 1][m - 1];
+ } else if (n == 1 || m == n - 1) {
+ mP[n][m] = cos * mP[n - 1][m];
+ mPDeriv[n][m] = -sin * mP[n - 1][m]
+ + cos * mPDeriv[n - 1][m];
+ } else {
+ assert n > 1 && m < n - 1;
+ float k = ((n - 1) * (n - 1) - m * m)
+ / (float) ((2 * n - 1) * (2 * n - 3));
+ mP[n][m] = cos * mP[n - 1][m] - k * mP[n - 2][m];
+ mPDeriv[n][m] = -sin * mP[n - 1][m]
+ + cos * mPDeriv[n - 1][m] - k * mPDeriv[n - 2][m];
+ }
+ }
+ }
+ }
+ }
+
+ /**
+ * Compute the ration between the Gauss-normalized associated Legendre
+ * functions and the Schmidt quasi-normalized version. This is equivalent to
+ * sqrt((m==0?1:2)*(n-m)!/(n+m!))*(2n-1)!!/(n-m)!
+ */
+ private static float[][] computeSchmidtQuasiNormFactors(int maxN) {
+ float[][] schmidtQuasiNorm = new float[maxN + 1][];
+ schmidtQuasiNorm[0] = new float[] { 1.0f };
+ for (int n = 1; n <= maxN; n++) {
+ schmidtQuasiNorm[n] = new float[n + 1];
+ schmidtQuasiNorm[n][0] =
+ schmidtQuasiNorm[n - 1][0] * (2 * n - 1) / (float) n;
+ for (int m = 1; m <= n; m++) {
+ schmidtQuasiNorm[n][m] = schmidtQuasiNorm[n][m - 1]
+ * (float) Math.sqrt((n - m + 1) * (m == 1 ? 2 : 1)
+ / (float) (n + m));
+ }
+ }
+ return schmidtQuasiNorm;
+ }
+} \ No newline at end of file