| /* |
| * 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; |
| |
| /** |
| * Estimates 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-2015 which is valid until 2020, but should |
| * produce acceptable results for several years after that. Future versions of |
| * Android may use a newer version of the model. |
| */ |
| 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 = 6356.7523142f; |
| 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 2015-2020 |
| static private final float[][] G_COEFF = new float[][] { |
| { 0.0f }, |
| { -29438.5f, -1501.1f }, |
| { -2445.3f, 3012.5f, 1676.6f }, |
| { 1351.1f, -2352.3f, 1225.6f, 581.9f }, |
| { 907.2f, 813.7f, 120.3f, -335.0f, 70.3f }, |
| { -232.6f, 360.1f, 192.4f, -141.0f, -157.4f, 4.3f }, |
| { 69.5f, 67.4f, 72.8f, -129.8f, -29.0f, 13.2f, -70.9f }, |
| { 81.6f, -76.1f, -6.8f, 51.9f, 15.0f, 9.3f, -2.8f, 6.7f }, |
| { 24.0f, 8.6f, -16.9f, -3.2f, -20.6f, 13.3f, 11.7f, -16.0f, -2.0f }, |
| { 5.4f, 8.8f, 3.1f, -3.1f, 0.6f, -13.3f, -0.1f, 8.7f, -9.1f, -10.5f }, |
| { -1.9f, -6.5f, 0.2f, 0.6f, -0.6f, 1.7f, -0.7f, 2.1f, 2.3f, -1.8f, -3.6f }, |
| { 3.1f, -1.5f, -2.3f, 2.1f, -0.9f, 0.6f, -0.7f, 0.2f, 1.7f, -0.2f, 0.4f, 3.5f }, |
| { -2.0f, -0.3f, 0.4f, 1.3f, -0.9f, 0.9f, 0.1f, 0.5f, -0.4f, -0.4f, 0.2f, -0.9f, 0.0f } }; |
| |
| static private final float[][] H_COEFF = new float[][] { |
| { 0.0f }, |
| { 0.0f, 4796.2f }, |
| { 0.0f, -2845.6f, -642.0f }, |
| { 0.0f, -115.3f, 245.0f, -538.3f }, |
| { 0.0f, 283.4f, -188.6f, 180.9f, -329.5f }, |
| { 0.0f, 47.4f, 196.9f, -119.4f, 16.1f, 100.1f }, |
| { 0.0f, -20.7f, 33.2f, 58.8f, -66.5f, 7.3f, 62.5f }, |
| { 0.0f, -54.1f, -19.4f, 5.6f, 24.4f, 3.3f, -27.5f, -2.3f }, |
| { 0.0f, 10.2f, -18.1f, 13.2f, -14.6f, 16.2f, 5.7f, -9.1f, 2.2f }, |
| { 0.0f, -21.6f, 10.8f, 11.7f, -6.8f, -6.9f, 7.8f, 1.0f, -3.9f, 8.5f }, |
| { 0.0f, 3.3f, -0.3f, 4.6f, 4.4f, -7.9f, -0.6f, -4.1f, -2.8f, -1.1f, -8.7f }, |
| { 0.0f, -0.1f, 2.1f, -0.7f, -1.1f, 0.7f, -0.2f, -2.1f, -1.5f, -2.5f, -2.0f, -2.3f }, |
| { 0.0f, -1.0f, 0.5f, 1.8f, -2.2f, 0.3f, 0.7f, -0.1f, 0.3f, 0.2f, -0.9f, -0.2f, 0.7f } }; |
| |
| static private final float[][] DELTA_G = new float[][] { |
| { 0.0f }, |
| { 10.7f, 17.9f }, |
| { -8.6f, -3.3f, 2.4f }, |
| { 3.1f, -6.2f, -0.4f, -10.4f }, |
| { -0.4f, 0.8f, -9.2f, 4.0f, -4.2f }, |
| { -0.2f, 0.1f, -1.4f, 0.0f, 1.3f, 3.8f }, |
| { -0.5f, -0.2f, -0.6f, 2.4f, -1.1f, 0.3f, 1.5f }, |
| { 0.2f, -0.2f, -0.4f, 1.3f, 0.2f, -0.4f, -0.9f, 0.3f }, |
| { 0.0f, 0.1f, -0.5f, 0.5f, -0.2f, 0.4f, 0.2f, -0.4f, 0.3f }, |
| { 0.0f, -0.1f, -0.1f, 0.4f, -0.5f, -0.2f, 0.1f, 0.0f, -0.2f, -0.1f }, |
| { 0.0f, 0.0f, -0.1f, 0.3f, -0.1f, -0.1f, -0.1f, 0.0f, -0.2f, -0.1f, -0.2f }, |
| { 0.0f, 0.0f, -0.1f, 0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.1f, -0.1f }, |
| { 0.1f, 0.0f, 0.0f, 0.1f, -0.1f, 0.0f, 0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f } }; |
| |
| static private final float[][] DELTA_H = new float[][] { |
| { 0.0f }, |
| { 0.0f, -26.8f }, |
| { 0.0f, -27.1f, -13.3f }, |
| { 0.0f, 8.4f, -0.4f, 2.3f }, |
| { 0.0f, -0.6f, 5.3f, 3.0f, -5.3f }, |
| { 0.0f, 0.4f, 1.6f, -1.1f, 3.3f, 0.1f }, |
| { 0.0f, 0.0f, -2.2f, -0.7f, 0.1f, 1.0f, 1.3f }, |
| { 0.0f, 0.7f, 0.5f, -0.2f, -0.1f, -0.7f, 0.1f, 0.1f }, |
| { 0.0f, -0.3f, 0.3f, 0.3f, 0.6f, -0.1f, -0.2f, 0.3f, 0.0f }, |
| { 0.0f, -0.2f, -0.1f, -0.2f, 0.1f, 0.1f, 0.0f, -0.2f, 0.4f, 0.3f }, |
| { 0.0f, 0.1f, -0.1f, 0.0f, 0.0f, -0.2f, 0.1f, -0.1f, -0.2f, 0.1f, -0.1f }, |
| { 0.0f, 0.0f, 0.1f, 0.0f, 0.1f, 0.0f, 0.0f, 0.1f, 0.0f, -0.1f, 0.0f, -0.1f }, |
| { 0.0f, 0.0f, 0.0f, -0.1f, 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(2015, 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 2015-2020 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.hypot(mX, 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; |
| } |
| } |