/*
* 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.Calendar;
import java.util.TimeZone;
/**
* 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-2020 which is valid until 2025, 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* Android may use a newer version of the model.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 nanoteslas 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 2020-2025
static private final float[][] G_COEFF = new float[][]{
{0.0f},
{-29404.5f, -1450.7f},
{-2500.0f, 2982.0f, 1676.8f},
{1363.9f, -2381.0f, 1236.2f, 525.7f},
{903.1f, 809.4f, 86.2f, -309.4f, 47.9f},
{-234.4f, 363.1f, 187.8f, -140.7f, -151.2f, 13.7f},
{65.9f, 65.6f, 73.0f, -121.5f, -36.2f, 13.5f, -64.7f},
{80.6f, -76.8f, -8.3f, 56.5f, 15.8f, 6.4f, -7.2f, 9.8f},
{23.6f, 9.8f, -17.5f, -0.4f, -21.1f, 15.3f, 13.7f, -16.5f, -0.3f},
{5.0f, 8.2f, 2.9f, -1.4f, -1.1f, -13.3f, 1.1f, 8.9f, -9.3f, -11.9f},
{-1.9f, -6.2f, -0.1f, 1.7f, -0.9f, 0.6f, -0.9f, 1.9f, 1.4f, -2.4f, -3.9f},
{3.0f, -1.4f, -2.5f, 2.4f, -0.9f, 0.3f, -0.7f, -0.1f, 1.4f, -0.6f, 0.2f, 3.1f},
{-2.0f, -0.1f, 0.5f, 1.3f, -1.2f, 0.7f, 0.3f, 0.5f, -0.2f, -0.5f, 0.1f, -1.1f, -0.3f}};
static private final float[][] H_COEFF = new float[][]{
{0.0f},
{0.0f, 4652.9f},
{0.0f, -2991.6f, -734.8f},
{0.0f, -82.2f, 241.8f, -542.9f},
{0.0f, 282.0f, -158.4f, 199.8f, -350.1f},
{0.0f, 47.7f, 208.4f, -121.3f, 32.2f, 99.1f},
{0.0f, -19.1f, 25.0f, 52.7f, -64.4f, 9.0f, 68.1f},
{0.0f, -51.4f, -16.8f, 2.3f, 23.5f, -2.2f, -27.2f, -1.9f},
{0.0f, 8.4f, -15.3f, 12.8f, -11.8f, 14.9f, 3.6f, -6.9f, 2.8f},
{0.0f, -23.3f, 11.1f, 9.8f, -5.1f, -6.2f, 7.8f, 0.4f, -1.5f, 9.7f},
{0.0f, 3.4f, -0.2f, 3.5f, 4.8f, -8.6f, -0.1f, -4.2f, -3.4f, -0.1f, -8.8f},
{0.0f, 0.0f, 2.6f, -0.5f, -0.4f, 0.6f, -0.2f, -1.7f, -1.6f, -3.0f, -2.0f, -2.6f},
{0.0f, -1.2f, 0.5f, 1.3f, -1.8f, 0.1f, 0.7f, -0.1f, 0.6f, 0.2f, -0.9f, 0.0f, 0.5f}};
static private final float[][] DELTA_G = new float[][]{
{0.0f},
{6.7f, 7.7f},
{-11.5f, -7.1f, -2.2f},
{2.8f, -6.2f, 3.4f, -12.2f},
{-1.1f, -1.6f, -6.0f, 5.4f, -5.5f},
{-0.3f, 0.6f, -0.7f, 0.1f, 1.2f, 1.0f},
{-0.6f, -0.4f, 0.5f, 1.4f, -1.4f, 0.0f, 0.8f},
{-0.1f, -0.3f, -0.1f, 0.7f, 0.2f, -0.5f, -0.8f, 1.0f},
{-0.1f, 0.1f, -0.1f, 0.5f, -0.1f, 0.4f, 0.5f, 0.0f, 0.4f},
{-0.1f, -0.2f, 0.0f, 0.4f, -0.3f, 0.0f, 0.3f, 0.0f, 0.0f, -0.4f},
{0.0f, 0.0f, 0.0f, 0.2f, -0.1f, -0.2f, 0.0f, -0.1f, -0.2f, -0.1f, 0.0f},
{0.0f, -0.1f, 0.0f, 0.0f, 0.0f, -0.1f, 0.0f, 0.0f, -0.1f, -0.1f, -0.1f, -0.1f},
{0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.1f}};
static private final float[][] DELTA_H = new float[][]{
{0.0f},
{0.0f, -25.1f},
{0.0f, -30.2f, -23.9f},
{0.0f, 5.7f, -1.0f, 1.1f},
{0.0f, 0.2f, 6.9f, 3.7f, -5.6f},
{0.0f, 0.1f, 2.5f, -0.9f, 3.0f, 0.5f},
{0.0f, 0.1f, -1.8f, -1.4f, 0.9f, 0.1f, 1.0f},
{0.0f, 0.5f, 0.6f, -0.7f, -0.2f, -1.2f, 0.2f, 0.3f},
{0.0f, -0.3f, 0.7f, -0.2f, 0.5f, -0.3f, -0.5f, 0.4f, 0.1f},
{0.0f, -0.3f, 0.2f, -0.4f, 0.4f, 0.1f, 0.0f, -0.2f, 0.5f, 0.2f},
{0.0f, 0.0f, 0.1f, -0.3f, 0.1f, -0.2f, 0.1f, 0.0f, -0.1f, 0.2f, 0.0f},
{0.0f, 0.0f, 0.1f, 0.0f, 0.2f, 0.0f, 0.0f, 0.1f, 0.0f, -0.1f, 0.0f, 0.0f},
{0.0f, 0.0f, 0.0f, -0.1f, 0.1f, 0.0f, 0.0f, 0.0f, 0.1f, 0.0f, 0.0f, 0.0f, -0.1f}};
static private final long BASE_TIME = new Calendar.Builder()
.setTimeZone(TimeZone.getTimeZone("UTC"))
.setDate(2020, Calendar.JANUARY, 1)
.build()
.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 2020-2025 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 Technical 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 nanoteslas.
*/
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;
}
}