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
17package android.hardware;
18
19import 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31 * Android may use a newer version of the model.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 */
33public 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.sqrt(mX * mX + mY * 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