1 /* Copyright 2011-2012 Space Applications Services
2 * Licensed to CS Communication & Systèmes (CS) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * CS licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.orekit.models.earth.troposphere;
18
19 import org.hipparchus.CalculusFieldElement;
20 import org.hipparchus.Field;
21 import org.hipparchus.analysis.interpolation.BilinearInterpolatingFunction;
22 import org.hipparchus.analysis.interpolation.LinearInterpolator;
23 import org.hipparchus.analysis.polynomials.PolynomialSplineFunction;
24 import org.hipparchus.util.FastMath;
25 import org.orekit.annotation.DefaultDataContext;
26 import org.orekit.bodies.FieldGeodeticPoint;
27 import org.orekit.bodies.GeodeticPoint;
28 import org.orekit.data.DataContext;
29 import org.orekit.data.DataProvidersManager;
30 import org.orekit.errors.OrekitException;
31 import org.orekit.errors.OrekitMessages;
32 import org.orekit.models.earth.weather.ConstantPressureTemperatureHumidityProvider;
33 import org.orekit.models.earth.weather.FieldPressureTemperatureHumidity;
34 import org.orekit.models.earth.weather.HeightDependentPressureTemperatureHumidityConverter;
35 import org.orekit.models.earth.weather.PressureTemperatureHumidity;
36 import org.orekit.models.earth.weather.PressureTemperatureHumidityProvider;
37 import org.orekit.models.earth.weather.water.Wang1988;
38 import org.orekit.time.AbsoluteDate;
39 import org.orekit.time.FieldAbsoluteDate;
40 import org.orekit.utils.FieldTrackingCoordinates;
41 import org.orekit.utils.InterpolationTableLoader;
42 import org.orekit.utils.ParameterDriver;
43 import org.orekit.utils.TrackingCoordinates;
44
45 import java.util.Collections;
46 import java.util.List;
47 import java.util.regex.Pattern;
48
49 /** The modified Saastamoinen model. Estimates the path delay imposed to
50 * electro-magnetic signals by the troposphere according to the formula:
51 * <pre>
52 * δ = 2.277e-3 / cos z * (P + (1255 / T + 0.05) * e - B * tan² z) + δR
53 * </pre>
54 * with the following input data provided to the model:
55 * <ul>
56 * <li>z: zenith angle</li>
57 * <li>P: atmospheric pressure</li>
58 * <li>T: temperature</li>
59 * <li>e: partial pressure of water vapour</li>
60 * <li>B, δR: correction terms</li>
61 * </ul>
62 * <p>
63 * The model supports custom δR correction terms to be read from a
64 * configuration file (saastamoinen-correction.txt) via the
65 * {@link DataProvidersManager}.
66 * </p>
67 * @author Thomas Neidhart
68 * @see "Guochang Xu, GPS - Theory, Algorithms and Applications, Springer, 2007"
69 * @since 12.0
70 */
71 public class ModifiedSaastamoinenModel implements TroposphericModel {
72
73 /** Default file name for δR correction term table. */
74 public static final String DELTA_R_FILE_NAME = "^saastamoinen-correction\\.txt$";
75
76 /** Default lowest acceptable elevation angle [rad]. */
77 public static final double DEFAULT_LOW_ELEVATION_THRESHOLD = 0.05;
78
79 /** Provider for water pressure. */
80 public static final Wang1988 WATER = new Wang1988();
81
82 /** First pattern for δR correction term table. */
83 private static final Pattern FIRST_DELTA_R_PATTERN = Pattern.compile("^\\^");
84
85 /** Second pattern for δR correction term table. */
86 private static final Pattern SECOND_DELTA_R_PATTERN = Pattern.compile("\\$$");
87
88 /** Base delay coefficient. */
89 private static final double L0 = 2.277e-5;
90
91 /** Temperature numerator. */
92 private static final double T_NUM = 1255;
93
94 /** Wet offset. */
95 private static final double WET_OFFSET = 0.05;
96
97 /** X values for the B function. */
98 private static final double[] X_VALUES_FOR_B = {
99 0.0, 500.0, 1000.0, 1500.0, 2000.0, 2500.0, 3000.0, 4000.0, 5000.0
100 };
101
102 /** Y values for the B function.
103 * <p>
104 * The values have been scaled up by a factor 100.0 due to conversion from hPa to Pa.
105 * </p>
106 */
107 private static final double[] Y_VALUES_FOR_B = {
108 115.6, 107.9, 100.6, 93.8, 87.4, 81.3, 75.7, 65.4, 56.3
109 };
110
111 /** Interpolation function for the B correction term. */
112 private static final PolynomialSplineFunction B_FUNCTION = new LinearInterpolator().interpolate(X_VALUES_FOR_B, Y_VALUES_FOR_B);
113
114 /** Interpolation function for the delta R correction term. */
115 private final BilinearInterpolatingFunction deltaRFunction;
116
117 /** Provider for atmospheric pressure, temperature and humidity at reference altitude. */
118 private final PressureTemperatureHumidityProvider pth0Provider;
119
120 /** Height dependent converter for pressure, temperature and humidity. */
121 private final HeightDependentPressureTemperatureHumidityConverter converter;
122
123 /** Lowest acceptable elevation angle [rad]. */
124 private double lowElevationThreshold;
125
126 /**
127 * Create a new Saastamoinen model for the troposphere using the given environmental
128 * conditions and table from the reference book.
129 *
130 * @param pth0Provider provider for atmospheric pressure, temperature and humidity at reference altitude
131 * @see #ModifiedSaastamoinenModel(PressureTemperatureHumidityProvider, String, DataProvidersManager)
132 */
133 public ModifiedSaastamoinenModel(final PressureTemperatureHumidityProvider pth0Provider) {
134 this(pth0Provider, defaultDeltaR());
135 }
136
137 /** Create a new Saastamoinen model for the troposphere using the given
138 * environmental conditions. This constructor uses the {@link DataContext#getDefault()
139 * default data context} if {@code deltaRFileName != null}.
140 *
141 * @param pth0Provider provider for atmospheric pressure, temperature and humidity at reference altitude
142 * @param deltaRFileName regular expression for filename containing δR
143 * correction term table (typically {@link #DELTA_R_FILE_NAME}), if null
144 * default values from the reference book are used
145 * @see #ModifiedSaastamoinenModel(PressureTemperatureHumidityProvider, String, DataProvidersManager)
146 */
147 @DefaultDataContext
148 public ModifiedSaastamoinenModel(final PressureTemperatureHumidityProvider pth0Provider,
149 final String deltaRFileName) {
150 this(pth0Provider, deltaRFileName,
151 DataContext.getDefault().getDataProvidersManager());
152 }
153
154 /** Create a new Saastamoinen model for the troposphere using the given
155 * environmental conditions. This constructor allows the user to specify the source of
156 * of the δR file.
157 *
158 * @param pth0Provider provider for atmospheric pressure, temperature and humidity at reference altitude
159 * @param deltaRFileName regular expression for filename containing δR
160 * correction term table (typically {@link #DELTA_R_FILE_NAME}), if null
161 * default values from the reference book are used
162 * @param dataProvidersManager provides access to auxiliary data.
163 */
164 public ModifiedSaastamoinenModel(final PressureTemperatureHumidityProvider pth0Provider,
165 final String deltaRFileName,
166 final DataProvidersManager dataProvidersManager) {
167 this(pth0Provider,
168 deltaRFileName == null ?
169 defaultDeltaR() :
170 loadDeltaR(deltaRFileName, dataProvidersManager));
171 }
172
173 /** Create a new Saastamoinen model.
174 *
175 * @param pth0Provider provider for atmospheric pressure, temperature and humidity at reference altitude
176 * @param deltaR δR correction term function
177 */
178 private ModifiedSaastamoinenModel(final PressureTemperatureHumidityProvider pth0Provider,
179 final BilinearInterpolatingFunction deltaR) {
180 this.pth0Provider = pth0Provider;
181 this.converter = new HeightDependentPressureTemperatureHumidityConverter(WATER);
182 this.deltaRFunction = deltaR;
183 this.lowElevationThreshold = DEFAULT_LOW_ELEVATION_THRESHOLD;
184 }
185
186 /** Create a new Saastamoinen model using a standard atmosphere model.
187 *
188 * <ul>
189 * <li>altitude: 0m</li>
190 * <li>temperature: 18 degree Celsius</li>
191 * <li>pressure: 1013.25 mbar</li>
192 * <li>humidity: 50%</li>
193 * <li>@link {@link Wang1988 Wang 1988} model to compute water vapor pressure</li>
194 * </ul>
195 *
196 * @return a Saastamoinen model with standard environmental values
197 */
198 public static ModifiedSaastamoinenModel getStandardModel() {
199 final double altitude = 0;
200 final double pressure = TroposphericModelUtils.HECTO_PASCAL.toSI(1013.25);
201 final double temperature = 273.15 + 18;
202 final double humidity = 0.5;
203 final PressureTemperatureHumidity pth = new PressureTemperatureHumidity(altitude,
204 pressure,
205 temperature,
206 WATER.waterVaporPressure(pressure,
207 temperature,
208 humidity),
209 Double.NaN,
210 Double.NaN);
211 final PressureTemperatureHumidityProvider pth0Provider = new ConstantPressureTemperatureHumidityProvider(pth);
212 return new ModifiedSaastamoinenModel(pth0Provider);
213 }
214
215 /** Get provider for atmospheric pressure, temperature and humidity at reference altitude.
216 * @return provider for atmospheric pressure, temperature and humidity at reference altitude
217 */
218 public PressureTemperatureHumidityProvider getPth0Provider() {
219 return pth0Provider;
220 }
221
222 /** {@inheritDoc}
223 * <p>
224 * The Saastamoinen model is not defined for altitudes below 0.0. for continuity
225 * reasons, we use the value for h = 0 when altitude is negative.
226 * </p>
227 * <p>
228 * There are also numerical issues for elevation angles close to zero. For continuity reasons,
229 * elevations lower than a threshold will use the value obtained
230 * for the threshold itself.
231 * </p>
232 * @see #getLowElevationThreshold()
233 * @see #setLowElevationThreshold(double)
234 */
235 @Override
236 public TroposphericDelay pathDelay(final TrackingCoordinates trackingCoordinates,
237 final GeodeticPoint point,
238 final double[] parameters, final AbsoluteDate date) {
239
240 // limit the height to model range
241 final double fixedHeight = FastMath.min(FastMath.max(point.getAltitude(), X_VALUES_FOR_B[0]),
242 X_VALUES_FOR_B[X_VALUES_FOR_B.length - 1]);
243
244 final PressureTemperatureHumidity pth0 = pth0Provider.getWeatherParameters(point, date);
245 final PressureTemperatureHumidity pth = converter.convert(pth0, fixedHeight);
246
247 // interpolate the b correction term
248 final double B = B_FUNCTION.value(fixedHeight);
249
250 // calculate the zenith angle from the elevation
251 final double z = FastMath.abs(0.5 * FastMath.PI -
252 FastMath.max(trackingCoordinates.getElevation(), lowElevationThreshold));
253
254 // get correction factor
255 final double deltaR = getDeltaR(fixedHeight, z);
256
257 // calculate the path delay in m
258 // beware since version 12.1 pressures are in Pa and not in hPa, hence the scaling has changed
259 final double invCos = 1.0 / FastMath.cos(z);
260 final double tan = FastMath.tan(z);
261 final double zh = L0 * pth.getPressure();
262 final double zw = L0 * (T_NUM / pth.getTemperature() + WET_OFFSET) * pth.getWaterVaporPressure();
263 final double sh = zh * invCos;
264 final double sw = (zw - L0 * B * tan * tan) * invCos + deltaR;
265 return new TroposphericDelay(zh, zw, sh, sw);
266
267 }
268
269 /** {@inheritDoc}
270 * <p>
271 * The Saastamoinen model is not defined for altitudes below 0.0. for continuity
272 * reasons, we use the value for h = 0 when altitude is negative.
273 * </p>
274 * <p>
275 * There are also numerical issues for elevation angles close to zero. For continuity reasons,
276 * elevations lower than a threshold will use the value obtained
277 * for the threshold itself.
278 * </p>
279 * @see #getLowElevationThreshold()
280 * @see #setLowElevationThreshold(double)
281 */
282 @Override
283 public <T extends CalculusFieldElement<T>> FieldTroposphericDelay<T> pathDelay(final FieldTrackingCoordinates<T> trackingCoordinates,
284 final FieldGeodeticPoint<T> point,
285 final T[] parameters, final FieldAbsoluteDate<T> date) {
286
287 // limit the height to model range
288 final T fixedHeight = FastMath.min(FastMath.max(point.getAltitude(), X_VALUES_FOR_B[0]),
289 X_VALUES_FOR_B[X_VALUES_FOR_B.length - 1]);
290
291 final FieldPressureTemperatureHumidity<T> pth0 = pth0Provider.getWeatherParameters(point, date);
292 final FieldPressureTemperatureHumidity<T> pth = converter.convert(pth0, fixedHeight);
293
294 final Field<T> field = date.getField();
295 final T zero = field.getZero();
296
297 // interpolate the b correction term
298 final T B = B_FUNCTION.value(fixedHeight);
299
300 // calculate the zenith angle from the elevation
301 final T z = FastMath.abs(FastMath.max(trackingCoordinates.getElevation(),
302 zero.newInstance(lowElevationThreshold)).negate().
303 add(zero.getPi().multiply(0.5)));
304
305 // get correction factor
306 final T deltaR = getDeltaR(fixedHeight, z, field);
307
308 // calculate the path delay in m
309 // beware since version 12.1 pressures are in Pa and not in hPa, hence the scaling has changed
310 final T invCos = FastMath.cos(z).reciprocal();
311 final T tan = FastMath.tan(z);
312 final T zh = pth.getPressure().multiply(L0);
313 final T zw = pth.getTemperature().reciprocal().multiply(T_NUM).add(WET_OFFSET).
314 multiply(pth.getWaterVaporPressure()).multiply(L0);
315 final T sh = zh.multiply(invCos);
316 final T sw = zw.subtract(B.multiply(tan).multiply(tan).multiply(L0)).multiply(invCos).add(deltaR);
317 return new FieldTroposphericDelay<>(zh, zw, sh, sw);
318
319 }
320
321 /** Calculates the delta R correction term using linear interpolation.
322 * @param height the height of the station in m
323 * @param zenith the zenith angle of the satellite
324 * @return the delta R correction term in m
325 */
326 private double getDeltaR(final double height, final double zenith) {
327 // limit the height to a range of [0, 5000] m
328 final double h = FastMath.min(FastMath.max(0, height), 5000);
329 // limit the zenith angle to 90 degree
330 // Note: the function is symmetric for negative zenith angles
331 final double z = FastMath.min(Math.abs(zenith), 0.5 * FastMath.PI);
332 return deltaRFunction.value(h, z);
333 }
334
335 /** Calculates the delta R correction term using linear interpolation.
336 * @param <T> type of the elements
337 * @param height the height of the station in m
338 * @param zenith the zenith angle of the satellite
339 * @param field field used by default
340 * @return the delta R correction term in m
341 */
342 private <T extends CalculusFieldElement<T>> T getDeltaR(final T height, final T zenith,
343 final Field<T> field) {
344 final T zero = field.getZero();
345 // limit the height to a range of [0, 5000] m
346 final T h = FastMath.min(FastMath.max(zero, height), zero.add(5000));
347 // limit the zenith angle to 90 degree
348 // Note: the function is symmetric for negative zenith angles
349 final T z = FastMath.min(zenith.abs(), zero.getPi().multiply(0.5));
350 return deltaRFunction.value(h, z);
351 }
352
353 /** Load δR function.
354 * @param deltaRFileName regular expression for filename containing δR
355 * correction term table
356 * @param dataProvidersManager provides access to auxiliary data.
357 * @return δR function
358 */
359 private static BilinearInterpolatingFunction loadDeltaR(
360 final String deltaRFileName,
361 final DataProvidersManager dataProvidersManager) {
362
363 // read the δR interpolation function from the config file
364 final InterpolationTableLoader loader = new InterpolationTableLoader();
365 dataProvidersManager.feed(deltaRFileName, loader);
366 if (!loader.stillAcceptsData()) {
367 final double[] elevations = loader.getOrdinateGrid();
368 for (int i = 0; i < elevations.length; ++i) {
369 elevations[i] = FastMath.toRadians(elevations[i]);
370 }
371 return new BilinearInterpolatingFunction(loader.getAbscissaGrid(), elevations,
372 loader.getValuesSamples());
373 }
374 throw new OrekitException(OrekitMessages.UNABLE_TO_FIND_FILE,
375 SECOND_DELTA_R_PATTERN.
376 matcher(FIRST_DELTA_R_PATTERN.matcher(deltaRFileName).replaceAll("")).
377 replaceAll(""));
378 }
379
380 /** Create the default δR function.
381 * @return δR function
382 */
383 private static BilinearInterpolatingFunction defaultDeltaR() {
384
385 // the correction table in the referenced book only contains values for an angle of 60 - 80
386 // degree, thus for 0 degree, the correction term is assumed to be 0, for degrees > 80 it
387 // is assumed to be the same value as for 80.
388
389 // the height in m
390 final double[] xValForR = {
391 0, 500, 1000, 1500, 2000, 3000, 4000, 5000
392 };
393
394 // the zenith angle
395 final double[] yValForR = {
396 FastMath.toRadians( 0.00), FastMath.toRadians(60.00), FastMath.toRadians(66.00), FastMath.toRadians(70.00),
397 FastMath.toRadians(73.00), FastMath.toRadians(75.00), FastMath.toRadians(76.00), FastMath.toRadians(77.00),
398 FastMath.toRadians(78.00), FastMath.toRadians(78.50), FastMath.toRadians(79.00), FastMath.toRadians(79.50),
399 FastMath.toRadians(79.75), FastMath.toRadians(80.00), FastMath.toRadians(90.00)
400 };
401
402 final double[][] fval = new double[][] {
403 {
404 0.000, 0.003, 0.006, 0.012, 0.020, 0.031, 0.039, 0.050, 0.065, 0.075, 0.087, 0.102, 0.111, 0.121, 0.121
405 }, {
406 0.000, 0.003, 0.006, 0.011, 0.018, 0.028, 0.035, 0.045, 0.059, 0.068, 0.079, 0.093, 0.101, 0.110, 0.110
407 }, {
408 0.000, 0.002, 0.005, 0.010, 0.017, 0.025, 0.032, 0.041, 0.054, 0.062, 0.072, 0.085, 0.092, 0.100, 0.100
409 }, {
410 0.000, 0.002, 0.005, 0.009, 0.015, 0.023, 0.029, 0.037, 0.049, 0.056, 0.065, 0.077, 0.083, 0.091, 0.091
411 }, {
412 0.000, 0.002, 0.004, 0.008, 0.013, 0.021, 0.026, 0.033, 0.044, 0.051, 0.059, 0.070, 0.076, 0.083, 0.083
413 }, {
414 0.000, 0.002, 0.003, 0.006, 0.011, 0.017, 0.021, 0.027, 0.036, 0.042, 0.049, 0.058, 0.063, 0.068, 0.068
415 }, {
416 0.000, 0.001, 0.003, 0.005, 0.009, 0.014, 0.017, 0.022, 0.030, 0.034, 0.040, 0.047, 0.052, 0.056, 0.056
417 }, {
418 0.000, 0.001, 0.002, 0.004, 0.007, 0.011, 0.014, 0.018, 0.024, 0.028, 0.033, 0.039, 0.043, 0.047, 0.047
419 }
420 };
421
422 // the actual delta R is interpolated using a a bilinear interpolator
423 return new BilinearInterpolatingFunction(xValForR, yValForR, fval);
424
425 }
426
427 /** {@inheritDoc} */
428 @Override
429 public List<ParameterDriver> getParametersDrivers() {
430 return Collections.emptyList();
431 }
432
433 /** Get the low elevation threshold value for path delay computation.
434 * @return low elevation threshold, in rad.
435 * @see #pathDelay(TrackingCoordinates, GeodeticPoint, double[], AbsoluteDate)
436 * @see #pathDelay(FieldTrackingCoordinates, FieldGeodeticPoint, CalculusFieldElement[], FieldAbsoluteDate)
437 * @since 10.2
438 */
439 public double getLowElevationThreshold() {
440 return lowElevationThreshold;
441 }
442
443 /** Set the low elevation threshold value for path delay computation.
444 * @param lowElevationThreshold The new value for the threshold [rad]
445 * @see #pathDelay(TrackingCoordinates, GeodeticPoint, double[], AbsoluteDate)
446 * @see #pathDelay(FieldTrackingCoordinates, FieldGeodeticPoint, CalculusFieldElement[], FieldAbsoluteDate)
447 * @since 10.2
448 */
449 public void setLowElevationThreshold(final double lowElevationThreshold) {
450 this.lowElevationThreshold = lowElevationThreshold;
451 }
452 }
453