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 java.util.Collections;
20 import java.util.List;
21 import java.util.regex.Pattern;
22
23 import org.hipparchus.CalculusFieldElement;
24 import org.hipparchus.Field;
25 import org.hipparchus.analysis.interpolation.BilinearInterpolatingFunction;
26 import org.hipparchus.analysis.interpolation.LinearInterpolator;
27 import org.hipparchus.analysis.polynomials.PolynomialSplineFunction;
28 import org.hipparchus.util.FastMath;
29 import org.orekit.annotation.DefaultDataContext;
30 import org.orekit.bodies.FieldGeodeticPoint;
31 import org.orekit.bodies.GeodeticPoint;
32 import org.orekit.data.DataContext;
33 import org.orekit.data.DataProvidersManager;
34 import org.orekit.errors.OrekitException;
35 import org.orekit.errors.OrekitMessages;
36 import org.orekit.models.earth.weather.ConstantPressureTemperatureHumidityProvider;
37 import org.orekit.models.earth.weather.FieldPressureTemperatureHumidity;
38 import org.orekit.models.earth.weather.HeightDependentPressureTemperatureHumidityConverter;
39 import org.orekit.models.earth.weather.PressureTemperatureHumidity;
40 import org.orekit.models.earth.weather.PressureTemperatureHumidityProvider;
41 import org.orekit.models.earth.weather.water.Wang1988;
42 import org.orekit.time.AbsoluteDate;
43 import org.orekit.time.FieldAbsoluteDate;
44 import org.orekit.utils.FieldTrackingCoordinates;
45 import org.orekit.utils.InterpolationTableLoader;
46 import org.orekit.utils.ParameterDriver;
47 import org.orekit.utils.TrackingCoordinates;
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 12.1
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 @DefaultDataContext
134 public ModifiedSaastamoinenModel(final PressureTemperatureHumidityProvider pth0Provider) {
135 this(pth0Provider, defaultDeltaR());
136 }
137
138 /** Create a new Saastamoinen model for the troposphere using the given
139 * environmental conditions. This constructor uses the {@link DataContext#getDefault()
140 * default data context} if {@code deltaRFileName != null}.
141 *
142 * @param pth0Provider provider for atmospheric pressure, temperature and humidity at reference altitude
143 * @param deltaRFileName regular expression for filename containing δR
144 * correction term table (typically {@link #DELTA_R_FILE_NAME}), if null
145 * default values from the reference book are used
146 * @see #ModifiedSaastamoinenModel(PressureTemperatureHumidityProvider, String, DataProvidersManager)
147 */
148 @DefaultDataContext
149 public ModifiedSaastamoinenModel(final PressureTemperatureHumidityProvider pth0Provider,
150 final String deltaRFileName) {
151 this(pth0Provider, deltaRFileName,
152 DataContext.getDefault().getDataProvidersManager());
153 }
154
155 /** Create a new Saastamoinen model for the troposphere using the given
156 * environmental conditions. This constructor allows the user to specify the source of
157 * of the δR file.
158 *
159 * @param pth0Provider provider for atmospheric pressure, temperature and humidity at reference altitude
160 * @param deltaRFileName regular expression for filename containing δR
161 * correction term table (typically {@link #DELTA_R_FILE_NAME}), if null
162 * default values from the reference book are used
163 * @param dataProvidersManager provides access to auxiliary data.
164 */
165 public ModifiedSaastamoinenModel(final PressureTemperatureHumidityProvider pth0Provider,
166 final String deltaRFileName,
167 final DataProvidersManager dataProvidersManager) {
168 this(pth0Provider,
169 deltaRFileName == null ?
170 defaultDeltaR() :
171 loadDeltaR(deltaRFileName, dataProvidersManager));
172 }
173
174 /** Create a new Saastamoinen model.
175 *
176 * @param pth0Provider provider for atmospheric pressure, temperature and humidity at reference altitude
177 * @param deltaR δR correction term function
178 */
179 private ModifiedSaastamoinenModel(final PressureTemperatureHumidityProvider pth0Provider,
180 final BilinearInterpolatingFunction deltaR) {
181 this.pth0Provider = pth0Provider;
182 this.converter = new HeightDependentPressureTemperatureHumidityConverter(WATER);
183 this.deltaRFunction = deltaR;
184 this.lowElevationThreshold = DEFAULT_LOW_ELEVATION_THRESHOLD;
185 }
186
187 /** Create a new Saastamoinen model using a standard atmosphere model.
188 *
189 * <ul>
190 * <li>altitude: 0m</li>
191 * <li>temperature: 18 degree Celsius</li>
192 * <li>pressure: 1013.25 mbar</li>
193 * <li>humidity: 50%</li>
194 * <li>@link {@link Wang1988 Wang 1988} model to compute water vapor pressure</li>
195 * </ul>
196 *
197 * @return a Saastamoinen model with standard environmental values
198 */
199 @DefaultDataContext
200 public static ModifiedSaastamoinenModel getStandardModel() {
201 final double altitude = 0;
202 final double pressure = TroposphericModelUtils.HECTO_PASCAL.toSI(1013.25);
203 final double temperature = 273.15 + 18;
204 final double humidity = 0.5;
205 final PressureTemperatureHumidity pth = new PressureTemperatureHumidity(altitude,
206 pressure,
207 temperature,
208 WATER.waterVaporPressure(pressure,
209 temperature,
210 humidity),
211 Double.NaN,
212 Double.NaN);
213 final PressureTemperatureHumidityProvider pth0Provider = new ConstantPressureTemperatureHumidityProvider(pth);
214 return new ModifiedSaastamoinenModel(pth0Provider);
215 }
216
217 /** Get provider for atmospheric pressure, temperature and humidity at reference altitude.
218 * @return provider for atmospheric pressure, temperature and humidity at reference altitude
219 */
220 public PressureTemperatureHumidityProvider getPth0Provider() {
221 return pth0Provider;
222 }
223
224 /** {@inheritDoc}
225 * <p>
226 * The Saastamoinen model is not defined for altitudes below 0.0. for continuity
227 * reasons, we use the value for h = 0 when altitude is negative.
228 * </p>
229 * <p>
230 * There are also numerical issues for elevation angles close to zero. For continuity reasons,
231 * elevations lower than a threshold will use the value obtained
232 * for the threshold itself.
233 * </p>
234 * @see #getLowElevationThreshold()
235 * @see #setLowElevationThreshold(double)
236 */
237 @Override
238 public TroposphericDelay pathDelay(final TrackingCoordinates trackingCoordinates,
239 final GeodeticPoint point,
240 final PressureTemperatureHumidity weather,
241 final double[] parameters, final AbsoluteDate date) {
242
243 // limit the height to model range
244 final double fixedHeight = FastMath.min(FastMath.max(point.getAltitude(), X_VALUES_FOR_B[0]),
245 X_VALUES_FOR_B[X_VALUES_FOR_B.length - 1]);
246
247 final PressureTemperatureHumidity pth = converter.convert(weather, fixedHeight);
248
249 // interpolate the b correction term
250 final double B = B_FUNCTION.value(fixedHeight);
251
252 // calculate the zenith angle from the elevation
253 final double z = FastMath.abs(0.5 * FastMath.PI -
254 FastMath.max(trackingCoordinates.getElevation(), lowElevationThreshold));
255
256 // get correction factor
257 final double deltaR = getDeltaR(fixedHeight, z);
258
259 // calculate the path delay in m
260 // beware since version 12.1 pressures are in Pa and not in hPa, hence the scaling has changed
261 final double invCos = 1.0 / FastMath.cos(z);
262 final double tan = FastMath.tan(z);
263 final double zh = L0 * pth.getPressure();
264 final double zw = L0 * (T_NUM / pth.getTemperature() + WET_OFFSET) * pth.getWaterVaporPressure();
265 final double sh = zh * invCos;
266 final double sw = (zw - L0 * B * tan * tan) * invCos + deltaR;
267 return new TroposphericDelay(zh, zw, sh, sw);
268
269 }
270
271 /** {@inheritDoc}
272 * <p>
273 * The Saastamoinen model is not defined for altitudes below 0.0. for continuity
274 * reasons, we use the value for h = 0 when altitude is negative.
275 * </p>
276 * <p>
277 * There are also numerical issues for elevation angles close to zero. For continuity reasons,
278 * elevations lower than a threshold will use the value obtained
279 * for the threshold itself.
280 * </p>
281 * @see #getLowElevationThreshold()
282 * @see #setLowElevationThreshold(double)
283 */
284 @Override
285 public <T extends CalculusFieldElement<T>> FieldTroposphericDelay<T> pathDelay(final FieldTrackingCoordinates<T> trackingCoordinates,
286 final FieldGeodeticPoint<T> point,
287 final FieldPressureTemperatureHumidity<T> weather,
288 final T[] parameters, final FieldAbsoluteDate<T> date) {
289
290 // limit the height to model range
291 final T fixedHeight = FastMath.min(FastMath.max(point.getAltitude(), X_VALUES_FOR_B[0]),
292 X_VALUES_FOR_B[X_VALUES_FOR_B.length - 1]);
293
294 final FieldPressureTemperatureHumidity<T> pth = converter.convert(weather, fixedHeight);
295
296 final Field<T> field = date.getField();
297 final T zero = field.getZero();
298
299 // interpolate the b correction term
300 final T B = B_FUNCTION.value(fixedHeight);
301
302 // calculate the zenith angle from the elevation
303 final T z = FastMath.abs(FastMath.max(trackingCoordinates.getElevation(),
304 zero.newInstance(lowElevationThreshold)).negate().
305 add(zero.getPi().multiply(0.5)));
306
307 // get correction factor
308 final T deltaR = getDeltaR(fixedHeight, z, field);
309
310 // calculate the path delay in m
311 // beware since version 12.1 pressures are in Pa and not in hPa, hence the scaling has changed
312 final T invCos = FastMath.cos(z).reciprocal();
313 final T tan = FastMath.tan(z);
314 final T zh = pth.getPressure().multiply(L0);
315 final T zw = pth.getTemperature().reciprocal().multiply(T_NUM).add(WET_OFFSET).
316 multiply(pth.getWaterVaporPressure()).multiply(L0);
317 final T sh = zh.multiply(invCos);
318 final T sw = zw.subtract(B.multiply(tan).multiply(tan).multiply(L0)).multiply(invCos).add(deltaR);
319 return new FieldTroposphericDelay<>(zh, zw, sh, sw);
320
321 }
322
323 /** Calculates the delta R correction term using linear interpolation.
324 * @param height the height of the station in m
325 * @param zenith the zenith angle of the satellite
326 * @return the delta R correction term in m
327 */
328 private double getDeltaR(final double height, final double zenith) {
329 // limit the height to a range of [0, 5000] m
330 final double h = FastMath.min(FastMath.max(0, height), 5000);
331 // limit the zenith angle to 90 degree
332 // Note: the function is symmetric for negative zenith angles
333 final double z = FastMath.min(Math.abs(zenith), 0.5 * FastMath.PI);
334 return deltaRFunction.value(h, z);
335 }
336
337 /** Calculates the delta R correction term using linear interpolation.
338 * @param <T> type of the elements
339 * @param height the height of the station in m
340 * @param zenith the zenith angle of the satellite
341 * @param field field used by default
342 * @return the delta R correction term in m
343 */
344 private <T extends CalculusFieldElement<T>> T getDeltaR(final T height, final T zenith,
345 final Field<T> field) {
346 final T zero = field.getZero();
347 // limit the height to a range of [0, 5000] m
348 final T h = FastMath.min(FastMath.max(zero, height), zero.add(5000));
349 // limit the zenith angle to 90 degree
350 // Note: the function is symmetric for negative zenith angles
351 final T z = FastMath.min(zenith.abs(), zero.getPi().multiply(0.5));
352 return deltaRFunction.value(h, z);
353 }
354
355 /** Load δR function.
356 * @param deltaRFileName regular expression for filename containing δR
357 * correction term table
358 * @param dataProvidersManager provides access to auxiliary data.
359 * @return δR function
360 */
361 private static BilinearInterpolatingFunction loadDeltaR(
362 final String deltaRFileName,
363 final DataProvidersManager dataProvidersManager) {
364
365 // read the δR interpolation function from the config file
366 final InterpolationTableLoader loader = new InterpolationTableLoader();
367 dataProvidersManager.feed(deltaRFileName, loader);
368 if (!loader.stillAcceptsData()) {
369 final double[] elevations = loader.getOrdinateGrid();
370 for (int i = 0; i < elevations.length; ++i) {
371 elevations[i] = FastMath.toRadians(elevations[i]);
372 }
373 return new BilinearInterpolatingFunction(loader.getAbscissaGrid(), elevations,
374 loader.getValuesSamples());
375 }
376 throw new OrekitException(OrekitMessages.UNABLE_TO_FIND_FILE,
377 SECOND_DELTA_R_PATTERN.
378 matcher(FIRST_DELTA_R_PATTERN.matcher(deltaRFileName).replaceAll("")).
379 replaceAll(""));
380 }
381
382 /** Create the default δR function.
383 * @return δR function
384 */
385 private static BilinearInterpolatingFunction defaultDeltaR() {
386
387 // the correction table in the referenced book only contains values for an angle of 60 - 80
388 // degree, thus for 0 degree, the correction term is assumed to be 0, for degrees > 80 it
389 // is assumed to be the same value as for 80.
390
391 // the height in m
392 final double[] xValForR = {
393 0, 500, 1000, 1500, 2000, 3000, 4000, 5000
394 };
395
396 // the zenith angle
397 final double[] yValForR = {
398 FastMath.toRadians( 0.00), FastMath.toRadians(60.00), FastMath.toRadians(66.00), FastMath.toRadians(70.00),
399 FastMath.toRadians(73.00), FastMath.toRadians(75.00), FastMath.toRadians(76.00), FastMath.toRadians(77.00),
400 FastMath.toRadians(78.00), FastMath.toRadians(78.50), FastMath.toRadians(79.00), FastMath.toRadians(79.50),
401 FastMath.toRadians(79.75), FastMath.toRadians(80.00), FastMath.toRadians(90.00)
402 };
403
404 final double[][] fval = new double[][] {
405 {
406 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
407 }, {
408 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
409 }, {
410 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
411 }, {
412 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
413 }, {
414 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
415 }, {
416 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
417 }, {
418 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
419 }, {
420 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
421 }
422 };
423
424 // the actual delta R is interpolated using a a bilinear interpolator
425 return new BilinearInterpolatingFunction(xValForR, yValForR, fval);
426
427 }
428
429 /** {@inheritDoc} */
430 @Override
431 public List<ParameterDriver> getParametersDrivers() {
432 return Collections.emptyList();
433 }
434
435 /** Get the low elevation threshold value for path delay computation.
436 * @return low elevation threshold, in rad.
437 * @see #pathDelay(TrackingCoordinates, GeodeticPoint, PressureTemperatureHumidity, double[], AbsoluteDate)
438 * @see #pathDelay(FieldTrackingCoordinates, FieldGeodeticPoint, FieldPressureTemperatureHumidity, CalculusFieldElement[], FieldAbsoluteDate)
439 * @since 10.2
440 */
441 public double getLowElevationThreshold() {
442 return lowElevationThreshold;
443 }
444
445 /** Set the low elevation threshold value for path delay computation.
446 * @param lowElevationThreshold The new value for the threshold [rad]
447 * @see #pathDelay(TrackingCoordinates, GeodeticPoint, PressureTemperatureHumidity, double[], AbsoluteDate)
448 * @see #pathDelay(FieldTrackingCoordinates, FieldGeodeticPoint, FieldPressureTemperatureHumidity, CalculusFieldElement[], FieldAbsoluteDate)
449 * @since 10.2
450 */
451 public void setLowElevationThreshold(final double lowElevationThreshold) {
452 this.lowElevationThreshold = lowElevationThreshold;
453 }
454 }
455