cET 318 6. observable and error Sources The Slxth Lecture 6. Observable and error 1. GPS Error Source? 2. How to improve the Observation Sources Book:p.87-129 Dr Guoqing Zhou 1. 1 Error Categories 1. Errors related to GPs Satellites 2. Errors related to GPS signal propagation 1. Error Sources 3. Error related to GPS receivers 1. Errors Related to GPs Satellites 1. 2 Basic Measurement of Eliminating These errors Relativistic effect 2. Errors Related to GPS Signal Propagation ionospheric refraction 2. Observation Approaches(relative surveying, Multi-path effect 3. GPS Receiver Selection( Hardware: good antenna 3. Error Related to GPS Receivers · Receiver clock error Receiver position Antenna geometric center
1 Dr. Guoqing Zhou 6. Observable and Error Sources CET 318 Book: p. 87-129 6. Observabnle and Error Sources 1. GPS Error Source? 2. How to improve the Observation Accuracy? 1. Error Sources 1.1 Error Categories 1. Errors related to GPS Satellites 2. Errors related to GPS signal propagation in atmosphere 3. Error related to GPS receivers 1. Errors Related to GPS Satellites • Ephemerides error • Clock error • Relativistic effect 2. Errors Related to GPS Signal Propagation • Ionospheric refraction • Tropospheric refraction • Multi-path effect 3. Error Related to GPS Receivers • Receiver clock error • Receiver position • Antenna geometric center 1.2 Basic Measurement of Eliminating These Errors 1. Correction by Models 2. Observation Approaches (relative surveying, DGPS), Observation Time (time, date) 3. GPS Receiver Selection (Hardware: good antenna for multipath, avoid building
2.1 Phase and Group velocity(why we use tw frequencies A single electromagnetic wave propagating: The velocity of phase. λ f GPS Li,2 2. Atmospheric Effect (n. 97-118) A group of waves with different ncies, the group ropagation velocity is ith refractive 2.2 ionospheric Refraction Refractive Index for single and group wave are The ionosphere, extending In various lavers from about 50 km to 1000 km above earth, is a dispersive medium n=1+ with respect to the gPs radio signal With different velocities, a group delay and a phase dvance pproximates the phase Why the phase observation can reach higher efractive index accuracy than the pseudoranges observation c4 1. GPS code measurements are delayed and the carrier phases are advanced. 2. The code pseudoranges are measured too long and the carrier phase pseudoranges are measured too short compared to the geometric range between the satellite and the receiver I Ionospheric Refraction (IR): A Measuring the TEC (p. 102 The difference between measured and geometric range is called IR 2. Estimating the TEC (p. 102) 2. Relationship: IR(Alon)& TEC (p. 100) 3. Computing the Effect of tEC by Model D103 TEC 4. Eliminating the Effect of TEc(p. 104) 3. TEC: Total Electron Content Taking all these effects into account, a gPs pseudorange TEC=N ionospheric the TEC computed by models, or eliminated
2 2. Atmospheric Effect (p. 97-118) 2.1 Phase and Group Velocity (Why we use two frequencies?) A single electromagnetic wave propagating: The velocity of phase. v f ph = λ A group of waves with different frequencies, the group velocity 2 λ d λ df v gr = Propagation velocity is related with refractive index. GPS L1, L2 The ionosphere, extending in various layers from about 50 km to 1000 km above earth, is a dispersive medium with respect to the GPS radio signal. 2.2 Ionospheric Refraction = + 2 + 3 + 4 + Λ 2 3 4 1 f c f c f c n ph The following series of approximates the phase refractive index. With different velocities, a group delay and a phase advance. 2 2 1 f c nph = + 2 2 1 f c ngr = − Refractive Index for single and group wave are 1. GPS code measurements are delayed and the carrier phases are advanced. 2. The code pseudoranges are measured too long and the carrier phase pseudoranges are measured too short compared to the geometric range between the satellite and the receiver. Why the phase observation can reach higher accuracy than the pseudoranges observation? 1. Ionospheric Refraction (IR): ∆Iono The difference between measured and geometric range is called IR. 2. Relationship: IR(∆Iono) & TEC (p.100) TEC f Iono ph 2 40.3 ∆ = − TEC f Iono gr 2 40.3 ∆ = 3. TEC: Total Electron Content ∫ TEC = Neds0 Error caused by the ionospheric & the determination of the TEC. The TEC may be measured, estimated, its effect computed by models, or eliminated. Taking all these effects into account, a GPS pseudorange may be wrong from about 0.15 m to 50 m. 1. Measuring the TEC (p.102) 2. Estimating the TEC (p.102) 3. Computing the Effect of TEC by Model (p.103) 4. Eliminating the Effect of TEC (p.104)
2.3 Tropospheric Refraction It is impossible to eliminate the tropospheric Definition: The effect of the mosphere (i.e. refraction by dual frequeney method fraction, tropospheric pat Why The neutral atr incorrect respect to radio waves up to fre it excludes hus, the propa equeneces t. GHz stratosphere hd≈40km which is another a distinction between carrier phases and code constituent of the / hull km h=0 derived from different carriers Ll or L2 is not cetral atmosphe parths Empirical Model: Model Comparison Models for the dry and wet refractivity at the surface of the When E>30%, the correction of troposphere correction is almost same. In other words the difference of 1. Hopfield Model different models is small when the zenith is >3 2. Improved Hopfield Model 2. The difference between Black model and Hopfield 3. Saastamoinen model model is small(<Imm) when Zenith angle is almost 3. The difference between Saast. Model and Hopfield 5. Model using the Mapping Function of Marini model is big. This difference largely depends on temperature, and water vapor, but not much the atmospheric pressure Model Problems: 1. There are many other tropospheric models which are similar to the models given here 2. Why so many different Model? One reason is the difficulty in modeling the water vapor 3. Relativistic effects Zenith Problems: I. Any standard model suffers from the estimation nd parameters 2. Another approach is to the zenith delay the least squares nt of the phas observations 3. Some processing software offers this option
3 2.3 Tropospheric Refraction Definition: The effect of the neutral atmosphere (i.e., the nonionized part) is denoted as tropospheric refraction, tropospheric path delay, or simply tropospheric delay. The naming is slightly incorrect because it excludes the stratosphere which is another constituent of the neutral atmosphere. The neutral atmosphere is a nondispersive medium with respect to radio waves up to frequencies of 1.5 GHz. Thus, the propagation is frequency independent. Thus, a distinction between carrier phases and code ranges derived from different carriers L1 or L2 is not necessary. It is impossible to eliminate the tropospheric refraction by dual frequency methods. Why ? Because: Models for the dry and wet refractivity at the surface of the earth have been modeled: Empirical Model: 1. Hopfield Model 2. Improved Hopfield Model 3. Saastamoinen Model 4. Block Model 5. Model using the Mapping Function of Marini Model Comparison: 1. When E>30°, the correction of troposphere correction is almost same. In other words, the difference of different models is small when the zenith is > 30° 2. The difference between Black model and Hopfield model is small (<1mm) when Zenith angle is almost 90°. 3. The difference between Saast. Model and Hopfield model is big. This difference largely depends on temperature, and water vapor, but not much the atmospheric pressure. 1. Any standard model suffers from the estimation of the zenith delay from measured ground parameters. 2. Another approach is to estimate the zenith delay in the least squares adjustment of the phase observations. 3. Some processing software offers this option. Zenith Problems: 1. There are many other tropospheric models which are similar to the models given here. 2. Why so many different Model? One reason is the difficulty in modeling the water vapor. Model Problems: 3. Relativistic Effects
L Overview of Basic Relativistic Theory 3.1 Special Relativity Why have to consider relativistic effect on GPS L. Lorentz transformation measurement? 2. Time dilation Velocity of GPS (TIME) 3. Lorentz Contraction Earth rotation(SPACE) 4. Second-Order Doppler Effect 5. Mass relation 3.2 General Relativity I. Relevant relativistic Effects on gps The theory of special and general An accelerated I. Relativity Affecting to Satellite Orbit relativity must be taken into RF (each GPS) 2. Relativity Affecting to Satellite Signal Relativistic effects are relevant for 1. Satellite orbit 2. Satellite signal propagation 3. Relativity Affecting to Satellite Clock 4. Relativity Affecting to Receiver Clock un, moon, all other masses in the solar system( negligible). The correction is usually performed by the receiver software at rest. in the the gravitational field of the earth must be considered earth Two Center: The phase center of the antennas is a point to which the radio signal measurement referred and generally is not identical with the geometric antenna center. 4. Antenna phase center offset variation azimuth, and the intensity of the satellite signal and is different for LI and L2 Two effects offset The precision of an antenna should be based on the antenna phase center variation and not on the offset
4 Why have to consider relativistic effect on GPS measurement? • Velocity of GPS (TIME) • Earth rotation (SPACE) 3.1 Special Relativity 1. Lorentz Transformation 2. Time Dilation 3. Lorentz Contraction 4. Second-Order Doppler Effect 5. Mass Relation I. Overview of Basic Relativistic Theory 3.2 General Relativity II. Relevant Relativistic Effects on GPS The theory of special and general relativity must be taken into account. Relativistic effects are relevant for 1. Satellite orbit 2. Satellite signal propagation 3. Satellite and receiver clock 4. Sun, moon, all other masses in the solar system ( negligible). RF(relatively) at rest: in the center of the earth. With respect to general relativity, Ash shows that only the gravitational field of the earth must be considered. An accelerated RF (each GPS) 1. Relativity Affecting to Satellite Orbit 2. Relativity Affecting to Satellite Signal Example: 3. Relativity Affecting to Satellite Clock 4. Relativity Affecting to Receiver Clock The correction is usually performed by the receiver software. 4. Antenna Phase Center Offset & Variation Two Center: The phase center of the antennas is a point to which the radio signal measurement is referred and generally is not identical with the geometric antenna center. Results: The offset depends on the elevation, the azimuth, and the intensity of the satellite signal and is different for L1 and L2. Two effects: • offset • variation of the antenna phase center The precision of an antenna should be based on the antenna phase center variation and not on the offset
Different Antennas: Helices 5. Multipath The direct computation of the antenna effects on the distance measurements with respect to azimuth an elevation was proposed Multipath: a satellite emitted signal arrives at the receiver via more than one path There is no general model of the multipath effect because of Causes: he arbitrarily different geometric situations 1. reflecting surfaces near the receiver Estimation methods: 2. reflections at the satellite during signal transmission The influence of the multipath can be estimated Result: oposphere, clock errors, and relativistic effects Phase differences differences of the path Improvement Methods: Er rror 1. Selecting an antenna that takes advantage of the signal 10-20 m for code pseudoranges 2. digital filtering, wideband antennas, radio frequency about 100 m in the vicinity of buildings absorbent antenna ground planes, and choke ring on carrier phases for relative positionin antennas baselines, generally, not be greater tha satellite geometry and a reasonably long 二c 3. The absorbent antenna ground plane reduces the interference of satellite signals with low or even negative nterval) elevation angles which occur in case of multipath 4. The height of th ver, or ground 5. With static surveys, observation times long, 6. With intermittent observation time long, metal trucks continually pass by the antenna
5 Different Antennas: • Conical spiral antennas, • Microstrip antennas, • Dipole antennas (crossed pair of horizontal, halfwavelength dipole) • Helices. The direct computation of the antenna effects on the distance measurements with respect to azimuth and elevation was proposed. 5. Multipath Multipath: a satellite emitted signal arrives at the receiver via more than one path. Causes: 1. reflecting surfaces near the receiver, 2. reflections at the satellite during signal transmission. • Phase offsets due to Multipath • Phase differences are proportional to the differences of the path lengths. Result: There is no general model of the multipath effect because of the arbitrarily different geometric situations. The influence of the multipath can be estimated by using a combination of L1 and L2 code and carrier phase measurements. The principle is based on the fact that the troposphere, clock errors, and relativistic effects influence code and carrier phases by the same amount. Modeling: Estimation Methods: Error: • 10-20 m for code pseudoranges • about 100 m in the vicinity of buildings • on carrier phases for relative positioning with short baselines, generally, not be greater than 1 cm (good satellite geometry and a reasonably long observation interval), 1. Selecting an antenna that takes advantage of the signal polarization. 2. digital filtering, wideband antennas, radio frequency absorbent antenna ground planes, and choke ring antennas. 3. The absorbent antenna ground plane reduces the interference of satellite signals with low or even negative elevation angles which occur in case of multipath 4. The height of the receiver, or ground 5. With static surveys, observation times long, 6. With intermittent observation time long, 7. Avoid to set up in the center of a highway and large metal trucks continually pass by the antenna. Improvement Methods:
Assignment 6 Summary 1. How do we reduce the ionospheric effect in practice surveying(15 points)? What have we learnt? 2. How do we reduce the tropospheric effect in hich parts are important? 3. How do the special and general relativity effect the 4. What is antenna offset(15 points)? 5. What is antenna variation(15 points) 6. How do we avoid the multi-path effect in practice surveying(20 points)?
6 Summary What have we learnt? Which parts are important? Assignment 6 1. How do we reduce the ionospheric effect in practice surveying (15 points)? 2. How do we reduce the tropospheric effect in practice surveying (15 points)? 3. How do the special and general relativity effect the GPS (15 points)? 4. What is antenna offset (15 points)? 5. What is antenna variation (15 points)? 6. How do we avoid the multi-path effect in practice surveying (20 points)?
