Preface |
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xv | |
Acknowledgments |
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xix | |
Abbreviations |
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xxi | |
1 Introduction |
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1 | (10) |
2 Least-Squares Adjustments |
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11 | (70) |
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2.1 Elementary Considerations |
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12 | (2) |
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2.1.1 Statistical Nature of Surveying Measurements |
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12 | (1) |
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2.1.2 Observational Errors |
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13 | (1) |
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2.1.3 Accuracy and Precision |
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13 | (1) |
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2.2 Stochastic and Mathematical Models |
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14 | (3) |
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17 | (6) |
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18 | (1) |
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2.3.2 Minimization and Solution |
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19 | (1) |
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20 | (1) |
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2.3.4 A Posteriori Variance of Unit Weight |
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21 | (1) |
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22 | (1) |
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2.4 Sequential Mixed Model |
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23 | (6) |
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29 | (8) |
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2.5.1 Observation Equation Model |
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29 | (1) |
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2.5.2 Condition Equation Model |
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30 | (1) |
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2.5.3 Mixed Model with Observation Equations |
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30 | (2) |
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2.5.4 Sequential Observation Equation Model |
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32 | (1) |
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2.5.5 Observation Equation Model with Observed Parameters |
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32 | (2) |
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2.5.6 Mixed Model with Conditions |
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34 | (1) |
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2.5.7 Observation Equation Model with Conditions |
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35 | (2) |
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2.6 Minimal and Inner Constraints |
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|
37 | (5) |
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2.7 Statistics in Least-Squares Adjustment |
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42 | (20) |
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42 | (6) |
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2.7.2 Testing Sequential Least Squares |
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48 | (1) |
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2.7.3 General Linear Hypothesis |
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49 | (3) |
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2.7.4 Ellipses as Confidence Regions |
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52 | (4) |
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2.7.5 Properties of Standard Ellipses |
|
|
56 | (4) |
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2.7.6 Other Measures of Precision |
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60 | (2) |
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62 | (8) |
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62 | (2) |
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2.8.2 Controlling Type-II Error for a Single Blunder |
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64 | (3) |
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2.8.3 Internal Reliability |
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67 | (1) |
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67 | (1) |
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2.8.5 External Reliability |
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68 | (1) |
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69 | (1) |
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70 | (2) |
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71 | (1) |
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71 | (1) |
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2.9.3 Changing Weights of Observations |
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72 | (1) |
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72 | (5) |
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|
77 | (4) |
3 Recursive Least Squares |
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81 | (48) |
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82 | (5) |
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3.2 Static Parameters and Arbitrary Time-Varying Variables |
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87 | (9) |
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96 | (16) |
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3.4 Static Parameters and Dynamic Constraints |
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112 | (13) |
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3.5 Static Parameter, Parameters Subject to Dynamic Constraints, and Arbitrary Time-Varying Parameters |
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125 | (4) |
4 Geodesy |
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129 | (78) |
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4.1 International Terrestrial Reference Frame |
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131 | (10) |
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132 | (1) |
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4.1.2 Tectonic Plate Motion |
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133 | (2) |
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135 | (1) |
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135 | (1) |
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4.1.5 Relating of Nearly Aligned Frames |
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136 | (2) |
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138 | (3) |
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4.2 International Celestial Reference System |
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141 | (10) |
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4.2.1 Transforming Terrestrial and Celestial Frames |
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143 | (6) |
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149 | (2) |
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151 | (15) |
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152 | (5) |
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4.3.2 Ellipsoid of Rotation |
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157 | (1) |
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4.3.3 Geoid Undulations and Deflections of the Vertical |
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158 | (4) |
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4.3.4 Reductions to the Ellipsoid |
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162 | (4) |
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166 | (24) |
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4.4.1 Partial Derivatives |
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169 | (1) |
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170 | (1) |
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4.4.3 Implementation Considerations |
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171 | (3) |
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4.4.4 GPS Vector Networks |
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174 | (2) |
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4.4.5 Transforming Terrestrial and Vector Networks |
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176 | (2) |
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4.4.6 GPS Network Examples |
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178 | (12) |
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4.4.6.1 Montgomery County Geodetic Network |
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178 | (4) |
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4.4.6.2 SLC Engineering Survey |
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182 | (1) |
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4.4.6.3 Orange County Densification |
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183 | (7) |
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190 | (7) |
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4.5.1 Reduction of Observations |
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191 | (4) |
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4.5.1.1 Angular Reduction to Geodesic |
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192 | (1) |
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4.5.1.2 Distance Reduction to Geodesic |
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193 | (2) |
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4.5.2 Direct and Inverse Solutions on the Ellipsoid |
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195 | (1) |
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4.5.3 Network Adjustment on the Ellipsoid |
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196 | (1) |
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4.6 Conformal Mapping Model |
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197 | (6) |
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4.6.1 Reduction of Observations |
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198 | (2) |
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|
200 | (1) |
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4.6.3 Direct and Inverse Solutions on the Map |
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201 | (1) |
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4.6.4 Network Adjustment on the Map |
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201 | (2) |
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4.6.5 Similarity Revisited |
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203 | (4) |
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204 | (3) |
5 Satellite Systems |
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207 | (50) |
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207 | (18) |
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208 | (2) |
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5.1.2 Normal Orbital Theory |
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210 | (9) |
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5.1.3 Satellite Visibility and Topocentric Motion |
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|
219 | (1) |
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5.1.4 Perturbed Satellite Motion |
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219 | (6) |
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5.1.4.1 Gravitational Field of the Earth |
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220 | (2) |
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5.1.4.2 Acceleration due to the Sun and the Moon |
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|
222 | (1) |
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5.1.4.3 Solar Radiation Pressure |
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222 | (1) |
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5.1.4.4 Eclipse Transits and Yaw Maneuvers |
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|
223 | (2) |
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5.2 Global Positioning System |
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225 | (20) |
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5.2.1 General Description |
|
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226 | (2) |
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5.2.2 Satellite Transmissions at 2014 |
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228 | (11) |
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229 | (8) |
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5.2.2.2 Navigation Message |
|
|
237 | (2) |
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5.2.3 GPS Modernization Comprising Block IIM, Block IIF, and Block III |
|
|
239 | (19) |
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5.2.3.1 Introducing Binary Offset Carrier (BOC) Modulation |
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241 | (2) |
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|
243 | (1) |
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|
243 | (1) |
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244 | (1) |
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244 | (1) |
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|
245 | (3) |
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248 | (2) |
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250 | (2) |
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252 | (2) |
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|
254 | (1) |
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5.8 SBAS: WAAS, EGNOS, GAGAN, MSAS, and SDCM |
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|
254 | (3) |
6 GNSS Positioning Approaches |
|
257 | (144) |
|
|
258 | (17) |
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6.1.1 Undifferenced Functions |
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|
261 | (10) |
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|
261 | (2) |
|
|
263 | (3) |
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6.1.1.3 Range plus Ionosphere |
|
|
266 | (1) |
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6.1.1.4 Ionospheric-Free Functions |
|
|
266 | (1) |
|
6.1.1.5 Ionospheric Functions |
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|
267 | (1) |
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6.1.1.6 Multipath Functions |
|
|
267 | (1) |
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6.1.1.7 Ambiguity-Corrected Functions |
|
|
268 | (1) |
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6.1.1.8 Triple-Frequency Subscript Notation |
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|
269 | (2) |
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271 | (2) |
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6.1.2.1 Across-Receiver Functions |
|
|
271 | (1) |
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6.1.2.2 Across-Satellite Functions |
|
|
272 | (1) |
|
6.1.2.3 Across-Time Functions |
|
|
272 | (1) |
|
|
273 | (2) |
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|
275 | (1) |
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|
275 | (24) |
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6.2.1 Computing the Topocentric Range |
|
|
275 | (1) |
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6.2.2 Satellite Timing Considerations |
|
|
276 | (6) |
|
6.2.2.1 Satellite Clock Correction and Timing Group Delay |
|
|
278 | (1) |
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6.2.2.2 Intersignal Correction |
|
|
279 | (3) |
|
|
282 | (1) |
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6.2.4 Phase Windup Correction |
|
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283 | (3) |
|
|
286 | (6) |
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6.2.6 Phase Center Offset and Variation |
|
|
292 | (3) |
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6.2.6.1 Satellite Phase Center Offset |
|
|
292 | (1) |
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6.2.6.2 User Antenna Calibration |
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|
293 | (2) |
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|
295 | (4) |
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|
295 | (3) |
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|
298 | (1) |
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|
299 | (5) |
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6.3.1 Linearized Solution |
|
|
299 | (2) |
|
6.3.2 DOPs and Singularities |
|
|
301 | (2) |
|
6.3.3 Nonlinear Closed Solution |
|
|
303 | (1) |
|
|
304 | (20) |
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6.4.1 Nonlinear Double-Difference Pseudorange Solution |
|
|
305 | (1) |
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6.4.2 Linearized Double- and Triple-Differenced Solutions |
|
|
306 | (4) |
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6.4.3 Aspects of Relative Positioning |
|
|
310 | (5) |
|
|
310 | (1) |
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6.4.3.2 Impact of a Priori Position Error |
|
|
311 | (1) |
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6.4.3.3 Independent Baselines |
|
|
312 | (2) |
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6.4.3.4 Antenna Swap Technique |
|
|
314 | (1) |
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6.4.4 Equivalent Undifferenced Formulation |
|
|
315 | (1) |
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|
316 | (3) |
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6.4.6 GLONASS Carrier Phase |
|
|
319 | (5) |
|
|
324 | (33) |
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6.5.1 The Constraint Solution |
|
|
324 | (3) |
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|
327 | (7) |
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|
334 | (3) |
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6.5.4 Lattice Reduction and Integer Least Squares |
|
|
337 | (20) |
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6.5.4.1 Branch-and-Bound Approach |
|
|
338 | (11) |
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6.5.4.2 Finke-Pohst Algorithm |
|
|
349 | (2) |
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6.5.4.3 Lattice Reduction Algorithms |
|
|
351 | (3) |
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6.5.4.4 Other Searching Strategies |
|
|
354 | (2) |
|
6.5.4.5 Connection Between LAMBDA and LLL Methods |
|
|
356 | (1) |
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6.6 Network-Supported Positioning |
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|
357 | (25) |
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|
357 | (6) |
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|
363 | (4) |
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6.6.2.1 Differential Phase and Pseudorange Corrections |
|
|
363 | (2) |
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|
365 | (2) |
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|
367 | (15) |
|
6.6.3.1 Single-Frequency Solution |
|
|
367 | (5) |
|
6.6.3.2 Dual-Frequency Solutions |
|
|
372 | (7) |
|
6.6.3.3 Across-Satellite Differencing |
|
|
379 | (3) |
|
6.7 Triple-Frequency Solutions |
|
|
382 | (16) |
|
6.7.1 Single-Step Position Solution |
|
|
382 | (4) |
|
|
386 | (9) |
|
6.7.2.1 Resolving EWL Ambiguity |
|
|
389 | (2) |
|
6.7.2.2 Resolving the WL Ambiguity |
|
|
391 | (2) |
|
6.7.2.3 Resolving the NL Ambiguity |
|
|
393 | (2) |
|
6.7.3 Geometry-Based TCAR |
|
|
395 | (1) |
|
|
396 | (1) |
|
6.7.5 Positioning with Resolved Wide Lanes |
|
|
397 | (1) |
|
|
398 | (3) |
7 Real-Time Kinematics Relative Positioning |
|
401 | (74) |
|
7.1 Multisystem Considerations |
|
|
402 | (1) |
|
7.2 Undifferenced and Across-Receiver Difference Observations |
|
|
403 | (5) |
|
7.3 Linearization and Hardware Bias Parameterization |
|
|
408 | (10) |
|
7.4 RTK Algorithm for Static and Short Baselines |
|
|
418 | (11) |
|
7.4.1 Illustrative Example |
|
|
422 | (7) |
|
7.5 RTK Algorithm for Kinematic Rovers and Short Baselines |
|
|
429 | (6) |
|
7.5.1 Illustrative Example |
|
|
431 | (4) |
|
7.6 RTK Algorithm with Dynamic Model and Short Baselines |
|
|
435 | (6) |
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7.6.1 Illustrative Example |
|
|
437 | (4) |
|
7.7 RTK Algorithm with Dynamic Model and Long Baselines |
|
|
441 | (4) |
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7.7.1 Illustrative Example |
|
|
442 | (3) |
|
7.8 RTK Algorithms with Changing Number of Signals |
|
|
445 | (5) |
|
7.9 Cycle Slip Detection and Isolation |
|
|
450 | (16) |
|
7.9.1 Solutions Based on Signal Redundancy |
|
|
455 | (11) |
|
7.10 Across-Receiver Ambiguity Fixing |
|
|
466 | (7) |
|
7.10.1 Illustrative Example |
|
|
470 | (3) |
|
7.11 Software Implementation |
|
|
473 | (2) |
8 Troposphere And Ionosphere |
|
475 | (38) |
|
|
476 | (3) |
|
8.2 Tropospheric Refraction and Delay |
|
|
479 | (8) |
|
8.2.1 Zenith Delay Functions |
|
|
482 | (1) |
|
|
482 | (3) |
|
8.2.3 Precipitable Water Vapor |
|
|
485 | (2) |
|
8.3 Troposphere Absorption |
|
|
487 | (9) |
|
8.3.1 The Radiative Transfer Equation |
|
|
487 | (3) |
|
8.3.2 Absorption Line Profiles |
|
|
490 | (2) |
|
8.3.3 General Statistical Retrieval |
|
|
492 | (2) |
|
|
494 | (2) |
|
8.4 Ionospheric Refraction |
|
|
496 | (17) |
|
8.4.1 Index of Ionospheric Refraction |
|
|
499 | (5) |
|
8.4.2 Ionospheric Function and Cycle Slips |
|
|
504 | (1) |
|
8.4.3 Single-Layer Ionospheric Mapping Function |
|
|
505 | (2) |
|
8.4.4 VTEC from Ground Observations |
|
|
507 | (2) |
|
8.4.5 Global Ionospheric Maps |
|
|
509 | (6) |
|
|
509 | (1) |
|
8.4.5.2 International Reference Ionosphere |
|
|
509 | (1) |
|
8.4.5.3 GPS Broadcast Ionospheric Model |
|
|
510 | (1) |
|
|
510 | (1) |
|
8.4.5.5 Transmission to the User |
|
|
511 | (2) |
9 GNSS Receiver Antennas |
|
513 | (140) |
|
9.1 Elements of Electromagnetic Fields and Electromagnetic Waves |
|
|
515 | (31) |
|
9.1.1 Electromagnetic Field |
|
|
515 | (3) |
|
9.1.2 Plane Electromagnetic Wave |
|
|
518 | (7) |
|
9.1.3 Complex Notations and Plane Wave in Lossy Media |
|
|
525 | (5) |
|
9.1.4 Radiation and Spherical Waves |
|
|
530 | (6) |
|
|
536 | (1) |
|
9.1.6 Polarization of Electromagnetic Waves |
|
|
537 | (7) |
|
|
544 | (2) |
|
9.2 Antenna Pattern and Gain |
|
|
546 | (19) |
|
9.2.1 Receiving GNSS Antenna Pattern and Reference Station and Rover Antennas |
|
|
546 | (7) |
|
|
553 | (5) |
|
9.2.3 Polarization Properties of the Receiving GNSS Antenna |
|
|
558 | (4) |
|
|
562 | (2) |
|
9.2.5 Antenna Effective Area |
|
|
564 | (1) |
|
|
565 | (13) |
|
9.3.1 Antenna Phase Pattern |
|
|
566 | (2) |
|
9.3.2 Phase Center Offset and Variations |
|
|
568 | (7) |
|
9.3.3 Antenna Calibrations |
|
|
575 | (2) |
|
9.3.4 Group Delay Pattern |
|
|
577 | (1) |
|
9.4 Diffraction and Multipath |
|
|
578 | (22) |
|
9.4.1 Diffraction Phenomena |
|
|
578 | (7) |
|
9.4.2 General Characterization of Carrier Phase Multipath |
|
|
585 | (2) |
|
9.4.3 Specular Reflections |
|
|
587 | (6) |
|
9.4.4 Antenna Down-Up Ratio |
|
|
593 | (4) |
|
9.4.5 PCV and PCO Errors Due to Ground Multipath |
|
|
597 | (3) |
|
|
600 | (9) |
|
9.5.1 Transmission Line Basics |
|
|
600 | (6) |
|
9.5.2 Antenna Frequency Response |
|
|
606 | (2) |
|
|
608 | (1) |
|
9.6 Signal-to-Noise Ratio |
|
|
609 | (11) |
|
|
609 | (2) |
|
9.6.2 Characterization of Noise Sources |
|
|
611 | (4) |
|
9.6.3 Signal and Noise Propagation through a Chain of Circuits |
|
|
615 | (4) |
|
9.6.4 SNR of the GNSS Receiving System |
|
|
619 | (1) |
|
|
620 | (33) |
|
|
620 | (9) |
|
9.7.2 Other Types of Antennas |
|
|
629 | (1) |
|
9.7.3 Flat Metal Ground Planes |
|
|
629 | (5) |
|
9.7.4 Impedance Ground Planes |
|
|
634 | (8) |
|
9.7.5 Vertical Choke Rings and Compact Rover Antenna |
|
|
642 | (2) |
|
9.7.6 Semitransparent Ground Planes |
|
|
644 | (1) |
|
|
645 | (5) |
|
9.7.8 Antenna Manufacturing Issues |
|
|
650 | (3) |
Appendixes |
|
|
|
653 | (44) |
|
A.1 Spherical Trigonometry |
|
|
653 | (4) |
|
|
657 | (1) |
|
|
657 | (24) |
|
A.3.1 Determinants and Matrix Inverse |
|
|
658 | (1) |
|
A.3.2 Eigenvalues and Eigenvectors |
|
|
659 | (1) |
|
A.3.3 Eigenvalue Decomposition |
|
|
660 | (1) |
|
|
661 | (3) |
|
A.3.5 Matrix Partitioning |
|
|
664 | (2) |
|
A.3.6 Cholesky Decomposition |
|
|
666 | (3) |
|
A.3.7 Partial Minimization of Quadratic Functions |
|
|
669 | (4) |
|
|
673 | (3) |
|
A.3.9 Rank One Update of Cholesky Decomposition |
|
|
676 | (5) |
|
|
681 | (2) |
|
|
683 | (14) |
|
A.5.1 One-Dimensional Distributions |
|
|
683 | (5) |
|
A.5.2 Distribution of Simple Functions |
|
|
688 | (1) |
|
|
689 | (2) |
|
A.5.4 Multivariate Distributions |
|
|
691 | (2) |
|
A.5.5 Variance-Covariance Propagation |
|
|
693 | (2) |
|
A.5.6 Multivariate Normal Distribution |
|
|
695 | (2) |
|
|
697 | (18) |
|
B.1 Geodetic Latitude, Longitude, and Height |
|
|
698 | (5) |
|
B.2 Computation of the Ellipsoidal Surface |
|
|
703 | (12) |
|
B.2.1 Fundamental Coefficients |
|
|
703 | (2) |
|
|
705 | (1) |
|
|
706 | (1) |
|
|
706 | (1) |
|
|
707 | (1) |
|
B.2.6 Differential Equation of the Geodesic |
|
|
708 | (3) |
|
B.2.7 The Gauss Midlatitude Solution |
|
|
711 | (2) |
|
|
713 | (1) |
|
B.2.9 Transformation in a Small Region |
|
|
713 | (2) |
|
|
715 | (26) |
|
C.1 Conformal Mapping of Planes |
|
|
716 | (3) |
|
C.2 Conformal Mapping of General Surfaces |
|
|
719 | (2) |
|
|
721 | (1) |
|
C.4 Popular Conformal Mappings |
|
|
722 | (19) |
|
C.4.1 Equatorial Mercator |
|
|
723 | (1) |
|
C.4.2 Transverse Mercator |
|
|
724 | (2) |
|
|
726 | (12) |
|
|
738 | (3) |
|
D Vector Calculus And Delta Function |
|
|
741 | (6) |
|
E Electromagnetic Field Generated By Arbitrary Sources, Magnetic Currents, Boundary Conditions, And Images |
|
|
747 | (8) |
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F Diffraction Over Half-Plane |
|
|
755 | (4) |
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G Single Cavity Mode Approximation With Patch Antenna Analysis |
|
|
759 | (4) |
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H Patch Antennas With Artificial Dielectric Substrates |
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|
763 | (6) |
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I Convex Patch Array Geodetic Antenna |
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|
769 | (4) |
References |
|
773 | (20) |
Author Index |
|
793 | (8) |
Subject Index |
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801 | |