Optimized Space S tation CV Method and Its Differences from GNSS CV

There will be better atomic clock system and micro-wave time comparison link in the 11 near earth space station, like Chinese Space Station and European ACES(Atomic Clock Ensemble in Space) system, than those in the GNSS(Global Navigation satellite 13 System) satellites. Therefore, the space station common-view (CV) will realize more accurate time comparison than GNSS CV in theory. But due to the orbit characteristic of the space station, there are some limitations if traditional GNSS CV time comparison method is applied to the space station. In order to solve these problems, the GNSS CV method is optimized and the method that is appropriate for the space station is proposed. First, the basic CV principle is analyzed, and the delay items which are needed to be considered for GNSS and space station CV are compared and analyzed. Then, the 20 differences between GNSS and space station CV are studied, and the influences of orbit error on these two CV methods are analyzed in detail. The GNSS CV method is optimized to be fit for the space station next. Finally, the performance of the optimized method is validated by simulated experiments. The simulation results show that the space station time comparison accuracy of several tens of picoseconds can be obtained by the optimized method. Furthermore, the problem of CV blind area is solved by the optimized method effectively.

( .  delay, they are in the magnitude of ten nanoseconds for the space station, but they are in 111 the magnitude of hundred nanoseconds for GNSS satellites.  The last terms on the right of (1) and (2) where AB T V denotes the time bias between ground station A and B. 141 The items less than one nanosecond can be neglected in (1) where there are no terms for the Shapiro delay and converting delay from the coordinate 145 time to the proper time. 146 Equations (7) and (8) show that differencing operation is the essence of CV principle. 147 The common errors can be canceled by the differencing operation, so the time 148 comparison accuracy is improved by CV method. But the CV time comparison requires 149 that two ground stations observe the spatial aircraft at the same time to compute their 150 clock bias by using the atomic clocks in the aircraft as a medium. By contrasting (7) and 151 (8), we can see that the Shapiro delay and the converting delay from coordinate time to 152 the proper time are computed in space station CV but not in GNSS CV. These two 153 items are greater than one picosecond but less than one nanosecond. So, these delay items cannot be neglected if we want to get several tens of picoseconds accuracy. But 155 they can be neglected in GNSS CV which aims at nanosecond time comparison 156 accuracy. 157

Comparising space station and GNSS CV 158
As mentioned above, due to the target accuracy between the space station CV and 159 GNSS CV is different, the delay items to be considered are also different. Furthermore, 160 there are several differences between them, such as the orbit characteristic and effect, 161 space atomic clock performance and down-link signal structure, and so on. These 162 differences limit the application of the traditional GNSS CV method to the space 163 station. 164

System design differences between space station and GNSS CV techniques 165
The system design differences between the space station and GNSS satellite mainly 166 contain three aspects: the orbit characteristics, space atomic clock system and signal 167 structure of the time comparison down-link. The space station visibility of one day to several representative cities in China is shown 178 in Then, the atomic clock carried by the space station is compared with that carried by 196 the GNSS satellite. The space station atomic clock has better performance. First, the 197 laser cooling techniques and the space microgravity environment will be combined to 198 improve the stability of the atomic clock in the space station. Although the GNSS 199 satellites are also in the space microgravity environment, there are no cooled atomic 200 clocks carried on the GNSS satellites. Second, the performance level of the space 201 station atomic clock is higher than that of the GNSS satellite clock. There will be two 202 atomic clocks carried in the ISS for the ACES project. One is a hydrogen maser whose 203 frequency stability is better than 1.5E-13 when the averaging time interval τ is equal 204 to 1 second and is better than 1.5E-15 whenτ is equal to 86400 seconds. The other is a 205 cold atom cesium clock, whose frequency stability should be better than 1 13 / E   . 206 These two clocks will be integrated to output better time and frequency signals, so the 207 frequency stability of ACES integrated signal is better than 1E-13 when τ is equal to 1 208 second and is better than 1E-15 when τ is equal to 86400 seconds. The payload of 209 Chinese Space Station not only contains ordinary atomic clocks, but also contains a 210 strontium atom light clock with the performance at least an order of magnitude higher 211 than that of ACES clocks. Most of clocks carried by GNSS satellites are rubidium or 212 cesium atomic clocks. Although there are some passive hydrogen atomic clocks in 213 Galileo satellites, the frequency stability of integrated signal is an order of magnitude 214 worse than the ACES signal. The atomic clocks of the space station and GNSS satellites 215 are the CV references. Although the clock errors have been canceled by the CV 216 algorithm, excellent clock reference is helpful to optimize the space station CV method 217 that will be mentioned latter. 218 Finally, the signal structure differences between these two systems are explained. The 219 differences related to time comparison performance consist of the code chip rate and the 220 signal frequency. The down link code chip rate of the space station is 100 Mchip/s, 221 which is nearly ten times the GPS P-code. Thus, the downlink signal pseudo code 222 ranging accuracy of the space station is higher than that of the GNSS satellite. The 223 signal frequency of GNSS is commonly in L band, but that of ACES is in the Ku band, 224 and that of the Chinese Space Station is higher and in Ku and Ka bands. The 225 ionospheric delay is inversely proportional to the square of the signal frequency. The 226 ionospheric delay of the space station is far less than that of GNSS. For GNSS CV, the 227 ionospheric delay is the main error source. But for space station CV, the ionospheric 228 delay can be calculated by the pseudorange combination of two or three carriers in 229 different frequencies with the accuracy of picosecond magnitude. Therefore, the time 230 comparison performance of the space station down link is better than that of GNSS, and 231 higher CV time comparison accuracy can be achieved by this link. 232

Effect differences of orbit error on space station and GNSS CV 233
Because the target accuracy of the space station CV is two orders magnitude higher than that of GNSS CV, their error correcting methods are different. The atmospheric delay, 235 the earth rotation, and the gravity delay are not explained here, and only the influence of 236 orbital error on the space station CV and GNSS CV is analyzed in detail. 237 From the equations (7) and (8), the differential coefficient of the aircraft position 238 error can be gotten by the following equation: 239 denotes the position error of the aircraft. Equation (9) can be rewritten as: 241 Assuming that SA SB     V , we can get the following equation: where BA  v denotes the distance vector from station B to A. After some simple 245 transformation of (11), the following inequality is obtained: 246 which shows that the effect of orbit error on CV time comparison is related to the 248 distance between the aircraft and the ground station, the length of the CV baseline and 249 the orbit error itself. kilometers and GNSS orbit error as one meter for example, the maximum influence 258 magnitude of the orbit error to GNSS CV is about 300 picoseconds according to (14). 259 This effect can be ignored for a 3 to 5 nanoseconds time comparison accuracy. 260 Additional orbital improvements need not to be made for GNSS CV, and the CV 261 algorithm itself is enough. 262 The orbit height of space station is about 400 kilometers. But the distance between 263 the space station and the ground station ranges from several hundred to several thousand 264 of kilometers. Thus, the following express is sometimes correct for the space station: 265 thus the effect of space station orbit error may be magnified. 267 On the other hand, the following express is also correct for the space station at most 268 times: 269 So, if the CV baseline length is longer than the distance between the space station and

Application limitations when using GNSS CV method to the space station
From the analysis results above, it is known that the traditional GNSS CV method 283 requires two ground stations observing the space station simultaneously. Due to the low 284 orbit and fast orbital speed of the space station, the ground stations in some areas cannot 285 observe the space station simultaneously all the time. Therefore, GNSS CV method 286 cannot be used for this case. This is the first application limitation. 287 The other limitation relates to CV time comparison accuracy. As mentioned above, 288 the GNSS CV method will result in great time comparison errors for the space station 289

CV. This limitation is validated by simulation experiments in which the GNSS CV 290
method is applied to the space station. 291 In the simulation, the orbit error is divided into three components, the radial (R), 292 tangential (T) and the normal (N) vector components. Each component is set to 0.1 293 meters in R, T and N. The mean value of observation noise is set to zero, and its 294 standard deviation is set to 1 picosecond. The ionospheric delay data is generated based 295 on the VTEC (Vertical Total Electronic Content) data provided by IGS. The 296 tropospheric delay is modeled by the Saastamoinen model. Minimum elevation of the 297 space station is taken as 10 。 . The temperature is set to 298 K, the pressure is set to 1 bar, 298 and the water vapor pressure is set to 0.5 bar. The two ground stations are located in Xi' 299 an and Sanya respectively, so the baseline length is about 2000 kilometers. The 300 frequency stability of the Xi'an atomic clock when τ is equal to 1 second is set to 1E-13, 301 and the frequency stability when τ is equal to 86400 seconds is set to 1E-15. The 302 frequency stability of the Sanya atomic clock when τ is equal to 1 second is set to 5E-13, 303 and the frequency stability when τ is equal to 86400 seconds is set to 1E-14.

Optimization of space station CV method 327
It is known that the traditional GNSS CV method cannot be used to the space station 328 directly for two aspects of reasons. One is the existence of the CV blind area. The other 329 is the time comparison accuracy is limited to hundreds of picoseconds. In order to solve these problems, the GNSS CV method is optimized. 331 The effect of orbit error on time comparison can also be expressed by the flowing 332 where flag denotes the decision factor, and Thod denotes the decision threshold. 352 Combining equation (17) and (18) Therefore, the influence of orbit error on CV time comparison can be adjusted by the 357 decision threshold Thod. For example, if the orbit errors in R, T and N are all less than 358 0.1 meters, and the decision threshold Thod is set to be 0.03, the time comparison error 359 caused by the orbit error will be less than ten picoseconds. If Thod is set to be 0.06, the 360 time comparison error caused by the orbit error will be up to twenty picoseconds. But it 361 is important to note that the decision threshold does not follow the rule less the better. 362 The less the decision threshold Thod is, the less position combination that meet the 363 judgment condition (18) will be found. In a general way, Thod in the range from 0.03 to 364 0.05 is ok. But for some long baseline CV, Thod need to be magnified properly. The atomic clock of the space station has the stability higher than that of the ground 383 atomic clock. The frequency stability of the space clock when τ is equal to 1 second is 384 better than 1E-13, and the frequency stability when τ is equal to 86400 seconds is better 385 than 1E-15. The ground clocks that need several tens of picoseconds time comparison 386 accuracy also have good stability and little frequency drift. Thus, we can use the linear 387 polynomial to model the clock bias between the ground station and the space station. 388 The modeling target is to compute the relative frequency deviation of these two clocks. 389 The clock bias model is shown as follows: 390 where a denotes the constant term, b denotes the first-order coefficient of the 392 polynomial, and 0 t denotes the model starting time.
the space station at t 2 based on the extrapolation principle. 395 denotes the clock bias between station A and the space station. Then, 397 we can compute the clock bias of station A and B by the following equation: 398 It can be seen from (20) that the modeling data source is the clock bias that is 403 calculated based on one-way time comparison method. So, the data source contains the 404 orbit error, and some modeling error must be applied to (22). 405 The error of where GNSS CV method is invalid. 432

Simulation verification of optimized method 433
In order to verify the validity of the optimized space station CV time comparison

Analysis of Xi'an and Sanya Simulation 438
The simulation condition of the optimized method is almost the same as that of GNSS 439 CV method. The decision threshold of (12) is set to be 0.03. The optimized method is 440 used to realize the CV time comparison of Xi'an and Sanya stations, the decision factor 441 is shown in Figure 3, and time comparison error is shown in Figure 4. These two figures are all in three-dimensional coordinate format. The data of X and Y axis indicates the 443 cumulative seconds of one day for Xi'an and Sanya, respectively. The data of Z axis of 444  It is noteworthy that the stability of Xi'an atomic clock is better than that of Sanya, so 453 Xi'an space-ground clock bias is modeled and extrapolated. By this means, less 454 modeling error is introduced, and higher accuracy is obtained. 455

Analysis of Kashi and Sanya Simulation 456
It can be seen from Table 1 that traditional GNSS CV method is invalid if one ground 457 station is in Kashi, and the other station is in Sanya. Because these two ground stations 458 cannot observe the space station simultaneously. But the optimized method is valid to 459 implement the CV time comparison of these ground stations. 460 The baseline length of Kashi and Sanya is longer than 5000 kilometers, and the 461 simulation condition is essentially the same as that of Xi'an and Sanya simulation 462 except for the atomic clock parameters of Kashi. The frequency stability of the Kashi 463 clock when τ is equal to 1 second is set to 5E-13, and the frequency stability when τ is 464 equal to 86400 seconds is set to 1E-14. The decision factor of Kashi and Sanya stations 465 is shown in Figure 5, and the time comparison error is shown in Figure 6. 466 Although the baseline length of Kashi-Sanya is almost two times that of Xi'an-Sanya, 467 and the atomic stability of Kashi is worse than that of Xi'an, but it can be seen from 468  The data of X and Y axis indicates the cumulative seconds of one day for Xi'an and 585 Sanya, respectively. The data of Z axis indicates the decision factor. 586 The data of X and Y axis indicates the cumulative seconds of one day for Xi'an and 588 Sanya, respectively. The data of Z axis indicates the value of time comparison error 589 between Xi'an and Sanya using optimized CV method. 590 The data of X and Y axis indicates the cumulative seconds of one day for Kashi and 592 Sanya, respectively. The data of Z axis indicates the decision factor. 593 The data of X and Y axis indicates the cumulative seconds of one day for Kashi and 595 Sanya, respectively. The data of Z axis indicates the value of time comparison error 596 between Kashi and Sanya using optimized CV method. 597 598