An Analysis of the Short- Term Stability of GNSS Satellite Clocks

Transcription

1 An Analysis of the Short- Term Stability of GNSS Satellite Clocks Erin Griggs, Dr. Rob Kursinski, Dr. Dennis Akos Aerospace Engineering Sciences University of Colorado 1

2 MOTIVATION 2

3 Radio Occulta.on Status Carrier Phase Doppler Amplitude Temperature Pressure Humidity GLONASS Galileo COMPASS Occul.ng GPS Satellite EARTH LEO Satellite U.lizing mul.ple constella.ons provides approximately 4x more occulta.ons Denser coverage for weather predic.on & climate 3

4 Why GLONASS? Fully ac.ve constella.on 24 satellites opera.onal Chipping rate ½ of GPS (0.511 MHz) Wider correla.on peak Single correlator will not lose lock as easily No cross- correla.on (FDMA) GPS GLONASS Correla.on Func.on 4

5 Clock Stability Ques.ons Unknown short- term clock stability Sample rate of 50 Hz by current RO missions Occulta.on dura.on is approximately 100 seconds What kind of satellite clock behavior do we expect at this high rate? Need to understand clock performance from 0.02 to 100 sec To u.lize GLONASS satellites for RO, is ground- based compensa.on required to eliminate satellite clock instability? 5

6 MEASUREMENT APPROACH 6

7 Where do we get clock data? High rate clock data unavailable for any constella.on Broadcast correc.ons given every 2 hours IGS produces precise clock produces at 30 second intervals Frequency of data puts a lower bound on the.mescales of the analysis Collect raw GNSS data and process with a So_ware Defined Radio (SDR) Use the raw carrier phase measurements to demonstrate clock behavior Able to obtain observa.ons at 1 khz rate Measurement independence reliant upon phase- lock loop bandwidth (vary with SDR) Dependence on signal strength 7

8 Carrier Phase to Clock Data Carrier phase observa.ons can be modeled as Isolate the satellite clock term Model pseudorange term with interpolated precise orbital data Single differencing between two satellites removes receiver clock influence Integer ambiguity removed by using SDR Ionosphere and troposphere influences assumed to be constant over short.me scales of interest Mul.path was ignored for this study 8

9 Allan Devia.on Analysis Allan Devia.on Standard for measuring oscillator instability in the.me domain Averages of all possible two- sample variances at a given interval U.lized the fixed interval formula.on of the Allan variance 9

10 Analysis of Satellite Clock Pairs Single difference Differencing the carrier phase measurements between pairs of GNSS satellites Removes Is it possible receiver to analysis clock an individual satellite clock error term without a precise receiver clock? Allows for satellite clock behavior to be analyzed Factor of 2 noise added to the system Rcvr 10

11 Isola.ng a Single Clock Sta.s.cally isolate carrier phase from a satellite by mul.plying two pairs of single differences Assumes independence between separate clock observa.ons 11

12 Methodology Summary U.lize a single frequency SDR No atomic reference is needed on the ground High- rate sampling Independence of observa.ons depends on the PLL Removal of geometric effects with interpola.on of precise orbital data Single difference to remove receiver clock error Mul.ply single difference pairs to obtain variance of a single satellite clock Assume atmospheric errors and mul.path are constant or negligible over short.me spans 12

13 RESULTS 13

14 GPS Clock Phase Data GLONASS Point values are the IGS clock products at 30 second intervals Smooth curves are the 1 khz clock values produced from carrier phase measurements 14

15 Single Differenced Allan Dev (GPS) Receiver Bandwidth 20 Hz 25 Hz 50 Hz 100 Hz IGS Receiver signal processing Crystal oscillator Atomic oscillator 15

16 Single Differenced Allan Dev (GLONASS) Receiver Bandwidth 20 Hz 25 Hz 50 Hz 100 Hz IGS Receiver signal processing Crystal oscillator Atomic oscillator 16

17 Bandwidth Dependence Phase error due to the thermal noise of the phase lock loop Dominates the clock phase.me intervals less than 5-10 seconds Dependence on the C/N0 of the received signal Can adjust with the antenna gain Characterize this noise with the following rela.onship 17

18 GPS PRN 23 Example 18

19 GLONASS ALM 20 Example 19

20 Allan Dev Comparison GLONASS GPS 2-7x difference! 20

21 Allan Dev Comparison GLONASS GPS Point values from Hauschild, et. al, Short- term analysis of GNSS clocks 21

22 CONCLUSIONS 22

23 Conclusions Three dis.nct phases present in the Allan Devia.on White phase region from receiver signal processing Challenging to analyze due to C/N 0 dependence Expected slope: White frequency from satellite clock GPS and GLONASS are comparable in this region Expected slope: Constant region from crystal oscillator Fairly large discrepancy between the GLONASS and GPS results in the 1-30 second region Large spread in the GLONASS results GPS Allan devia.ons 2-7x bemer than those from GLONASS 23

24 RO Implica.ons (Preliminary) Approximately an order of magnitude τ = 4 sec Larger frac.onal error discrepancies between GPS and GLONASS Possible solu.on Difference out GLONASS clock noise by monitoring the GLONASS clocks with a 2 nd non- occul.ng receiver for each 50 km, 250 K Case σ(τ = 1 sec ) Frac Error Est. Temp GPS Best 4* K Worst 1* K GLONASS Best 9* K Worst 3* K Figure from Kursinski et al., Observing Earth s atmosphere with radio occulta?on measurements using the Global Posi?oning System 24

25 QUESTIONS 25

26 Back Up Slides 26

27 Methodology Technique that can characterize satellite clock behavior at short.me scales Precise receiver oscillator not necessary Works especially well when orbit characteris.cs are well known Mul.plying pairs of single differences allows for the clock behavior of an individual satellite to become apparent 27

28 Limita.ons More difficult to process GLONASS data Addi.onal quadra.c detrending required to remove long- term orbital effects Could contribute in resul.ng Allan analysis results Quality of GLONASS orbital products Sub- second satellite clock behavior Behavior a func.on of bandwidth and signal strength Analysis of GNSS clocks possible if Reduce PLL bandwidth Increase C/N0 28

29 Predicted ADEV for a Stronger Signal 50 Hz, C/N0: 60 db- Hz 29

30 RO implica.ons FYI: the scaling from.me to ver.cal scales in the stratosphere comes from the occulta.on raypath descent rate is ~2.5 km/sec. So 1 second corresponds to 2.5 km ver.cal scale atmospheric structure 5 sec corresponds to 12.5 km ver.cal scale atmospheric structures 30