Article Figures & Data
Figures
- FIGURE 1
Different tracking errors suffered by tracking pairs with different spacings
- FIGURE 2
Overall logical relationships of operational SQM and its design methodology
- FIGURE 3
Design methodology of CDO-based SQM
- FIGURE 4
Framework of the verification platform for massive simulations of SQM design
- FIGURE 5
Diagram of risky group and CMB for BDS B1C signal
- FIGURE 6
FoM contours with 1-second integral accumulation only
- FIGURE 7
100-second metric-smoothing-improved FoM contours for individual station
- FIGURE 8
Reference-smoothing-improved FoM curves at BIN = 0.025 chips
- FIGURE 9
Improved FoMs for individual station at BIN = 0.025 chips
- FIGURE 10
Results of assessment examples
- FIGURE 11
Critical performance comparisons with three signals
- FIGURE 12
Examinations on the detection ability of CDOs
- FIGURE B1
Illustration of the featured lengths with nominal signal
Tables
Signal Signal Components Carrier
Frequency (MHz)Modulation Phase Power Ratio Symbol
Rate (sps)GPS L1 C/A sL1CA(t) 1575.42 BPSK(1) — — 50 BDS B1C data SB1C_data(t) 1575.42 BOC(1, 1) 0 11/44 100 pilot SB1C_pilot_a(t) QMBOC(6, 1, 4/33) BOC(1, 1) 90 29/44 0 SB1C_pilot_b(t) BOC(6, 1) 0 4/44 BDS B2a data SB2a_data(t) 1176.45 BPSK(10) 0 1/2 200 pilot SB2a_pilot(t) 90 1/2 0 Signal Threat Model Δ (Chips) fd (MHz) σ (MNp/s) GPS L1 C/A TM-A −0.12 – 0.12 — — TM-B — 4 – 17 0.8 – 8.8 TM-C −0.12 – 0.12 7.3 – 13 0.8 – 8.8 BDS B1C TM-A −0.05 – 0.05 — — TM-B — 1.5 – 18 0.1 – 20 TM-C −0.05 – 0.05 1.5 – 18 0.1 – 20 BDS B2a TM-A −0.5 – 0.5 — — TM-B — 4 – 18 0.1 – 18 TM-C −0.5 – 0.5 4 – 18 0.1 – 18 Receiver Reference User Tracking L1 C/A E-L (BPSK(1) local replica) B1C E-L (BOC(1,1) local replica) B2a E-L (BPSK(10) local replica) Correlator Spacing L1 C/A 0.10 chips 0.08, 0.10, 0.12 chips B1C B2a 1.0 chips 0.9, 1.0, 1.1 chips PCBw (double-sided) 24 MHz 12, 14, 16, 18, 20, 22, 24 MHz Filter sixth-order Butterworth (1) sixth-order Butterworth
(2) mixed Butterworth
(3–6) four resonators
Algorithm phase Influential Factor Name Symbol Effect Raw-CDO measurement of a raw CDO Integration period Tint Determines the total amount of chips, hence, bins in measuring a raw CDO Proportion of a code-phase bin to a chip BIN Determines the length of each bin, hence, the number of sample points probably incorporated by the measurement Sampling frequency FS Determines the density of sample points on chip waveforms Double-sided PCBw BW Determines the shape of chip waveforms, hence, the values of sample points and the shape of the correlation function (signal amplitude estimate) CDO normalization Signal amplitude estimate IP Determines normalized magnitudes of CDOs Metric definition Rising edge rate RER Determines the total amount of rising edges within a given integration period in measuring CDOs applied to form metrics Metric-smoothing Metric-smoothing period Tsmt Decreases the magnitudes of standard deviations of poorly temporally-correlated nominal errors Determination of nominal metrics and detection thresholds Nominal scale multiplier K Determines the inflated scales of nominal noise on metrics Minimum number of stations for reference-smoothing Nref Decreases the magnitudes of standard deviations of poorly- and/or non-spatially-correlated nominal errors Carrier-to-noise ratio C/N0 Determines the raw magnitudes of nominal noise on received signals Signal Min_Rcv_C/N0
(dB-Hz)Total PRN Parameter Mean Median Maximum Minimum GPS L1 C/A 39 32 
0.4944 0.4959 0.5108 0.4804 BDS B1C (MEO) 37.5 63 0.8432 0.8431 0.8458 0.8409 BDS B2a (MEO) 39.3 63 single-chip (−1, +1) 0.4552 0.4550 0.4586 0.4511 dual-chip (−1, −1, + 1, +1) 0.2271 0.2271 0.2344 0.2199 triple-chip (−1, −1, −1, +1, +1, +1) 0.1133 0.1125 0.1234 0.1025 quad-chip (−1, −1, −1, −1, +1, +1, +1, +1)…… Domain Constraint (chips) Combined Constraint (chips) Nominal Distorted Rigid Fs
(MHz)Nref GPS L1 C/A BDS B1C SIF = 1.5 SIF = 2.3 SIF = 1.5 SIF = 2.3 72 1 1 1 1 66 1 1 1 1 60 1 1 2 1 54 1 1 2 1 48 2 1 2 1 42 2 1 3 2 36 2 1 4 2 30 3 2 5 3 24 5 3 8 4 Signal Threat Model Δ (chips) fd (MHz) σ (MNp/s) GPS L1 C/A TM-A −0.12 : 0.01 : −0.01, 0.01 : 0.01 : 0.12 — — TM-B — 4 : 0.1 : 17 0.8 : 0.5 : 8.8 TM-C −0.12 : 0.01 : −0.01, 0.01 : 0.01 : 0.12 7.3 : 0.1 : 13 0.8 : 0.5 : 8.8 BDS B1C TM-A −0.05 : 0.01 : −0.01, 0.01 : 0.01 : 0.05 — — TM-B — 1.5 : 0.5 : 18 0.1, 0.5 : 0.5 : 20 TM-C −0.05 : 0.01 : −0.01, 0.01 : 0.01 : 0.05 1.5 : 0.5 : 18 0.1, 0.5 : 0.5 : 20 BDS B2a TM-A −0.9 : 0.1 : −0.1, 0.1 : 0.1 : 0.9 — — TM-B — 2 : 1 : 20 0.1, 1 : 1 : 20 TM-C −0.9 : 0.1 : −0.1, 0.1 : 0.1 : 0.9 2 : 1 : 20 0.1, 1 : 1 : 20 ITEMS CONFIGURATIONS Name SCSQM8r Carrier frequency L1/B1 L5/B2 Correlator Observable CDO Location
(chips)Baseline ±1/80, ±3/80, ±5/80, ±7/80 ±1/8, ±3/8, ±5/8, ±7/8 Simplified −1/80, +1/80, +3/80, +5/80, +7/80 −1/8, +1/8, +3/8, +5/8, +7/8 Integration period(seconds) 1 Detection metrics Baseline 8 Simplified 5 Metric-smoothing Period (seconds) 100 — Improvement factor 1.5 – 2.3 Signal GPS L1 C/A BDS B1C MEO BDS B2a MEO Theoretical minimum receiving C/N0
(dB-Hz)39 37.5 39.3 Sampling frequency (MHz) ≥33 Reference-smoothing stations SIF = 1.5 ⌈(0.0199 · FS + 0.0176)−2⌉ ⌈(0.0151 · FS+0.0055)−2⌉ — SIF = 2.3 ⌈(0.0306 · FS + 0.0270)−2⌉ ⌈(0.0231 · FS + 0.0084)−2⌉ Probability of false-alert 1.5 ×10−7 per test Probability of miss-detection 1 ×10−3 per test MERR (meters) 1.61 2.89 Sgn Fs Ref-Smt Mtr-Smt Gain
(dB)Theo_Min_C/N0 Min_Eqv_C/N0 Asmt Result Nref Gain
(dB)Rcv SQM (dB-Hz) GPS L1 C/A 72 1 0.0 4.0 39.0 43.0 39.5 bound 69 1 0.0 40.0 bound 66 1 0.0 39.8 bound 63 1 0.0 40.2 bound 60 1 0.0 40.8 bound 57 1 0.0 41.5 bound 54 1 0.0 41.9 bound 51 1 0.0 42.2 bound 48 2 3.0 46.0 43.1 bound 45 2 3.0 43.4 bound 42 2 3.0 43.8 bound 39 2 3.0 44.1 bound 36 2 3.0 45.3 bound 33 3 4.8 47.8 46.2 bound BDS B1C 72 1 0.0 4.0 37.5 41.5 40.3 bound 69 1 0.0 40.6 bound 66 1 0.0 41.1 bound 63 2 3.0 44.5 41.6 bound 60 2 3.0 41.9 bound 57 2 3.0 42.4 bound 54 2 3.0 42.8 bound 51 2 3.0 43.3 bound 48 2 3.0 43.8 bound 45 3 4.8 46.3 44.6 bound 42 3 4.8 45.0 bound 39 3 4.8 45.6 bound 36 4 6.0 47.5 46.4 bound 33 4 6.0 46.8 bound Note: The terms Ref-Smt and Mtr-Smt refer to the reference-smoothing and metric-smoothing processes, respectively. The theoretical minimum C/N0 for either ground receivers or SQM-detection equivalency is included in the term Theo_Min_C/N0.
Jump to section
- Article
- Abstract
- 1 INTRODUCTION
- 2 CONTEXTS OF THIS STUDY
- 3 OVERVIEWS OF CDO-BASED SQM AND ITS DESIGN METHODOLOGY
- 3.2 Overview of Design Methodology for CDO-Based SQM
- 4 DESIGN PROCESS OF CDO-BASED SQM
- 5 ASSESSMENT AND SIMPLIFICATION OF BASELINE ALGORITHM
- 6 CONCLUSION AND FUTURE WORK
- HOW TO CITE THIS ARTICLE
- ACKNOWLEDGMENTS
- APPENDIX A DERIVATION OF THE APPROXIMATE MEAN OF THE EIGHT MDES
- APPENDIX B DEFINITIONS OF THE FEATURED LENGTHS FOR CONSTRAINTS ON SELECTION OF CODE-PHASE BIN LENGTH WITH NOMINAL SIGNALS
- APPENDIX C RESULTS OF ASSESSMENTS FOR L1 SIGNALS
- REFERENCES
- Figures & Data
- Supplemental
- References
- Info & Metrics
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