About the teaching of radio navigation theory

Povalyaev A.A.

JCS “Russian space systems” Moscow aviation institute (National research university)

Krasnoyarsk, 20 may 2015 г

1 Reviewed literature

1. GLONASS. Global satellite radionavigation system. Edited by A.I. Petrov, V.N. Kharisov.- M.: Radiotechnica.- 2005. 2. Malishev V.V., Kurshin V.V., Revnivykh S.G. Introduction to satellite navigation. Text edition. M.: Publishing house MAI-PRINT. – 2008. 3. Information technology in radiotechnical systems. Text edition. Edited by Fedorov I.B. Second edition, revised and corrected edition. M.: MSTU Bauman Publishing house.- 2004. 4. Solovyov Y.A. Systems of satellite navigation. Monograph. M.: EKO- TRENDZ.- 2000. 5. Boriskin A.D., Weitzel A.V., Weitzel V.A., Jodzishskiy M.I., Milutin D.S. High-precision positioning equipment on the signals of global navigation satellite systems: receivers – navigation data users. Scientific publication. - M.: MAI-PRINT.- 2010. 6. Bakulev P.A., Sosnovskiy A.A. Radionavigation systems. Course manual. - М.: Radiotechnics.- 2011. 7. Guide to GPS Positioning. Prepared under the leadership of David Wells. Canadian GPS Associates. Second printing, with corrections, May 1987 2 Review of ideas, used in modern scientific and teaching literature for GNSS activity description Ttr

STS t01 t02 t03 t j j τ d τ d j τpd τpd RTS tdo1 tr1 tdo2 tr2 tdo3 t ΔT Ttr ΔT ΔT

t01, t02, t03, … is called “a priori known” [3, 4], or moments with nominal time of transmission [5]

j j ΔТ = t0i – tdoi τpd = τd + ΔT

j j j j 2 j 2 j 2 ρ = cτpd = c(τd + ΔT)= (xr − x ) + (yr − y ) + (zr − z ) + ΔRr 3 Kriticism of ideas used in modern scientific and teaching literature for GNSS activity description (1)

Ttr

STS t01 t02 t03 t

Ttr j τd j τpd j τapd RTS tdo1 tr0 tdo2 tr1 tdo3 t ΔT Ttr ΔT ΔT

j j j τpd = τapd + k Ttr

j Ambiguous pseudodelay measurements under τ d > Ttr 4 Kriticism of ideas used in modern scientific and teaching literature for GNSS activity description (2)

Ttr

STS t01 t02 t03 t

Ttr j j τз τ з j j j τpd τapd τapd

tdo0 ΔT tr1 tdo1 tr2 tdo2 t RTS ΔT Ttr

j j j τpd = τapd + k Ttr

Ambiguous pseudodelay measurements under Δ T > Ttr 5 Kriticism of ideas used in modern scientific and teaching literature for GNSS activity description (3)

Ttr a) STS t01 t02 t03 t j j τ R τ R j j τmeas τmeas b) RTS j t t j t do1 t r1 do2 t do3 t ΔT r2 Ttr ΔT ΔT

k k τ R τ R k k τmeas τmeas c) RTS t k t k t t do1 t r1 do2 tr2 do3 ΔT Ttr ΔT ΔT

Arrival times of j-th and k-th satellites signals 6 Kriticism of ideas used in modern scientific and teaching literature for GNSS activity description ГНСС (4)

Ttr t k t j tk t j tk t j a) STS tr1 tr1 tr2 tr2 tr3 tr3 t01 t02 t03 t j j j τ R τ R τ R τj j j ΔT meas ΔT τmeas ΔT τmeas b) RTS j j t tmeas2 t t meas1 t r1 tr2 meas3 ΔT Ttr ΔT ΔT

k k k τ R τ R τ R k k k ΔT τmeas ΔT τmeas ΔT τmeas c) RTS k k tmeas1 t tmeas2 t tmeas3 t ΔT r1 r2 Ttr ΔT ΔT

Measurement moment tmeas and appropriate for it j к transmission times for j-th t tr and k-th t tr satellites. 7 Meaning content of harmonic signal phase φ(t) definition

8 Meaning content of PRN signal phase definition

9 Time scale and time on the scale meaning content definition

Clock indication (clock process full phase) 17 or scale time 16 Clock indication (first 15 clock process full phase) 14 or the time on first scale 13 12 11 Clock indication (first Shift of first scale 10 clock process full relative to second phase) or the time on scale in the moment 9 second scale 8 defined on the second 7 scale 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Physical time t 1 Moments, appropriate for two different time scales 0 Satellite clock indication resolution

ˆ j ˆ j j −3 j j ˆ j ξ (tизм )= b a − fraction phase T (t пр )=10 (ζмс + n + ξ (t изм )) 11 Visual navigational receiver model and pseudorange idea definition

j ˆ j j −3 j j ˆ j Tchan (tmeas )= T (ttr )=10 (ζмс + n + ξ (tmeas )) ˆ j ˆ j j j 12 П (tmeas )= Tr (tmeas )− T (ttr )= Tr (tmeas )− Tchan (tmeas ) OMEGA system navigational frame

10.2 (0.09804 mc) 13.6 34/3 KHz least common multiple is 60/17 mc OMEGA frame duration 10 c, hence least common multiple is 30 c

13 L. Fey. definitions L. Fey. Time Disseminations Capabilities of the Omega System. Pros. 25th Ann. Symp. Frequency Control (Electron. Indust. Ass., Washington, D.C.) pp. 167-170, Apr. 1971

ˆ j j j T (ttr )= Nday ⋅86400 + Nhour ⋅3600 + Nmin ⋅60 + N30 ⋅30 + ξс (tmeas ) 14 Summary • Primary radionavigation concept is “time on scale”, for wich stands moments of physical time, indicated by clock, basic for every scale. Clock reading is a full phase of a signal given by a clock generator. • “Time on scale” concept is used to determine a pseudo-delay, as well as for calculating in a receiver a satellite coordinates in the moment of emission. • A pseudodelay is secondary concept formed as the difference between the readings of the receiver clock and the channel clock in the moment of measurement. • In radionavigation systems pseudodelay ambiguity resolution is made by ambiguity resolution of satellites (stations) clock ambiguity in the moment of emission

(channel clock readings). 15 Summary (continuation)

• Reading of curriculum a on bases of radionavigation systems functioning should be started from:

- Definition of “time on scale” as full phase of a periodical signal, lying in a basis of every scale (clock).

- Transmission of the radionavigation stations clock readings with use of emitted signals phase.

- Use in a receiver a received signal phase for calculating a satellites coordinates in the moment of emission and for forming a pseudodelay measurements as a difference of full phases (difference of a receiver clock readings in the moment of measurement and a moment of emission) 16 Summary (continuation) • After presenting the general principles of radionavigation systems functioning one should move to the illustration how these principles are implemented in specific terrestrial systems (OMEGA, ALPHA, Loran-C, Chaika) and GNSS.

• Examine characteristics of a common functioning principles in exact GNSS: GPS, GLONASS, BDS, Galileo. Example: in GPS, satellites migration is binded to the system scale time, whereas in GLONASS -- to the Moscow decret time. In GLONASS, board timescale is the phase of a signal transmitted in L1, whereas in GPS it is ionospherefree combination of signal phases, transmitted by satellites in L1 and L2. Etc…

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Thanks for you attention.

Questions?

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