In a GPS L1 receiver simulation, extended-integration mode was associated with lower reported frequency fluctuation. The reported root-mean-square (RMS) frequency deviation was no more than 1 hertz in extended-integration mode, versus about 2.6 hertz initially.
The author-developed simulator generated simplified GPS signals with adjustable carrier phase shift, Doppler frequency and code delay. It added pseudo-random white Gaussian noise to reach a target carrier-to-noise density ratio (C/N0), and the analysis compared Type I with Type II second-order and Type III third-order filters.
In the stationary ideal simulation, the first 2 seconds used 1-millisecond integration before switching to 10 milliseconds. The phase-lock loop (PLL) bandwidth was 5 hertz and the delay-lock loop (DLL) bandwidth 1 hertz; all three filters showed similar behavior in that setup.
For signals carrying navigation data, the integration interval could not exceed the data-bit length. The stated limits were 20 milliseconds for classic GPS L1 and 10 milliseconds for GLONASS L1; the document also reports that switching to extended integration can be associated with loss of lock and recommends a smooth transition algorithm.
Filter behavior varied in dynamic simulations
One dynamic simulation used a harmonic signal-frequency variation with an amplitude of 11 hertz at 2.5 hertz and a 5-hertz PLL bandwidth. In that trace, Type III showed stability advantages, while Types I and II were less stable and lost lock.
With 10-millisecond integration and a 1-hertz DLL bandwidth, the reported RMS frequency deviation was 0.07 hertz for Type III, compared with 0.11-0.12 hertz for Types I and II. In a transient test starting with a 40-hertz carrier-frequency offset, all three filters showed fast oscillatory responses at high C/N0, while the document reports longer responses at higher noise levels.
A code-delay test began with an initial delay of 20 samples; the Type II DLL transient had not completed within the 2-second observation window.
Reduced correlator spacing was linked to lower reported DLL noise
At C/N0 = 39 dB-Hz, the reported Type II RMS deviation was approximately 0.07 at 0.5 chip and 0.036 at 0.1 chip. The comparison associated the narrower spacing with the lower reported value.
In a real-signal test, the receiver tracked one GPS satellite for 10 seconds at about 44 dB-Hz using a Type II filter. It started with 1-millisecond integration and changed to 10 milliseconds after about 2 seconds; PLL bandwidth changed from 25 to 5 hertz, DLL bandwidths were 3 and 0.8 hertz, and spacing changed from 0.5 to about 0.1 chips. The paper reports a consistent association between reduced correlator spacing and lower DLL NCO noise in that test.
The recommendations remain configuration-specific
The authors' recommendation is configuration-specific: Type II is close to optimal under low-dynamic conditions, while Type III is preferable under highly dynamic conditions, with stability carefully monitored.
The evidence combined an experimental GPS L1 receiver, author-developed simulation software, Xilinx Vivado, and recordings of real navigation signals from full-scale tests; the real-signal test tracked one satellite. No formal inferential tests or confidence intervals were reported, and no replicate-level uncertainty was reported for the comparisons.
These are tracking-loop engineering results, not a demonstration of end-to-end position or navigation accuracy. The study does not establish performance across other GNSS signals, constellations, receiver architectures or field conditions, and it does not show universal superiority of one filter under all dynamics, noise levels or transition conditions.
Paper data and sources
Original title: Some Practical Issues of the Tracking Process in GNSS Receivers
Authors: S. V. Shafran, I. A. Kudryavtsev, A. A. Kumarin
Journal/Repository: published in the journal "Infokommunikacionnye Tehnologii" by Povolzhskiy State University of Telecommunications and Informatics (Samara) No.1 2026
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text