Abstract
Tracking error estimation is of great importance in global navigation satellite system (GNSS) receivers. Any inaccurate estimation for tracking error will decrease the signal tracking ability of signal tracking loops and the accuracies of position fixing, velocity determination, and timing. Tracking error estimation can be done by traditional discriminator, or Kalman filter-based pre-filter. The pre-filter can be divided into two categories: coherent and non-coherent. This paper focuses on the performance improvements of non-coherent pre-filter. Firstly, the signal characteristics of coherent and non-coherent integration—which are the basis of tracking error estimation—are analyzed in detail. After that, the probability distribution of estimation noise of four-quadrant arctangent (ATAN2) discriminator is derived according to the mathematical model of coherent integration. Secondly, the statistical property of observation noise of non-coherent pre-filter is studied through Monte Carlo simulation to set the observation noise variance matrix correctly. Thirdly, a simple fault detection and exclusion (FDE) structure is introduced to the non-coherent pre-filter design, and thus its effective working range for carrier phase error estimation extends from (−0.25 cycle, 0.25 cycle) to (−0.5 cycle, 0.5 cycle). Finally, the estimation accuracies of discriminator, coherent pre-filter, and the enhanced non-coherent pre-filter are evaluated comprehensively through the carefully designed experiment scenario. The pre-filter outperforms traditional discriminator in estimation accuracy. In a highly dynamic scenario, the enhanced non-coherent pre-filter provides accuracy improvements of 41.6%, 46.4%, and 50.36% for carrier phase error, carrier frequency error, and code phase error estimation, respectively, when compared with coherent pre-filter. The enhanced non-coherent pre-filter outperforms the coherent pre-filter in code phase error estimation when carrier-to-noise density ratio is less than 28.8 dB-Hz, in carrier frequency error estimation when carrier-to-noise density ratio is less than 20 dB-Hz, and in carrier phase error estimation when carrier-to-noise density belongs to (15, 23) dB-Hz (26, 50) dB-Hz.
Highlights
A Global Navigation Satellite System (GNSS) is a satellite system to provide autonomous positioning worldwide [1]
This section first reviews some of the relevant baseband signal models that can be used in the tracking error estimation phase
The red lines in these figures represent the shape of Gaussian probability density distribution whose mean and variance are same as those of corresponding statistical results. These figures function whose mean and variance are same as those of corresponding statistical results. These imply that there is an obvious difference between the actual estimation noise distribution of the figures imply that there is an obvious difference between the actual estimation noise distribution of ATAN/ATAN2/non-coherent early minus late envelope (NC-EMLE) discriminator and a Gaussian distribution
Summary
A Global Navigation Satellite System (GNSS) is a satellite system to provide autonomous positioning worldwide [1]. The GNSS receiver performs the measurement for pseudo-range, pseudo-range rate, and carrier phase according to the signal parameters estimated by signal tracking function. Compared with the traditional discriminator, the pre-filter would provide more accurate tracking error estimation because it fully utilizes the smoothing effect of the system model and the statistical characteristics of observation noise. It performs well in both strong signal and weak signal conditions Since it takes the discriminator outputs as observations, the performance of the non-coherent pre-filter is affected by drawbacks of the traditional discriminator. This paper is organized as follows: Section 2 provides the necessary basic knowledge about tracking error estimation, including the relevant baseband signal model, ATAN/ATAN2/NC-EMLE discriminator algorithms, and coherent/non-coherent pre-filter design.
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