### Book chapter

## A Method of Evaluating the g-sensitivity of Quartz Oscillators in GNSS Receivers

Modern global navigation satellite systems (GNSS) receivers use temperature-compensated crystal oscillators (TCXO) as generators of reference frequency. One of the parameters of quartz oscillators is its stability to output frequency when oscillators are subject to acceleration and vibrations. Such a stability is assessed by g-sensitivity value. Relatively high g-sensitivity of quartz oscillators can result in large tracking errors within circuits of GNSS receivers operating in hard vibrational-dynamic conditions, up to loss of tracking which negatively affect functional capacities of GNSS receivers. The current paper describes a method of estimating g-sensitivity of TCXO mounted on GNSS receiver printed circuit board (PCB). Experimental results have proved the advantage of this method over other known methods of g-sensitivity assessment for TCXO used in GNSS receivers.

This paper is a continuation of the author’s previous study on methods of velocity measurements of navigation receivers and devoted to their comparative analysis.

Each method of measuring velocity has a few parameters. Let us fix all parameters except for one (main) and vary this parameter. The value of each varied parameter corresponds to some noise error of velocity measurements which can be characterized by standard deviation, or SD (cm/s). A dynamic model of GNSS receiver motion determines dynamic errors. Maximal dynamic error (MDE) (cm/s) is of interest in this case. This error depends on “maneuver phase”, i.e., a shift of the maneuver start time from the starting point of PLL control period and also the starting point of the secondary processing period. The maximal value of MDE is of interest in these shifts.

So, for each value of the varied parameter there is a pair of numbers: SD and MDE. Let us arrange these numbers in plane of the coordinate system: x-axis is MDE, and y-axis is SD. Connect nearest points and obtain a curve which is called an exchange diagram. Since SD and MDE vary within a wide range, the diagrams should be built in logarithmic scale, that is in dB relative to 1 cm/s. Let us call them logarithmic exchange diagrams (LED). Different LED were plotted for tough and soft dynamic scenarios for different methods of velocity measurements including the conventional one frequently discussed in the literature.

As a result of the analysis, a method of generating frequency estimates of the input signal and their further filtering using an after-satellite second order tracking filter, and a method based on quasi-optimal estimates of the input signal phase and further after-satellite filtration using the third order tracking filter have been recommended for tougher dynamic conditions. Under more favorable conditions in addition to the two above, a method of generating coordinate increments over one period with further after-coordinate filtration using the second order tracking filter, and a method of generating local coordinates with further aftercoordinate filtration using the third order tracking filter have been also recommended. In conclusion, a law of velocity estimate SD variation for one of the best recommended methods was investigated in the process of varying method parameters.

The present paper discusses different techniques of measuring Carrier-to-Noise density ratio (C/N0) in navigation and information-communication systems. C/N0 means the ratio of the received signal power to the noise spectral density N0 at receiver's input (at the output of an antenna with a low-noise amplifier (LNA)). Correlation processing is performed in the receiver to obtain in-phase (I) and quadra-phase (Q) components of the input signal. Three estimation algorithms of C/N0 [Hz] have been analyzed in the paper. The first algorithm is robust: it requires minimal a priori information about signals, noise and receiver configuration. This algorithm is based on estimation in real time both expected value and the variance of in-phase component I. The second algorithm is called I-noise-immune, since it provides much more accurate estimates for C/N0, than the robust one but it needs a priori data about variance of component I. This requirement can be satisfied if value N0 is mainly determined by internal receiver noise (more precisely, - LNA noise), but not by received external interference. Both algorithms are applicable when Phase locked loop (PLL) operates quite precisely in the receiver. The third algorithm called Z-noise-immune, unlike the two first algorithms, does not need precise operation of PLL or even PLL availability in the receiver at all, but similar to the second algorithm is based on the assumption that value N0 is determined by internal noise rather than external interference. There were shown the third algorithm produces unbiased estimate of C/N0.

Measurements of velocity in navigation receivers are performed in two stages. At the primary (after-satellite) processing stage each of received signals is synchronized using a separate PLL, after that an estimation block (EB) estimates nonenergy (phase and frequency) and energy (SNR) parameters of the received signal. Doppler primary estimations can be subject to after-satellite filtration to obtain secondary frequency estimates. A number of Doppler estimates are conversed into primary estimates of velocity vector projections (for example, onto axes of the local Cartesian coordinate system) using the least square method (LSM). Primary estimates of velocity can be filtered at the secondary (after-coordinate) processing. Secondary velocity vector coordinates are outputted to users.

The present paper considers different methods of measuring velocity, they being different from each other by different tracking filters of primary and secondary processing and different EB. Primary filters operate at the same control frequency Fc as PLL (for instance, at Fc= 200 Hz), and LSM and secondary filters – at lower frequency FE < Fc (for example, at FE=100 Hz or FE=10 Hz). To shift from Fc to FE, some samples are rejected (intermediate samples are thrown). EB generates either primary estimates of instantaneous frequency or instantaneous phase of the input signal, or primary estimates of average input phase over control period Tc=Fc^-1. These primary estimates are fed to the filters of primary processing. At the outputs of these filters either secondary estimates of instantaneous frequency or estimates of averaged frequency and it’s derivative over period Tc are outputted which further are recalculated in estimates of instantaneous frequency. Based on thinned instantaneous phase estimates sometimes there are generated increments of these phase estimates over period TE = FE^-1. Primary estimates of either coordinates of the instantaneous velocity vector or averaged over period TE are fed to the input of secondary processing filters. In the first case, secondary estimates of instantaneous coordinates of the velocity vector are obtained at filter outputs at once. In the second case, at the filter outputs there are estimates of averaged velocities and accelerations over period TE which are further calculated in estimates of instantaneous velocity vector coordinates.

It has been shown that frequency estimation typically used in analog systems brings about a biased frequency (and hence, velocity) estimate when a receiver with digital PLLs has constant non-zero acceleration. Various algorithms of non-biased estimation have been also considered.

A subject of the study are systems of synchronization and motion parameters estimation for global positioning satellite systems (GLONASS, GPS, Galileo and others) receivers. Two synchronization systems are considered in the paper: a traditionally used system with separate synchronization in each navigation channel and an alternative one – with joint synchronization of all the signals. The latter system is called CQLL (coordinate-quartz locked loop). There are four common loops in the CQLL (three coordinate loops and one quartz loop) and N individual loops in accordance with the number of synchronized satellite signals. The common loops are designed for tracking general highly dynamic impacts (such as receiver motion and quartz fluctuation, especially due to shaking), while individual loops – for synchronizing less intensive individual effects (ionosphere, troposphere and some other effects). The aim of this study is to develop recommendations on selecting one of the systems and system parameters depending on environment conditions. A modification of the existing joint synchronization system has been proposed in the paper which leads to full unloading of individual loops from the general effects enabling bandwidths of the individual loops to be very narrow (units of Hz). Experiments based on simulation modeling have been performed, which demonstrated the benefit of the proposed modified system (CQLL system with full unloading of individual loops). It has been shown that within pre-threshold regions both separate and modified joint synchronization systems provide the same dynamic and fluctuation errors for position and velocity estimates if the bandwidth of common loops matches that of the separate synchronization system. However, the joint synchronization system typically has smaller fluctuation errors for tracking phases of each navigation signals which eventually should improve threshold properties of such systems (when narrow bandwidths of individual loops are employed).

The present paper discusses different techniques of measuring Carrier-to-Noise density ratio (C/N0) in navigation and information-communication systems. C/N0 means the ratio of the received signal power to the noise spectral density N0 at receiver's input (at the output of an antenna with a low-noise amplifier (LNA)). Correlation processing is performed in the receiver to obtain in-phase (I) and quadra-phase (Q) components of the input signal. Three estimation algorithms of C/N0 [Hz] have been analyzed in the paper. The first algorithm is robust: it requires minimal a priori information about signals, noise and receiver configuration. This algorithm is based on estimation in real time both expected value and the variance of in-phase component I. The second algorithm is called I-noise-immune, since it provides much more accurate estimates for C/N0, than the robust one but it needs a priori data about variance of component I. This requirement can be satisfied if value N0 is mainly determined by internal receiver noise (more precisely, - LNA noise), but not by received external interference. Both algorithms are applicable when Phase locked loop (PLL) operates quite precisely in the receiver. The third algorithm called Z-noise-immune, unlike the two first algorithms, does not need precise operation of PLL or even PLL availability in the receiver at all, but similar to the second algorithm is based on the assumption that value N0 is determined by internal noise rather than external interference. There were shown the third algorithm produces unbiased estimate of C/N0.