An Algorithm for a Group Time Scale Using a Moving Average Over Multiple Time Scales

Abstract

A new algorithm is presented for the formation of an analytical time scale that takes into account the fl uctuations of atomic clock signal frequencies over several time scales. Numerical simulation shows that the algorithm can obtain a group time scale for an ensemble of atomic clocks with rather high frequency stability characteristics. The proposed algorithm is compared with the algorithm for calculating a time scale based on the Kalman fi lter. Analytical time scales are widely used in time and frequency standards based on an ensemble of atomic clocks to increase precision and stability characteristics. At this time, there are a large number of algorithms for computing analytic time scales. Among them there are algorithms which process results a posteriori and algorithms in which the corrections for atomic clock signals constituting a reference group are calculated in real time. The most frequently used computational methods are various modifi cations of the basic equations of the time scale (ALGOS, FAT, AT1, METS) [1-6], Kalman fi ltering (Kred, IEM) [7-9], as well as their combination (KAS-2, KPW) [10 -11]. Algorithms based on the Kalman fi lter enable a suffi ciently precise estimate of signal frequency and phase; as a rule, they give better results compared with algorithms based only on the basic equations of the time scale, such as AT1 and ALGOS. However, their operation requires a priori information about the parameters of the phase noise of atomic clock signals; moreover, the Kalman fi lter signifi cantly complicates accounting for fl icker frequency noise [12]. We also note that the computational complexity of algorithms based on the Kalman fi lter increases nonlinearly with increasing number of atomic clocks in the ensemble, and the procedure for adding or excluding an atomic clock from the group turns out to be more complicated than in other methods.Previously there was proposed an algorithm using a frequency-locked loop with an auxiliary generator relative to an ensemble of quantum clocks to form the group signal [13]. This algorithm uses the moving average method to estimate the fl uctuation frequency of the input signals over different time intervals. Unlike the Kalman fi lter, it does not require information about the model of the random process and its parameters for describing the atomic clock signals. According to the simulation results presented in [13], the Allan deviation of the group signal generated by this algorithm is close to the minimum possible values for the entire range of measurement time intervals considered. Thus, the control algorithm has to be comparable in stability characteristics of the formed weighted average frequency to the presently known algorithms for the

Research on a time scale algorithm based on multi-dimensional weighted average

“…This causes the stability of the ensemble time scale can only be optimized in a specific average time, which means the long-term, mid-term and short-term stability cannot be considered simultaneously. Moreover, there is a theoretical limit for the weighted average algorithm to improve the time scale stability [2].…”

“…Time scales are widely used in time and frequency standards based * Authors to whom any correspondence should be addressed. on an ensemble of atomic clocks to increase precision and stability characteristics [2].…”

Adaptive time series models in the measurement data processing systems

“…В настоящее время существует большое количество алгоритмов для вычисления шкал времени, характеризующих состояние эталона. Наиболее часто используемые методы расчета являются различными модификациями базовых уравнений шкалы времени [1][2][3][4][5][6] либо используют фильтрацию Калмана [4][5][6][7][8][9]. Алгоритмы, основанные на фильтре Калмана, в том числе и субоптимальной фильтрации, позволяют достаточно точно оценить состояние группового эталона и, как правило, дают лучшие результаты по сравнению с методами, основанными на модификации базового уравнения шкалы времени.…”

“…Практически все современные алгоритмы оценивания вектора состояния групповых ЭВиЧ, опирающиеся на использование прогнозирующих моделей, используют в качестве таких моделей линейные модели, а прогноз значения частоты стандартов частоты вычисляется на основе разделения исследуемого процесса изменения частоты на две составляющие: детерминированную (линейный тренд частоты) и стохастическую, описываемую процессом скользящего среднего первого порядка [3,4,6].…”

“…-прогноз частоты i-го генератора на один шаг вперед на такте s. Полученные в выражении (2) оценки имеют погрешность меньшую, нежели погрешность МНК-оценок, примерно на 30 %[3,5, 9].…”