A reference timing
signal apparatus with a phase-locked loop (PLL) has a
computer algorithm which adaptively models the multiple frequencies of an oscillator following a
training period. The oscillator is part of a PLL and the oscillation frequency thereof is controlled in response to the
phase detector output. The
computer algorithm processes the
control signal applied to the oscillator. The
computer algorithm updates the characteristics of the model relating to the aging and temperature of the oscillator, using for example, a
Kalman filter as an
adaptive filter, in accordance with a cumulative
phase error in the PLL calculated during a given time interval. By the
algorithm, the subsequent model predicts the future frequency state of the oscillator on which it was trained. The predicted frequency of the model functions as a reference to correct the frequency of the oscillator in the event that no input reference timing
signal is available. Also, the calculated
phase error is stored and is used while no input reference timing
signal or accurate predicted frequency value is available. With the model updating
algorithm, oscillators of low stability performance may be used as cellular
base station reference oscillator, which is based on
satellite systems, for example, GPS,
GLONASS or Galileo systems.