Track likelihood statistic for the I Q locked loop

The IQ locked loop has been an effective phase-frequency tracker for a variety of applications. An important tracking requirement is a reliable statistic to measure when the loop is locked. In this paper we derive a track likelihood statistic which is calculated by correlating the estimated quadrature components with the measurements. We show that this statistic can be used to determine when the loop has been initialized and when loss of lock has occurred. We also give examples of the usefulness of the statistic for adapting loop gains to unmodeled dynamics and variations in signal to noise ratio.