  Statistical estimation theory determines the optimal way of estimating
parameters of a fluctuating noisy signal. However, if the estimation is
performed on unreliable hardware, a sub-optimal estimation procedure can
outperform the previously optimal procedure. Here, we compare classes of
circadian clocks by viewing them as phase estimators for the periodic day-night
light signal. We find that continuous attractor-based free running clocks, such
as those found in the cyanobacterium Synechococcus elongatus and humans, are
nearly optimal phase estimators since their flat attractor directions
efficiently project out light intensity fluctuations due to weather patterns
(`external noise'). However, such flat directions also make these continuous
limit cycle attractors highly vulnerable to diffusive 'internal noise'. Given
such unreliable biochemical hardware, we find that point attractor-based damped
clocks, such as those found in a smaller cyanobacterium with low protein copy
number, Prochlorococcus marinus, outperform continuous attractor-based clocks.
By interpolating between the two types of clocks found in these organisms, we
demonstrate a family of biochemical phase estimation strategies that are best
suited to different relative strengths of external and internal noise.
