  In numerous systems in biophysics and related fields, scientists measure
(with very smart methods) individual molecules (e.g. biopolymers (proteins,
DNA, RNA, etc), nano - crystals, ion channels), aiming at finding a model from
the data. But the noise is not solved accurately in not so few cases and this
may lead to misleading models. Here, we solve the noise. We consider two state
photon trajectories from any on off kinetic scheme (KS): the process emitting
photons with a rate {\gamma}on when it is in the on state, and emitting with a
rate {\gamma}off when it is in the off state. We develop a filter that removes
the noise resulting in clean data also in cases where binning fails. The filter
is a numerical algorithm with various new statistical treatments. It is based
on a new general likelihood function developed here, with observable dependent
form. The filter can solve the noise, in the detectable region of the rate
space: that is, we also find a region where the data is "too" noisy.
Consistency tests will find the region's type from the data. If the data is
ruled "too noisy", binning obviously fails, and one should apply simpler
methods on the raw data and realizing that the extracted information is
partial. We show that not applying the filter while cleaning results in
erroneous rates. This filter (with minor adjustments) can solve the noise in
any discrete state trajectories, yet extensions are needed in "tackling" the
noise from other data, e.g. continuous data and FRET data.
  The filter developed here is complementary with our previous projects in this
field, where we have solved clean two state data with the development of
reduced dimensions forms (RDFs): only the combined procedures enabling building
the most accurate model from noisy trajectories from single molecules
