Hidden Markov modeling (HMM) can be applied to extract single channel kinet
ics at signal-to-noise ratios that are too low for conventional analysis. T
here are two general HMM approaches: traditional Baum's reestimation and di
rect optimization. The optimization approach has the advantage that it opti
mizes the rate constants directly. This allows setting constraints on the r
ate constants, fitting multiple data sets across different experimental con
ditions, and handling nonstationary channels where the starting probability
of the channel depends on the unknown kinetics. We present here an extensi
on of this approach that addresses the additional issues of low-pass filter
ing and correlated noise. The filtering is modeled using a finite impulse r
esponse (FIR) filter applied to the underlying signal, and the noise correl
ation is accounted for using an autoregressive (AR) process, In addition to
correlated background noise, the algorithm allows for excess open channel
noise that can be white or correlated. To maximize the efficiency of the al
gorithm, we derive the analytical derivatives of the likelihood function wi
th respect to all unknown model parameters. The search of the likelihood sp
ace is performed using a variable metric method. Extension of the algorithm
to data containing multiple channels is described. Examples are presented
that demonstrate the applicability and effectiveness of the algorithm. Prac
tical issues such as the selection of appropriate noise AR orders are also
discussed through examples.