  We provide a detailed stochastic description of the swimming motion of an
E.coli bacterium in two dimension, where we resolve tumble events in time. For
this purpose, we set up two Langevin equations for the orientation angle and
speed dynamics. Calculating moments, distribution and autocorrelation functions
from both Langevin equations and matching them to the same quantities
determined from data recorded in experiments, we infer the swimming parameters
of E.coli . They are the tumble rate ${\lambda}$, the tumble time $r^{-1}$ ,
the swimming speed $v_0$ , the strength of speed fluctuations ${\sigma}$, the
relative height of speed jumps ${\eta}$, the thermal value for the rotational
diffusion coefficient $D_0$ , and the enhanced rotational diffusivity during
tumbling $D_T$ . Conditioning the observables on the swimming direction
relative to the gradient of a chemoattractant, we infer the chemotaxis
strategies of E.coli . We confirm the classical strategy of a lower tumble rate
for swimming up the gradient but also a smaller mean tumble angle (angle bias).
The latter is realized by shorter tumbles as well as a slower diffusive
reorientation. We also find that speed fluctuations are increased by about 30%
when swimming up the gradient compared to the reversed direction.
