  We present an improved numerical kludge waveform model for circular,
equatorial EMRIs. The model is based on true Kerr geodesics, augmented by
radiative self-force corrections derived from perturbative calculations, and in
this paper for the first time we include conservative self-force corrections
that we derive by comparison to post-Newtonian results. We present results of a
Monte Carlo simulation of parameter estimation errors computed using the Fisher
Matrix and also assess the theoretical errors that would arise form omitting
the conservative correction terms we include here. We present results for three
different types of system, namely the inspirals of black holes, neutron stars
or white dwarfs into a supermassive black hole (SMBH). The analysis shows that
for a typical source (a 10 solar mass compact object captured by a one million
solar mass SMBH at signal to noise ratio of 30) we expect to determine the two
masses to within a fractional error of ~0.0001, measure the spin parameter q to
~0.00003 and determine the location of the source on the sky and the spin
orientation to within 0.001 steradians. We show that, for this kludge model,
omitting the conservative corrections leads to a small error over much of the
parameter space, i.e., the ratio R of the theoretical model error to the Fisher
Matrix error is R<1 for all ten parameters in the model. For the few systems
with larger errors typically R<3 and hence the conservative corrections can be
marginally ignored. In addition, we use our model and first order self-force
results for Schwarzschild black holes to estimate the error that arises from
omitting the second-order radiative piece of the self-force. This indicates
that it may not be necessary to go beyond first order to recover accurate
parameter estimates.
