  We present a new method for determining the local dark matter density using
kinematic data for a population of tracer stars. The Jeans equation in the
$z$-direction is integrated to yield an equation that gives the velocity
dispersion as a function of the total mass density, tracer density, and the
tilt term that describes the coupling of vertical and radial motions. We then
fit a dark matter mass profile to tracer density and velocity dispersion data
to derive credible regions on the vertical dark matter density profile. Our
method avoids numerical differentiation, leading to lower numerical noise, and
is able to deal with the tilt term while remaining one dimensional. In this
study we present the method and perform initial tests on idealised mock data.
We also demonstrate the importance of dealing with the tilt term for tracers
that sample $\gtrsim 1$ kpc above the disc plane. If ignored, this results in a
systematic underestimation of the dark matter density.
