  We demonstrate that a Kalman filter applied to estimate the position of an
optically levitated nanoparticle, and operated in real-time within a Field
Programmable Gate Array (FPGA), is sufficient to perform closed-loop parametric
feedback cooling of the centre of mass motion to sub-Kelvin temperatures. The
translational centre of mass motion along the optical axis of the trapped
nanoparticle has been cooled by three orders of magnitude, from a temperature
of 300K to a temperature of 162 +/- 15mK.
