In this paper we present a wearable positioning system that requires less than 10~mW to operate. The system consists of an infrastructure of ultrasonic transmitting devices, and a receiver device on the wearable. The receiver comprises an ultrasonic pick-up, an op-amp, and a PIC. The PIC implements a particle filter for estimating X and Y positions. The transmitter layout has been chosen to simplify the maths in the PIC so that the particle filter reduces to just two multiplication operations per particle. We have modified the traditional particle filter in order to operate on a micro-controller with severely limited memory capabilities. The advantage of using a particle filter over other filtering techniques is that a particle filter is robust in environments with limited precision; all our data is stored as 8-bit. The number of particles is only limited by the amount of memory on the PIC; we only use 5% of the PIC's computational power.