We consider a calibration problem, where we determine an unknown sensor location using the known track of a calibration target and a known reference sensor location. We cast the calibration problem as a sparse approximation problem where the unknown sensor location is determined over a discrete spatial grid with respect to the reference sensor. To achieve the calibration objective, low dimensional random projections of the sensor data are passed to the reference sensor, which significantly reduces the inter-sensor communication bandwidth. The unknown sensor location is then determined by solving an l(1)-norm minimization problem (linear program). Field data results are provided to demonstrate the effectiveness of the approach.