Digital Data Combinations for Low Frequency Radio Navigation

The accuracy with which an airborne receiver of a low frequency radio navigation system can be located in real time can be improved considerably by combining the position information from the receiver with velocity information from a velocity sensor such as a Doppler radar. Since aircraft maneuvers and hence the dynamics of the aircraft position and velocity are not known apriori, it is advantageous to combine position and velocity in a filter having a distortionless constraint, that is, a filter whose output has no position error resulting from the dynamics of the inputs. The theory of optimization of such distortionless filters, which are by definition analog filters, has been described in the literature. However, the long range and inherently high accuracy of a low frequency radio navigation system dictate a digital filter combination. In this paper, optimum digital filters combining position and velocity information under an approximate distortionless constraint are synthesized. Four types of digital filters are analyzed and compared: filters having a single sample rate and containing zero order or first order integrators, and filters having a dual sampling rate and containing zero order or first order integrators. These filters are optimized for minimum variance in their position outputs in response to band-limited Gaussian noise in their position and velocity inputs. Position error resulting from random noise and aircraft maneuvers are derived as a function of sample rate. Curves of position error versus sampling rate for a typical low frequency radio navigation system are presented.