Analysis of Noise and Cycle Selection in a Loran Receiver

—Thermal and atmospheric noise distort envelope measurements in a Loran receiver, and may cause the receiver to select the wrong cycle during signal acquisition. A cycle error would persist during signal tracking and result in a ranging error of 3,000 km. The probability of a wrong cycle selection is dependent on the signal-to-noise ratio and on the algorithm used in signal acquisition. In this paper, we develop a mathematical model to predict the probability of wrong cycle selection in a Loran receiver, which uses a ratio test as a cycle selection algorithm, when subjected to Gaussian noise. Previous methods of calculating the probability of wrong cycle selection have been based on empirical data from an Austron 5000 Loran receiver. These data are used to produce a Gaussian approximation of envelope-to-cycle delay (ECD) and to derive the probability of wrong cycle selection from excursions of ECD in excess of 5 s. Through simulation, we show this empirical method provides a conservative over-bound of the probability of wrong cycle selection versus SNR. However, the novel methods developed in the paper show a theoretical bound which is 1 to 4 dB lower.