A novel Technique for Improving the Angular Accuracy of Doppler VOR Receivers

Doppler VOR (D-VOR) transmitters are used as navigation aids in aviation. They transmit an omnidirectional phase reference in an amplitude-modulated (AM) sideband and directional phase information on a frequency-modulated (FM) subcarrier. In an airborne D-VOR navigation receiver, a directional information (azimuth angle) related to the position of the aircraft and the location of the transmitter can be derived from the difference of these two phase signals. In this work, the accuracy of AM and FM phase signals is firstly investigated analytically and afterwards verified by measurements. It will be shown that in established procedures, phase inaccuracy is dominated by the AM signal, since the FM signal is about 21 dB less noisy. Subsequently, a novel method is presented that improves the accuracy of the azimuth angle by orders of magnitude in case of D-VOR transmitters. This new method inherently reduces noise of the AM phase and thus yields a significant increase in accuracy. As a result, the remaining FM phase uncertainty becomes dominant for the total uncertainty of the bearing indication. Finally, the application of the new method to real measured signals confirms the theoretical expectations.

Precipitation phase uncertainty in cold region conceptual models resulting from meteorological forcing time-step intervals

Precipitation phase determination is a known source of uncertainty in surface-based hydrological, ecological, safety, and climate models. This is primarily due to the surface precipitation phase being a result of cloud and atmospheric properties not measured at surface meteorological or hydrological stations. Adding to the uncertainty, many conceptual hydrological models use a 24-h average air temperature to determine the precipitation phase. However, meteorological changes to atmospheric properties that control the precipitation phase often substantially change at sub-daily timescales. Model uncertainty (precipitation phase error) using air temperature (AT), dew-point temperature (DP), and wet-bulb temperature (WB) thresholds were compared using averaged and time of observation readings at 1-, 3-, 6-, 12-, and 24-h periods. Precipitation phase uncertainty grew 35–65% from the use of 1–24 h data. Within a sub-dataset of observations occurring between AT −6 and 6 °C representing 57% of annual precipitation, misclassified precipitation was 7.9% 1 h and 11.8% 24 h. Of note, there was also little difference between 1 and 3 h uncertainty, typical time steps for surface meteorological observations.

Phase diffusion and the small-noise approximation in linear amplifiers: Limitations and beyond

The phase of an optical field inside a linear amplifier is widely known to diffuse with a diffusion coefficient that is inversely proportional to the photon number. The same process occurs in lasers which limits its intrinsic linewidth and makes the phase uncertainty difficult to calculate. The most commonly used simplification is to assume a narrow photon-number distribution for the optical field (which we call the small-noise approximation). For coherent light, this condition is determined by the average photon number. The small-noise approximation relies on (i) the input to have a good signal-to-noise ratio, and (ii) that such a signal-to-noise ratio can be maintained throughout the amplification process. Here we ask: For a coherent input, how many photons must be present in the input to a quantum linear amplifier for the phase noise at the output to be amenable to a small-noise analysis? We address these questions by showing how the phase uncertainty can be obtained without recourse to the small-noise approximation. It is shown that for an ideal linear amplifier (i.e. an amplifier most favourable to the small-noise approximation), the small-noise approximation breaks down with only a few photons on average. Interestingly, when the input strength is increased to tens of photons, the small-noise approximation can be seen to perform much better and the process of phase diffusion permits a small-noise analysis. This demarcates the limit of the small-noise assumption in linear amplifiers as such an assumption is less true for a nonideal amplifier.