Carrier Phase-Based Ionospheric Gradient Monitor Under the Mixed Gaussian Distribution

Anomalous ionospheric gradient is a critical risk to be monitored by ground-based augmentation systems (GBASs) utilized for safety-of-life navigation applications. A dual-frequency carrier phase-based ionospheric gradient monitoring method is proposed under the mixed Gaussian distribution. The minimum detection error of the proposed method can be greatly reduced by allowing acceptable ambiguity resolution failure modes, given the required averaging length. The real BeiDou navigation satellite system data were utilized to test the proposed method. The experimental results showed that the minimum detection error (MDE) of the proposed dual-frequency ionospheric gradient monitoring method can be reduced by at least 30% in comparison with the maximum acceptable anomalous ionospheric gradient of category III GBAS. This study demonstrated that the proposed method can be used to protect against the ionospheric gradient for a ground-based augmentation system.

Optimal Quantiser Performance with a Small Dither

A quantiser is a non-smooth function and no inverse function exist that can be applied to correct for the error it introduces. Applying a dither signal and averaging to a quantiser produces a smooth image for which an inverse function does exist. This article describes methods for minimising the error after inverse compensation. We show that there is an optimal dither variance that minimises the error after inversion. Simple rules for choosing the optimal dither variance are presented. The error after inversion can be made arbitrarily small by increasing the averaging length. This can be done by oversampling the signal by the same factor as the number of averages. Quantisation of a dither signal with a continuous probability distribution, produces a discrete probability mass function. We discuss a method for recovering an unknown continuous probability distribution from the empirical discrete probability mass function of the quantised dither signal. This enables inverse compensation in systems where exact control of the dither signal is not possible, as inverse compensation requires information about the continuous probability distribution of the dither signal and the step-size of the quantiser.

Dynamics of a small surge-type glacier using one-dimensional geophysical inversion

We investigate the dynamics of a small surge-type valley glacier as part of a study to characterize glacier response to climate in the Donjek Range, southwest Yukon, Canada. Pole displacements were measured using kinematic GPS techniques during three consecutive summer field seasons. Measured surface velocities range from <10 m a−1over the lower 1500 m of the 5 km long glacier to a maximum of ∼25–35 m a−1over the upper 3500 m. Basal velocities along an approximate flowline are reconstructed from the measured surface velocities using inverse methods. Control tests are used to validate the inversion scheme, and sensitivity tests are performed to evaluate the influence of the flow-law coefficient, shape factor and longitudinal averaging length. Inversion of the real data shows that basal motion accounts for 50–100% of the total surface motion along the flowline. Based on these results, and several other lines of evidence, we suggest this glacier may be undergoing a slow surge.