It is well known that reflected signals from Global Navigation Satellite Systems (GNSS) can be used for altimetry applications, such as monitoring of water levels and determining snow height. Due to the interference of these reflected signals and the motion of satellites in space, the signal-to-noise ratio (SNR) measured at the receiver slowly oscillates. The oscillation rate is proportional to the change in the propagation path difference between the direct and reflected signals, which depends on the satellite elevation angle. Assuming a known receiver position, it is possible to compute the distance between the antenna and the surface of reflection from the measured oscillation rate. This technique is usually known as the interference pattern technique (IPT). In this paper, we propose to normalize the measurements in order to derive an alternative model of the SNR variations. From this model, we define a maximum likelihood estimate of the antenna height that reduces the estimation time to a fraction of one period of the SNR variation. We also derive the Cramér–Rao lower bound for the IPT and use it to assess the sensitivity of different parameters to the estimation of the antenna height. Finally, we propose an experimental framework, and we use it to assess our approach with real GPS L1 C/A signals.

This article is dedicated to the design of a linear-circular regression technique and to its application to ground-based GNSS-Reflectometry (GNSS-R) altimetry. The altimetric estimation is based on the observation of the phase delay between a GNSS signal sensed directly and after a reflection off of the Earth’s surface. This delay evolves linearly with the sine of the emitting satellite elevation, with a slope proportional to the height between the reflecting surface and the receiving antenna. However, GNSS-R phase delay observations are angular and affected by a noise assumed to follow the von Mises distribution. In order to estimate the phase delay slope, a linear-circular regression estimator is thus defined in the maximum likelihood sense. The proposed estimator is able to fuse phase observations obtained from several satellite signals. Moreover, unlike the usual unwrapping approach, the proposed estimator allows the sea-surface height to be estimated from datasets with large data gaps. The proposed regression technique and altimeter performances are studied theoretically, with further assessment on both synthetic and real data.

Lock-in amplification (LIA) is an effective approach for recovery of weak signal buried in noise. Determination of the input signal amplitude in a classical dual-phase LIA is based on incoherent detection which leads to a biased estimation at low signal-to-noise ratio. This article presents, for the first time to our knowledge, a new architecture of LIA involving phase estimation with a linear-circular regression for coherent detection. The proposed phase delay estimate, between the input signal and a reference, is defined as the maximum-likelihood of a set of observations distributed according to a von Mises distribution. In our implementation this maximum is obtained with a Newton Raphson algorithm. We show that the proposed LIA architecture provides an unbiased estimate of the input signal amplitude. Theoretical simulations with synthetic data demonstrate that the classical LIA estimates are biased for SNR of the input signal lower than −20 dB, while the proposed LIA is able to accurately recover the weak signal amplitude. The novel approach is applied to an optical sensor for accurate measurement of NO ${}_2$ concentrations at the sub-ppbv level in the atmosphere. Side-by-side intercomparison measurements with a commercial LIA (SR830, Stanford Research Inc., Sunnyvale, CA, USA ) demonstrate that the proposed LIA has an identical performance in terms of measurement accuracy and precision but with simplified hardware architecture.

This article presents the implementation of an indoor localization approach that combines map matching and a circular particle filter defined in a Bayesian framework. The technique relies only on velocity and heading observations coupled with a map of the road network. No prior knowledge of the initial position is given. A circular distribution is used to match the vehicle's heading with the roads direction. This allows to detect turns and provide a more accurate position estimate. The algorithm is assessed with a synthetic dataset in a real context.

Mean wind speeds and mean wind directions are important input parameters for environmental models and applications. In many practical cases, anemometer sensor provides measurements of direction and wind speed, supposed to be Gaussian and piecewise stationary. In this work we use a von Mises distribution and a Log-normal distribution in order to model sensor data with distributions having a physical reality. We derive from these distributions an ¿on-line¿ recursive estimate of the change point in the wind speed and direction processes. We present numerical results obtained using synthetic and real data to demonstrate the ability of these estimates.

In this article, we propose a multimodel filter for circular data. The so-called Circular Interacting Multimodel filter is derived in a Bayesian framework with the circular normal von Mises distribution. The aim of the proposed filter is to obtain the same performance in the circular domain as the classical IMM filter in the linear domain. In our approach, the mixing and fusion stages of the Circular Interacting Multimodel filter are, respectively, defined from the a priori and from the a posteriori circular distributions of the state angle knowing the measurements and according to a set of models. We propose in this article a set of circular models that will be used in order to detect the vehicle maneuvers from heading measurements. The Circular Interacting Multimodel filter performances are assessed on synthetic data and we show on real data a vehicle maneuver detection application.