Georges Stienne

Normalized GNSS Interference Pattern Technique for Altimetry

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.

GNSS dataless signal tracking with a delay semi-open loop and a phase open loop

In this article we propose to process the code and phase delay of a dataless GNSS signal in open and semi-open loops. The aims of this processing are to get an accurate estimate of the phase and code delays by integration of the GNSS signal. We show that in an open loop the code delay evolution is a piecewise stationary process and we propose to model the phase delay as a circular random variable distributed according to a von Mises distribution. In this context the code tracking is realised on the GNSS signal by estimating the abrupt changes in the code discriminator values. We propose a Bayesian modeling of the problem in order to define the change point estimator. The proposed estimator involves in its definition the inaccurate prior information of Doppler and signal to noise density ratio provided by the phase delay tracking loop. Furthermore we propose a circular Bayesian modeling of the observations provided by the phase open loop. From this model, we derive a circular recursive filter for the estimation of phase delay and frequency of the carrier. The proposed tools are assessed using synthetic and real data. Highlights? We propose a Delay Semi Open Loop for the tracking of the code of a GNSS signal. ? We propose a Bayesian change point detector for this code tracking loop. ? We propose a Phase Open Loop for the tracking of the phase of a GNSS signal. ? We propose a Bayesian circular filter for this phase tracking loop. ? The proposed methods are assessed on synthetic and real data.

Circular data processing tools applied to a Phase Open Loop architecture for multi-channels signals tracking

This paper proposes circular data processing tools dedicated to the tracking of the phase of GNSS signals in a Phase Open Loop, particularly in case of multi-channel signal structure. The objective of processing the phase in an open loop is to avoid time-correlation between two successive measurements. This allows the use of loop filters in order to smooth the measurements without producing unwanted oscillations in the phase estimations. In order to process the angular values produced by the Phase Open Loop, the choice had been made to develop a filter and a fusion operator in a Bayesian framework with circular statistics distributions. The proposed tools are assessed on synthetic and real data.

Accurate Pseudorange Estimation by Means of Code and Phase Delay Integration: Application to GNSS-R Altimetry

This article presents a new estimator of the pseudorange between a global navigation satellite systems (GNSS) satellite and a stand-alone receiver, and its application to GNSS-reflectometry (GNSS-R) altimetry. In our approach, we use as independent observations the difference between the code delay provided by successive acquisitions of the GNSS signal and the code delay truncated using the phase and Doppler information. We show that the mean value of these observations is an estimate of the first pseudorange of the observed time series. The ability of the proposed estimator to provide the centimeter accuracy is theoretically evaluated. In ground-based altimetry applications using GNSS signals, the direct pseudorange and the pseudorange associated to the reflected signal can be assumed to have the same dynamic evolution. Based on this assumption, the proposed estimate uses as observations the difference between the code delays obtained by successive acquisitions of both signals, without using phase measurement. The assessment of the method for ground-based GNSS-R is realized with real data.

Airborne P-band Signal of Opportunity (SoOP) demonstrator instrument; status update

The instrument is currently under development with science flights planned aboard a Beechcraft Super King Air B200 aircraft. The flights will include NASAs SLAP L-Band radar and radiometer to provide coincident measurements. The instrument comprises two dual-polarization antennas (one each for sky and Earth views), a four-channel RF receiver with internal calibration network, and a digital receiver to correlated signal pairs. Brass boards of the P-band receivers have been fabricated and have been used to monitor P-Band satellite transmissions to develop spectrum population statistics and survey unwanted RFI. These results have led to requirements for channel processing and RFI mitigation in both the RF and digital portions of the system. The instrument will store complex correlation coefficients for all pairs of elements formed by the two dual-polarization antennas. These coefficients will be averaged in ground processing to reduce noise prior to estimating reflectivity and retrieving soil moisture. A “Smart Antenna” approach will be used in ground processing to steer an antenna pattern null towards the unwanted reflected signal as seen by the sky-view antenna. The background and status of the SoOp-AD instrument will be discussed along with sources of error and mitigation strategies.

Cycle slip detection and repair with a circular on-line change-point detector

In this article, we propose a circular change-point detector for on-line processing of the phase and the frequency of a GPS-L1 signal. The aims of this processing are to get an accurate estimation of the phase and to use it to get centimeter precise position estimates every millisecond. We propose to track the phase of the GPS signal in an open loop and the frequency in a semi-open loop. In an open loop, the phase delay evolves as a circular random variable. Furthermore, the phase is subject to cycle slips. These abrupt changes must be detected and repaired. We propose a circular generalized likelihood test for the on-line detection of changes in the phase measurements. With the estimation and detection being non-linear, we propose a particle filter defined according to the circular von Mises distribution for the estimation of the phase and frequency. The proposed architecture is assessed using synthetic and real data.

Bayesian Change-Points Estimation Applied to GPS Signal Tracking

A hierarchical Bayesian model is applied to off-line segmentation of the GPS signal discriminator. The purpose of this work is to estimate the code delay of the receiving GPS CDMA code in order to retime the local receiver code and to estimate the pseudorange satellite receiver. The goal of our approach is to obtain a high-rate accurate positioning in the dynamic navigation case. We show that the behaviour of the coherent discriminator of a GPS pilot channel can be modelized by a piecewise stationary process. In our approach the discriminator behaviour in each stationary segment is approximated by a constant acceleration model, and the code delay at each end of the segments is known. The interest of this approach is that we use the coherent values of the discriminator in each segment to estimate the change instants of the process and to get in this case an accurate estimation of the code delays. In this context, a simultaneous estimation of the change instants is considered. We define the a posteriori distribution which integrates in its expression the signal change instants and the parameters of its statistical model. The proposed model leads after marginalization to a penalized contrast function that we minimize to estimate the discriminator change instants. The interest of the proposed model is that we can integrate in our estimate prior information on the roughly known values of the signal-to-noise ratio and relative speed satellite receiver. The potential of the proposed method is shown on experimentations realized on synthetic and real data for millisecond receiver localization.

Circular Regression Applied to GNSS-R Phase Altimetry

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.

High rate interference pattern technique applied to real time altimetry

GNSS-R techniques use direct and reflected signals coming from GNSS satellites to characterize the reflecting surface. In altimetry applications, the height of the surface is derived from the path difference between these two signals. The aim of this article is to propose a receiver architecture for high rate estimation of this path difference using an Interference Pattern Technique. An original receiver front-end architecture is presented, aiming at providing noisy observations of a non-linear function of the height. In order to invert this non-linear observation function and to smooth the height estimation, a particle filter is used. The proposed approach is assessed on synthetic data.

GNSS code and phase processing techniques in a ground-based mobile altimetry system

This article is dedicated to a ground-based altimeter using GNSS signals. This altimeter has been developed in order to be easily movable and able to estimate soil moisture as well, for swamps monitoring. New signal processing techniques are proposed in order to estimate the code, frequency and phase observables of a GNSS signal needed to solve the altimetry problem.