Serge Reboul

A recursive fusion filter for angular data

Many practical application in the field of robotic and perception are using angular data. In this work we present a multi-sensor multi-temporal data fusion filter for angular data. Most of the time, statistic filters, are designed on linear domain. In this work we propose a recursive filter defined on the circular domain with a von Mises distribution. In our application we consider a set of measurement taking at different instants and provided by different sensors. The sequential implementation of the recursive fusion filter we propose is deduced from the a posteriori distribution of the state vector, containing the angular direction and velocity. Temporal measurements are coming from several sensors. The feasibility and the contribution of our method are shown on synthetic data.

Joint segmentation of the wind speed and direction

We present in this article a Bayesian estimation method for the joint segmentation of a set of piecewise stationary processes. The estimate we propose is based on the maximization of the posterior distribution of the change instants conditionally to the process parameter estimation. It is defined as a penalized contrast function with a first term related to the fit to the observation and a second term of penalty. The expression of the contrast function is deduced from the log-likelihood of the parametric distribution that models the statistic evolution of processes in the stationary segments. In the case of joint segmentation the penalty term is deduced from the prior law of change instants. It is composed of parameters that guide the number and the position of changes and of parameters that will bring prior information on the joint behavior of processes. This work is applied to the estimation of wind statistics parameters. We use data available from a cup anemometer and a wind vane, supposed to be piecewise stationary. The contrast function is deduced from the circular Von Mises distribution for the wind direction and from the log-normal distribution for the speed. The feasibility and the contribution of our method are shown on synthetic and real data.

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.

A hybrid fusion system applied to off-line detection and change-points estimation

In this paper we investigate the problem of off-line detection and estimation of change-point instants on data provided by two sensors. In this context sensors synchronization, that provides simultaneous change-point instants on the data, is in practice a constraint hard to maintain. The contribution of this work is the proposition of a hybrid fusion system that performs as well as the centralized fusion detector respectively optimal for simultaneous and not simultaneous change. The system we propose is composed of two GLR tests (Generalized Likelihood Ratio) defined as centralized fusion detectors for the two configurations of change-point (simultaneous and not simultaneous). Decisions of these fusion detectors are combined in a fusion operator. The system is hybrid (centralized and distributed) because the distributed decisions supplied by the centralized fusion systems are combined in a global fusion operator. The contribution of our method is shown on synthetic data. The application to the treatment of a real multi-carrier GPS signal shows the feasibility of the method.

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.

Beach soil moisture measurement with a land reflected GPS bistatic radar technique

In this work we investigate the potential for sensing beach soil moisture with the L band GPS bistatic radar concept. Characterisation of sediment surface (properties like humidity) is indeed important to better understand morphodynamic activity of intertidal part of beaches. In our approach we compare the direct GPS Signal to Noise Ratio with the reflected one in order to measure the soil moisture. We use a bit grabber to digitize and store the GPS L1 carrier (1.5 Ghz) samples. In this context the signal processing is off-line. In this work we proposed a model of the received signal after demodulation and demultiplexing. We deduce from this model a MAP estimate of the navigation message and of the signal SNR. In our case the signal model is a piecewise stationary process with change instants at bit edge position. We present preliminary SNR measurement with this technique for the discrimination of water and humid sand.

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.

A recursive change point estimate of the wind speed and direction

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.

Information fusion in a multi-frequencies GPS receiver

The works presented in this paper deals with the design of a tracking fusion filter for the future multi-carrier G.P.S signal. The estimation of the distance and speed between the satellite and the G.P.S receiver is realised with a Kalman track fusion algorithm. In this system, inspired from the modified track-to-track algorithm, the observations of the same type are merged with a measurement fusion algorithm and the measurements of different types are fused with a state vector fusion Kalman filter. This hybrid model can fuse the measurement obtained from the three frequencies of the future G.P.S. system. It can also fuse the state vectors that describe distances and speed which are supposed to come from different sensors. The simulation result obtained on synthetic data show the feasibility of the method and the contribution of the fusion over the accuracy of the localization.