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A multipath mitigation technique for GNSS is proposed.The technique exploites the change of polarization when a signal is reflected.A novel statistic based on the outputs of a correlator bank is introduced to estimate the multipath DoA and polarization.Applying the technique increases the estimation performance in the case of highly temporally or spatially correlated multipath and line-of-sight signal. This paper treats the problem of line-of-sight (LOS) parameter estimation in strong multipath environments. In the case of highly temporally and spatially correlated LOS and multipath signals, such as urban canyons, common multipath mitigation methods are highly degraded, as signal separation cannot be performed in the spatio temporal domain. In this case, we exploit the LOS and multipath polarization diversity to decouple the signals using an antenna array with right-hand-circular polarization (RHCP) and left-hand-circular polarization (LHCP) feeds. The multipath direction- of-arrival (DOA) and polarization coefficients can effectively be estimated from the LHCP spatial covariance matrix. The LOS DOA can be estimated from the RHCP spatial covariance matrix. The spatial covariance matrices are calculated from the outputs of a matched correlator bank. The DOA and polarization estimates are used to implement a dual polarization beamformer, which maximizes the LOS energy and suppresses multipath energy over both polarizations. The LOS time-delay is estimated from the beamformer output with a maximum-likelihood estimator with a significantly reduced number of parameters and computational complexity in comparison to a full model estimator. Simulation results for GPS show that the proposed dual polarization beamforming algorithm performs better than an equivalent single-polarization beamformer in a dense multipath environment.

Die für die inertiale low-cost Navigation verwendete, sehr kleine, leichte und hochverfügbare Hardware erlaubt die Nutzung MEMS-basierter inertialer Sensoren, die eine besonders kostengünstige und flexible Realisierbarkeit einer breiten Fülle industrieller, medizinischer oder konsumorientierter Anwendungen bieten. Die Anwendbarkeit dieser Sensoren wurde bislang allerdings aufgrund ihrer Leistungsfähigkeit lediglich auf einfache, nichtintelligente Anwendungen in Smartphones, Tablet-PCs, etc. begrenzt, beispielsweise zur Schockerkennung, zur Vibrations¬messung oder zur orientierungsabhängigen Rotation der Bildschirmanzeige. Die Motivation der vorliegenden Arbeit liegt in der Erweiterung der aktuell verfügbaren Anwendungsbandbreite kostengünstiger inertialer Navigationssysteme (auch: INS) um intelligente Applikationen der langzeitstabilen Objektverfolgung und Bewegungserkennung. Bei der Objektverfolgung wird eine Sensordatenfusion zwischen einem Low-cost INS und einem GPS-Referenznavigationssystem auf Basis einer indirekten Kalman-Filterung realisiert. Dabei wird das Potential der Zweifilterglättung validiert, die während möglicher Ausfälle der Referenznavigation schnell anwachsenden Fehler der inertialen Navigation zu reduzieren. Eine Vereinfachungsmethode wird angewandt, um die Berechnung inverser Kovarianzmatrizen bei der Glättung zu vermeiden, sodass numerischen Instabilitäten vorgebeugt und die algorithmische Effizienz gesteigert werden können. Mit dem Ziel der Entwicklung einer zuverlässigen und einfachen Möglichkeit einer computergestützten Bewegungsanalyse und –validierung als einer Schlüsseltechnologie zur Optimierung von Bewegungsabläufen stellt die vorliegende Arbeit eine algorithmische Grundlage zur referenzlosen Bewegungserkennung unter Nutzung kosten-günstiger inertialer Sensoren zur Verfügung. Der vorgestellte Ansatz basiert auf der Theorie der Hidden-Markov-Modelle sowie auf der stochastischen Modellierung inertial messbarer Bewegungsprofile mit Hilfe von Markov-Ketten. Die Ergebnisse der Arbeit werden durch eine Reihe von Experimenten hinsichtlich der Zuverlässigkeit und der Stabilität der vorgestellten Ansätze validiert. Die finalen Lösungen arbeiten eigenständig, sind kostengünstig, klein, leicht und lassen dabei eine unbeschränkte Langzeitanwendung zu. Since the required hardware for low-cost inertial navigation is very small, low-weight and widely available in the market, using MEMS-based sensors promises various industrial, medical or consumer entertainment applications to be realized at very low manufacturing costs. Due to the performance these sensors have shown, their applicability such as shaking detection, vibration measurement or orientation-dependent screen view rotation, has been limited to just simple, non-intelligent tasks in smart phones, tablets etc. The present research is motivated by enhancing the currently available applicability of low-cost inertial navigation systems (also: INS), towards intelligent applications of long-term object tracking and motion recognition. The object tracking makes use of a loose coupling integration method based on Kalman-filtering in order to realize a sensor fusion between low-cost INS and GPS reference navigation. This work shows the performance of two-filter-smoothing to reduce the growth of errors during potential outages of the reference navigation. A simplification technique is applied to avoid the calculation of inverse covariance matrices for the smoothing, which reduces the possibility of numerical instabilities while increasing the algorithms’ efficiency. Aiming towards a reliable and simple possibility of computer-assisted motion analysis and validation as a key for motion optimization, the present work provides an algo-rithmic framework for reference-less motion analysis and validation using low-cost inertial sensors. The developed algorithms are based on the theory of Hidden-Markov-Models and on stochastical modelling of inertially measurable motion profiles using Markov-chains. The research results are validated by a series of experiments in order to verify the reliability and the stability of the present approaches. The final solutions are stand-alone, low-cost, miniature-size and low-weight, while being capable of unlimited long-term operation.

A novel oriented volume over ground (OVoG) inversion scheme is developed and tested on a data set of simulated agricultural scenarios and real SAR acquisitions. The algorithm makes use of multibaseline measurements to estimate the whole set of the OVoG structural parameters (e.g., crop height, differential extinction between eigenpolarizations, and ground-to-volume ratios) and is significantly robust against nonvolumetric decorrelation contributions. The theoretical assessment points out that, in the dual-baseline case, the vegetation height $h_{V}$ can be estimated with a relative root-mean-square deviation (%RMSD) of 7.8% if the selected baselines fulfill the condition $1.2 ( $\kappa_{z}$ is the vertical wavenumber). Furthermore, the variance of the estimates is inversely related to the number of baselines $Nb$ . Compared with the dual-baseline case, the RMSD of the differential extinction is reduced by 45% (from 1.1 to 0.6 dB/m) when $Nb=5$ baselines are employed, whereas its mean bias is independent of $Nb$ . The proposed scheme has been assessed using a set of repeat-pass F-SAR acquisitions at L-, C-, and X-band of an agricultural area in Germany. Using two baselines, the height of maize and rape fields is estimated with an average 10% %RMSD if the inversion is carried out over L-band acquisitions. On the other hand, when X-band data are employed, one can obtain reliable estimates of wheat and barley height, with a %RMSD better than 24%. The study also indicates the existence of differential wave propagation effects through maize ( $\Delta\sigma=\sigma_\mathrm{VV}-\sigma_\mathrm{HH}$ between 0.7 and 1 dB/m) and rape $(\Delta\sigma=-0.8\ \text{dB/m})$ canopies at L-band.

Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are often unknown and have to be estimated from experimental data. Due to partial observations and measurement noise, these parameter estimates are subject to uncertainty. This uncertainty can be assessed using profile likelihoods, a reliable but computationally intensive approach. In this paper, we present the integration based approach for the profile likelihood calculation developed by (Chen and Jennrich 2002 J. Comput. Graph. Stat. 11 714–32) and adapt it to inverse problems with PDE constraints. While existing methods for profile likelihood calculation in parameter estimation problems with PDE constraints rely on repeated optimization, the proposed approach exploits a dynamical system evolving along the likelihood profile. We derive the dynamical system for the unreduced estimation problem, prove convergence and study the properties of the integration based approach for the PDE case. To evaluate the proposed method, we compare it with state-of-the-art algorithms for a simple reaction-diffusion model for a cellular patterning process. We observe a good accuracy of the method as well as a significant speed up as compared to established methods. Integration based profile calculation facilitates rigorous uncertainty analysis for computationally demanding parameter estimation problems with PDE constraints.

In the context of parameter estimation, subspace-based methods like ESPRIT have become common. They require a subspace separation e.g. based on eigenvalue/-vector decomposition. In time-varying environments, this can be done by subspace trackers. One class of these is based on the PAST algorithm. Our non-linear parameter estimation algorithm DaPT builds on-top of the ESPRIT algorithm. Evaluation of the different variants of the PAST algorithm shows which variant of the PAST algorithm is worthwhile in the context of frequency estimation.

Finding maneuvers for parameter estimation in flight data records is a laborious task and traditionally performed post-flight on ground. Two different data parser approaches to automatically detect these maneuvers in flight are presented. Both methods search the control input signals for significant changes that correspond to test maneuvers. The first algorithm is based on the signal time derivative of the input signal whereas the second method uses a fast orthogonal wavelet transform. Both algorithms are tested with flight test data recorded with the DLR research aircraft ATTAS. Performance results are compared and potential problems when applying the parsers to other data are discussed. Results indicate that both methods are applicable in an online parameter estimation tool. The intention of the work in this paper is to develop an algorithm with a high level of automation for in-flight use, but both approaches could also be applied to offline flight data mining problems.

International audience; Simulations were used to study the influence of model adequacy and data structure on the estimation of genetic parameters for traits governed by direct and maternal effects. To test model adequacy, several data sets were simulated according to different underlying genetic assumptions and analysed by comparing the correct and incorrect models. Results showed that omission of one of the random effects leads to an incorrect decomposition of the other components. If maternal genetic effects exist but are neglected, direct heritability is overestimated, and sometimes more than double. The bias depends on the value of the genetic correlation between direct and maternal effects. To study the influence of data structure on the estimation of genetic parameters, several populations were simulated, with different degrees of known paternity and different levels of genetic connectedness between flocks. Results showed that the lack of connectedness affects estimates when flocks have different genetic means because no distinction can be made between genetic and environmental differences between flocks. In this case, direct and maternal heritabilities are under-estimated, whereas maternal environmental effects are overestimated. The insufficiency of pedigree leads to biased estimates of genetic parameters.

International audience; A strategy of multi-step minimal conditional regression analysis has been developed to determine the existence of statistical testing and parameter estimation for a quantitative trait locus (QTL) that are unaffected by linked QTLs. The estimation of marker-QTL recombination frequency needs to consider only three cases: 1) the chromosome has only one QTL, 2) one side of the target QTL has one or more QTLs, and 3) either side of the target QTL has one or more QTLs. Analytical formula was derived to estimate marker-QTL recombination frequency for each of the three cases. The formula involves two flanking markers for case 1), two flanking markers plus a conditional marker for case 2), and two flanking markers plus two conditional markers for case 3). Each QTL variance and effect, and the total QTL variance were also estimated using analytical formulae. Simulation data show that the formulae for estimating marker-QTL recombination frequency could be a useful statistical tool for fine QTL mapping. With 1 000 observations, a QTL could be mapped to a narrow chromosome region of 1.5 cM if no linked QTL is present, and to a 2.8 cM chromosome region if either side of the target QTL has at least one linked QTL.; Détection d'un QTL et estimation de son effet par analyses de régression sur plusieurs marqueurs. On a développé une stratégie basée sur l'analyse de régression en plusieurs étapes et à partir d'un nombre minimum de marqueurs pour détecter un QTL et évaluer son effet individuel sur le caractère indépendamment de l'existence d'autres QTL liés. Trois cas sont à considérer pour estimer la fréquence de recombinaison entre le marqueur et le QTL : 1) Il y a un seul QTL, 2) Il existe au moins un autre QTL sur un des côtés du QTL recherché, 3) Il existe au moins un QTL sur chacun des deux côtés du QTL recherché. La fréquence de recombinaison a été estimée analytiquement dans les trois cas. La formule obtenue utilise l'information sur les deux marqueurs flanquants dans le cas 1), sur les deux marqueurs flanquants et sur un marqueur plus éloigné dans le cas 2), sur les deux marqueurs flanquants et sur deux marqueurs plus éloignés dans le cas 3). Pour chaque QTL ainsi détecté, on a aussi développé analytiquement une estimation de son effet et de sa variance, et, pour l'ensemble des QTL ainsi validés, de leur contribution totale à la variance génétique. On a montré par simulation que les formules pour la fréquence de recombinaison pouvaient être utiles pour la cartographie fine de QTL. Ainsi, 1 000 observations permettaient de placer un QTL dans un intervalle de seulement 1,5 cM s'il n'était pas lié à un autre QTL, et de 2,8 cM s'il était lié à un autre QTL à sa droite ou à sa gauche.

This paper presents techniques of parameter estimation in heteroskedastic mixed models having i) heterogeneous log residual variances which are described by a linear model of explanatory covariates and ii) log residual and log u-components linearly related. This makes the intraclass correlation a monotonic function of the residual variance. Cases of a homogeneous variance ratio and of a homogeneous u-component of variance are also included in this parameterization. Estimation and testing procedures of the corresponding dispersion parameters are based on restricted maximum likelihood procedures. Estimating equations are derived using the standard and gradient EM. The analysis of a small example is outlined to illustrate the theory., Cet article présente des techniques d’estimation des paramètres intervenant dans des modèles mixtes caractérisés i) par des logvariances résiduelles décrites par un modèle linéaire de covariables explicatives et ii) par des composantes u et e liées par une fonction affine. Cela conduit à un coefficient de corrélation intraclasse qui varie comme une fonction monotone de la variance résiduelle. Le cas d’une corrélation constante et celui d’une composante u constante sont également inclus dans cette paramétrisation. L’estimation et les tests relatifs aux paramètres de dispersion correspondants sont basés sur les méthodes du maximum de vraisemblance restreint (REML). Les équations à résoudre pour obtenir ces estimations sont établies à partir de l’algorithme EM standard et gradient. La théorie est illustrée par l’analyse numérique d’un petit exemple.

Die vorliegende Arbeit präsentiert eine neue Methode zur simultanen Schätzung von Topographie und Bewegung polarer Gletscher und Eisflächen aus multi-temporalen SAR Interferogrammen. Die unbekannten Parameter Topographie und Bewegung werden dabei aus einer redundanten Anzahl an Beobachtungen geschätzt. Die Redundanz wird systematisch zur Ableitung realistischer Genauigkeitsaussagen sowie zur Aufdeckung möglicher grober Fehler bzw. Modellfehler genutzt. Die Überbestimmung eröffnet ebenfalls die Möglichkeit, restriktive Modellkomponenten durch flexiblere Modellkomponenten mit einer größeren Anzahl an freien Parametern zu ersetzen und gewährleistet dadurch eine bessere Beschreibung der tatsächlichen Verhältnisse. Der Ansatz basiert auf der Kombination einer Anzahl von SAR Interferogrammen in einer Kleinste-Quadrate-Ausgleichung nach dem Gauss-Markov Modell. Zur Verknüpfung der multi-temporalen Datensätze wird ein räumlich-zeitliches Modell vorgeschlagen, das die Eigenschaften der beobachteten Oberfläche und deren zeitliche Veränderung beschreibt. Die Parametrisierung des räumlich-zeitlichen Modells kann dabei an die Eigenschaften des Untersuchungsobjekts angepasst werden. Simulationsrechnungen zeigen, dass die Topographie und die Bewegung polarer Gletscher je nach Konfiguration der Ausgleichung mit einer Genauigkeit von wenigen Höhenmetern bzw. wenigen Dezimetern pro Jahr bestimmt werden können. Die Genauigkeit der geschätzten Parameter wird dabei vor allem durch die Genauigkeit der Phasenbeobachtungen, die Aufnahmegeometrie und die Anzahl der kombinierten Datensätze bestimmt. Zuverlässigkeitsanalysen zeigen zudem eine hohe Robustheit der Schätzwerte gegenüber groben Fehlern in den Beobachtungen. Der Einfluss der atmosphärischen Laufzeitverzögerung auf die Unbekannten wurde für verschiedene Beobachtungskonfigurationen und verschiedene atmosphärische Bedingungen untersucht und quantifiziert. Fehler im Bewegungsmodell führen zu einer signifikanten Verfälschung der geschätzten Unbekannten. Auf eine sorgfältige Konfiguration des räumlich-zeitlichen Modells ist daher zu achten. Neben der Ermittlung der Schätzwerte ermöglichen das Verfahren und dessen inhärente Analysestrategien, die zum Erreichen eines vorgegebenen Genauigkeitsniveaus notwendige Beobachtungskonfiguration im Voraus zu bestimmen. Die Analysestrategien sind daher ein nützliches Werkzeug für die Projektplanung. Anhand einer Fallstudie, bei der ein großer Eisdom in der russischen Arktis beobachtet wurde, wird die Umsetzbarkeit des Verfahrens unter realen Bedingungen gezeigt. This thesis presents a new technique to simultaneously estimate topography and motion of polar glaciers and ice sheets from multi-temporal SAR interferograms. In this approach the unknown parameters, i.e. topography and surface displacement, are estimated from a redundant number of observations. The resulting redundancy is systematically used to attach realistic accuracy and robustness measures to all estimated unknowns and to reveal possible gross errors in the observations or errors in the model. Additionally, the redundancy facilitates replacing very restrictive model components by more flexible models with a higher amount of free parameters. This leads to a better description of the real behavior of the object. The approach combines several SAR interferograms into a least-squares adjustment based on the Gauss-Markov model. In order to connect the multi-temporal data sets, a spatio-temporal model is proposed that describes the properties of the surface and its temporal evolution. The parameterization of the model can be adapted considering the properties of the object under investigation. Tests with simulated data show that, with this technique, both topography and motion of polar ice caps can be estimated with an accuracy of a few meters or a few centimeters per day, depending on the configuration of the adjustment. The quality of the estimated parameters depends on the accuracy of the phase observations, the observation geometry, and the number of involved data sets. Analyses of the robustness of the approach additionally indicate a high robustness of the estimated unknowns with respect to gross errors in the observations. The influence of the atmospheric path delay on the unknowns is analyzed and quantified for various observation geometries and different atmospheric conditions. It is shown that errors in the assumed deformation model significantly falsify the estimated parameters. Thus, the configuration of the spatio-temporal model must be chosen carefully. In addition to the estimation of surface topography and motion, the method and its inherent analysis tools allow to determine the observation geometry that is necessary to reach a pre-defined accuracy level in advance. Therefore, the method is a very useful tool for project planing. By means of a case study aimed at the observation of a huge ice dome in the Russian arctic the feasibility of the approach in real-life situations is demonstrated.

Summary - A method is described for the simultaneous estimation of variance components due to several genetic and environmental effects from unbalanced data by restricted maximum likelihood (REML). Estimates are obtained by evaluating the likelihood explicitly and using standard, derivative-free optimization procedures to locate its maximum. The model of analysis considered is the so-called Animal Model which includes the additive genetic merit of animals as a random effect, and incorporates all information on relationships between animals. Furthermore, random effects in addition to animals’ additive genetic effects, such as maternal genetic, dominance or permanent environmental effects are taken into account. Emphasis is placed entirely upon univariate analyses. Simulation is employed to investigate the efficacy of three different maximization techniques and the scope for approximation of sampling errors. Computations are illustrated with a numerical example. variance components - restricted maximum likelihood - animal model - additional random effects - derivative - free approach

This paper presents a novel low complexity high resolution timing and Doppler acquisition algorithm for direct-sequence code division multiple access (DS-CDMA) systems. We apply the two-dimensional unitary estimation of signal parameters via rotational invariant techniques (ESPRIT) algorithm to the joint delay and Doppler acquisition task in multipath environments. Additionally, we use the advantageous beam space (BS) implementation of unitary ESPRIT, which reduces the computational complexity once again remarkably. The exploitation of a-priori knowledge according to the BS version of unitary ESPRIT also reduces the root mean square error (RMSE) at low signal to noise ratios (SNRs). Furthermore, we enhance the delay and Doppler multipath acquisition by the two-dimensional structured least squares (SLS) algorithm. Thus, our delay and Doppler RMSE reaches the Cramer-Rao bound (CRB) almost as good as maximum likelihood (ML) delay and Doppler acquisition. However, our algorithms save computational complexity compared to the ML algorithm by several orders of magnitude.