Autonomous vehicle state estimation using a LPV Kalman filter and SLAM

© 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThis paper presents an optimal approach for state estimation and Simultaneous Localization and Mapping (SLAM) correction using Kalman gain obtained via Linear Matrix Inequality (LMI). The technique utilizes a Linear Parameter Varying (LPV) represention of the system, which allows to model the complex non-linear dynamics in a way that linearization is not required for the estimator or controller design. In addition, the LPV polytopic representation is exploited to obtain a real-time Kalman gain, avoiding expensive optimization of LMIs at every step. The estimation schema is integrated with a Non-linear Model Predictive Control (NMPC) in charge of controlling the vehicle. For the demonstration, the approach is tested in the simulation and for the practical validity, a small-scale autonomous car is used.Peer ReviewedPostprint (author's final draft

Probability-guaranteed set-membership state estimation for polynomially uncertain linear time-invariant systems

2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksConventional deterministic set-membership (SM) estimation is limited to unknown-but-bounded uncertainties. In order to exploit distributional information of probabilistic uncertainties, a probability-guaranteed SM state estimation approach is proposed for uncertain linear time-invariant systems. This approach takes into account polynomial dependence on probabilistic uncertain parameters as well as additive stochastic noises. The purpose is to compute, at each time instant, a bounded set that contains the actual state with a guaranteed probability. The proposed approach relies on the extended form of an observer representation over a sliding window. For the offline observer synthesis, a polynomial-chaos-based method is proposed to minimize the averaged H2 estimation performance with respect to probabilistic uncertain parameters. It explicitly accounts for the polynomial uncertainty structure, whilst most literature relies on conservative affine or polytopic overbounding. Online state estimation restructures the extended observer form, and constructs a Gaussian mixture model to approximate the state distribution. This enables computationally efficient ellipsoidal calculus to derive SM estimates with a predefined confidence level. The proposed approach preserves time invariance of the uncertain parameters and fully exploits the polynomial uncertainty structure, to achieve tighter SM bounds. This improvement is illustrated by a numerical example with a comparison to a deterministic zonotopic method.Peer ReviewedPostprint (author's final draft

Bayesian inference for partial orders from random linear extensions: power relations from 12th Century Royal Acta

We give a new class of models for time series data in which actors are listed in order of precedence. We model the lists as a realisation of a queue in which queue-position is constrained by an underlying social hierarchy. We model the hierarchy as a partial order so that the lists are random linear extensions. We account for noise via a random queue-jumping process. We give a marginally consistent prior for the stochastic process of partial orders based on a latent variable representation for the partial order. This allows us to introduce a parameter controlling partial order depth and incorporate actor-covariates informing the position of actors in the hierarchy. We fit the model to witness lists from Royal Acta from England, Wales and Normandy in the eleventh and twelfth centuries. Witnesses are listed in order of social rank, with any bishops present listed as a group. Do changes in the order in which the bishops appear reflect changes in their personal authority? The underlying social order which constrains the positions of bishops within lists need not be a complete order and so we model the evolving social order as an evolving partial order. The status of an Anglo-Norman bishop was at the time partly determined by the length of time they had been in office. This enters our model as a time-dependent covariate. We fit the model, estimate partial orders and find evidence for changes in status over time. We interpret our results in terms of court politics. Simpler models, based on bucket orders and vertex-series-parallel orders, are rejected. We compare our results with a stochastic process extension of the Plackett-Luce model.Comment: 70 pages, 38 figures and 2 tables including appendix and supplemen

Robust zonotopic set-membership approach for model-based prognosis: application on linear parameter-varying systems

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksA robust set-membership Prognostics and Health Management (PHM) methodology is presented in this paper. The key advantages of the set-membership approach for states and parameters estimation are enhanced by employing zonotopes that are less conservative and computationally complex than other sets. The optimal tuning of the proposed observer is formulated using the Linear Matrix Inequality (LMI) approach. Moreover, the Joint Estimation of States and Parameters (JESP) leads to a non-linear representation of a monitored system that is transformed into a Linear Parameter-Varying (LPV) system by means of the non-linear embedding approach. The considered case study is based on a slowly degraded DC-DC converter. The aim of the proposed PHM approach is to forecast the Remaining Useful Life (RUL) on a system level. Additionally, the proposed RUL forecasting approach is independent of previous knowledge of the degradation behaviors being only dependent on the estimated zonotopic parameters. Finally, the obtained results demonstrate the efficiency of the proposed approach.Peer ReviewedPostprint (published version

Ship detection in SAR images based on Maxtree representation and graph signal processing

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper discusses an image processing architecture and tools to address the problem of ship detection in synthetic-aperture radar images. The detection strategy relies on a tree-based representation of images, here a Maxtree, and graph signal processing tools. Radiometric as well as geometric attributes are evaluated and associated with the Maxtree nodes. They form graph attribute signals which are processed with graph filters. The goal of this filtering step is to exploit the correlation existing between attribute values on neighboring tree nodes. Considering that trees are specific graphs where the connectivity toward ancestors and descendants may have a different meaning, we analyze several linear, nonlinear, and morphological filtering strategies. Beside graph filters, two new filtering notions emerge from this analysis: tree and branch filters. Finally, we discuss a ship detection architecture that involves graph signal filters and machine learning tools. This architecture demonstrates the interest of applying graph signal processing tools on the tree-based representation of images and of going beyond classical graph filters. The resulting approach significantly outperforms state-of-the-art algorithms. Finally, a MATLAB toolbox allowing users to experiment with the tools discussed in this paper on Maxtree or Mintree has been created and made public.Peer ReviewedPostprint (author's final draft

A Lambda Term Representation Inspired by Linear Ordered Logic

We introduce a new nameless representation of lambda terms inspired by ordered logic. At a lambda abstraction, number and relative position of all occurrences of the bound variable are stored, and application carries the additional information where to cut the variable context into function and argument part. This way, complete information about free variable occurrence is available at each subterm without requiring a traversal, and environments can be kept exact such that they only assign values to variables that actually occur in the associated term. Our approach avoids space leaks in interpreters that build function closures. In this article, we prove correctness of the new representation and present an experimental evaluation of its performance in a proof checker for the Edinburgh Logical Framework. Keywords: representation of binders, explicit substitutions, ordered contexts, space leaks, Logical Framework.Comment: In Proceedings LFMTP 2011, arXiv:1110.668

Cluster membership probabilities from proper motions and multiwavelength photometric catalogues: I. Method and application to the Pleiades cluster

We present a new technique designed to take full advantage of the high dimensionality (photometric, astrometric, temporal) of the DANCe survey to derive self-consistent and robust membership probabilities of the Pleiades cluster. We aim at developing a methodology to infer membership probabilities to the Pleiades cluster from the DANCe multidimensional astro-photometric data set in a consistent way throughout the entire derivation. The determination of the membership probabilities has to be applicable to censored data and must incorporate the measurement uncertainties into the inference procedure. We use Bayes' theorem and a curvilinear forward model for the likelihood of the measurements of cluster members in the colour-magnitude space, to infer posterior membership probabilities. The distribution of the cluster members proper motions and the distribution of contaminants in the full multidimensional astro-photometric space is modelled with a mixture-of-Gaussians likelihood. We analyse several representation spaces composed of the proper motions plus a subset of the available magnitudes and colour indices. We select two prominent representation spaces composed of variables selected using feature relevance determination techniques based in Random Forests, and analyse the resulting samples of high probability candidates. We consistently find lists of high probability (p > 0.9975) candidates with $\approx$ 1000 sources, 4 to 5 times more than obtained in the most recent astro-photometric studies of the cluster. The methodology presented here is ready for application in data sets that include more dimensions, such as radial and/or rotational velocities, spectral indices and variability.Comment: 14 pages, 4 figures, accepted by A&

Isomorphism of graph classes related to the circular-ones property

We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc graphs, \Gamma-circular-arc graphs, proper circular-arc graphs and convex-round graphs.Comment: 25 pages, 9 figure