Modular Localization Research Articles

Learning From FM Communications: Toward Accurate, Efficient, All-Terrain Vehicle Localization

Vehicle localization service is a fundamental component of intelligent transportation systems. The widely used satellite navigation systems perform poorly in urban areas because the lines of sight to satellites are blocked by complex terrain characteristics, e.g., buildings, elevated streets and interchanges. In this paper, we design RadioLoc, a novel system achieving accurate, efficient, all-terrain vehicle localization with two key design points. First, RadioLoc harvests the frequency modulation (FM) signal, which has higher availability than satellite signal in complex terrains, as the signal source for localization. Second, RadioLoc integrates modern machine learning techniques into the processing of FM signals to efficiently learn the accurate vehicle localization in all-terrain environments. We validate the feasibility of FM-based vehicle localization and corresponding challenges and practical issues via field tests (e.g., signal distortion, signal inconsistency and limited in-vehicle radio bandwidth), and develop a series of advanced techniques in RadioLoc to address them, including adaptive batching, frequency sweeping, a novel multipath delay spread filter, a reconstructive PCA denoiser and a tailored FM feature extractor. We then develop a generic, modular localization module in RadioLoc, and design different learning-based 3D position identification algorithms for this module. We implement a prototype of RadioLoc and perform extensive field experiments to evaluate its efficiency and efficacy. Results show that (1) RadioLoc achieves a real-time localization latency of less than 100 milliseconds; (2) RadioLoc achieves a worst-case localization accuracy of <inline-formula> <tex-math notation="LaTeX">$99.6\%$</tex-math> </inline-formula> even in an underground parking lot, and (3) the horizontal error of RadioLoc is only one sixth of a dedicated GPS device even when the vehicle is moving at a high-speed (i.e., <inline-formula> <tex-math notation="LaTeX">$80$</tex-math> </inline-formula> km/h) in a complex highway scenario.

Revisiting the Okubo–Marshak Argument

Modular localization and the theory of string-localized fields have revolutionized several key aspects of quantum field theory. They reinforce the contention that local symmetry emerges directly from quantum theory, but global gauge invariance remains in general an unwarranted assumption to be examined case by case. Armed with those modern tools, we reconsider here the classical Okubo–Marshak argument on the non-existence of a “strong CP problem” in quantum chromodynamics.

Real-Time Lidar-based Localization of Mobile Ground Robot

Paper discusses modern methods for localization of mobile ground robot in outdoor environment. Special attention is payed to lidar-based methods which allow to do precise simultaneous localization and mapping (SLAM) independently to lighting conditions. Modular approach to lidar-based localization is proposed. It consists of three modules: map reconstructor, map merger and corrector, localization module. As map reconstructor we use 3D Lidar-based Graph SLAM, state-of-the-art method LOAM and its modification with point cloud segmentation techniques A-LeGO-LOAM. As map merger and corrector we apply the technique of interactive map correction for 3D Graph SLAM. For localization module we compare different real-time approaches: NDT scan matching and Localization with scan batch processing. They do not allow to localize the robot with an unknown initial position. To overcome this problem, a stage of global Monte Carlo localization is proposed, which allows to generate a switching condition and a rough initial pose. Matrix of localization convergence speed is introduced to study influence of possible inaccuracies of initial pose estimation to the convergence of real-time localization approach. An important emphasis in the paper is made to the evaluation of the localization quality with relative and absolute metrics. Experimental results are obtained for own data from mobile ground robot ClearPath Husky equipped with Velodyne HDL-32E lidar. Proposed approach to robot localization achieves real-time performance for different hardware platforms in particular single-board computer Nvidia Jetson Xavier. It demonstrates possibility for integration of studied modular localization approach to onboard control systems of autonomous vehicles.

Antiunitary representations and modular theory

Antiunitary representations of Lie groups take values in the group of unitary and antiunitary operators on a Hilbert space H. In quantum physics, antiunitary operators implement time inversion or a PCT symmetry, and in the modular theory of operator algebras they arise as modular conjugations from cyclic separating vectors of von Neumann algebras. We survey some of the key concepts at the borderline between the theory of local observables (Quantum Field Theory (QFT) in the sense of Araki--Haag--Kastler) and modular theory of operator algebras from the perspective of antiunitary group representations. Here a central point is to encode modular objects in standard subspaces V in H which in turn are in one-to-one correspondence with antiunitary representations of the multiplicative group R^x. Half-sided modular inclusions and modular intersections of standard subspaces correspond to antiunitary representations of Aff(R), and these provide the basic building blocks for a general theory started in the 90s with the ground breaking work of Borchers and Wiesbrock and developed in various directions in the QFT context. The emphasis of these notes lies on the translation between configurations of standard subspaces as they arise in the context of modular localization developed by Brunetti, Guido and Longo, and the more classical context of von Neumann algebras with cyclic separating vectors. Our main point is that configurations of standard subspaces can be studied from the perspective of antiunitary Lie group representations and the geometry of the corresponding spaces, which are often fiber bundles over ordered symmetric spaces. We expect this perspective to provide new and systematic insight into the much richer configurations of nets of local observables in QFT.

Towards more autonomous ROV operations: Scalable and modular localization with experiment data

Abstract: Remotely Operated Vehicles (ROVs) are pivotal for subsea inspection, maintenance and repair (IMR) operations. Increased autonomy in such IMR operations may constitute significant improvements in HSE (Health- Safety, Environment) and cost-effectiveness of operations. Localization is an enabling technology for autonomy. In this paper, we extend a localization framework called Vind (developed by SINTEF) from 2D mobile robot localization to 3D ROV localization. Vind framework keywords include modularity, scalability and reconfigurability. This includes that the framework facilitates easy change of, e.g., system modules, integration filters and sensors. We experimentally validate the system with real sensor data from an ROV mission. The localization systems performs even after we add additional drop-outs and varying noise characteristics to the sensor data. In the paper, we also discuss aspects concerning autonomy in IMR operations with unmanned underwater vehicles.

Robust 3/6 DoF self-localization system with selective map update for mobile robot platforms

Mobile robot platforms capable of operating safely and accurately in dynamic environments can have a multitude of applications, ranging from simple delivery tasks to advanced assembly operations. These abilities rely heavily on a robust navigation stack, which requires stable and accurate pose estimations within the environment. To solve this problem, a modular localization system suitable for a wide range of mobile robot platforms was developed. By using LIDAR/RGB-D data, the proposed system is capable of achieving 1–2 cm in translation error and 1°–3° degrees in rotation error while requiring only 5–35 ms of processing time (in 3 and 6 DoF respectively). The system was tested in three robot platforms and in several environments with different sensor configurations. It demonstrated high accuracy while performing pose tracking with point cloud registration algorithms and high reliability when estimating the initial pose using feature matching techniques. The system can also build a map of the environment with surface reconstruction and incrementally update it with either the full field of view of the sensor data or only the unknown sections, which allows to reduce the mapping processing time and also gives the possibility to update a CAD model of the environment without degrading the detail of known static areas due to sensor noise.

Modular localization and the holistic structure of causal quantum theory, a historical perspective

Recent insights into the conceptual structure of localization in QFT (modular localization) led to clarifications of old unsolved problems. The oldest one is the Einstein–Jordan conundrum which led Jordan in 1925 to the discovery of quantum field theory. This comparison of fluctuations in subsystems of heat bath systems (Einstein) with those resulting from the restriction of the QFT vacuum state to an open subvolume (Jordan) leads to a perfect analogy; the globally pure vacuum state becomes upon local restriction a strongly impure KMS state. This phenomenon of localization-caused thermal behavior as well as the vacuum-polarization clouds at the causal boundary of the localization region places localization in QFT into a sharp contrast with quantum mechanics and justifies the attribute “holstic”. In fact it positions the E–J Gedankenexperiment into the same conceptual category as the cosmological constant problem and the Unruh Gedankenexperiment. The holistic structure of QFT resulting from “modular localization” also leads to a revision of the conceptual origin of the crucial crossing property which entered particle theory at the time of the bootstrap S-matrix approach but suffered from incorrect use in the S-matrix settings of the dual model and string theory.The new holistic point of view, which strengthens the autonomous aspect of QFT, also comes with new messages for gauge theory by exposing the clash between Hilbert space structure and localization and presenting alternative solutions based on the use of stringlocal fields in Hilbert space. Among other things this leads to a reformulation of the Englert–Higgs symmetry breaking mechanism.

A Hilbert Space Setting for Interacting Higher Spin Fields and the Higgs Issue

Wigner's famous 1939 classification of positive energy representations, combined with the more recent modular localization principle, has led to a significant conceptual and computational extension of renormalized perturbation theory to interactions involving fields of higher spin. Traditionally the clash between pointlike localization and the the Hilbert space was resolved by passing to a Krein space setting which resulted in the well-known BRST gauge formulation. Recently it turned out that maintaining a Hilbert space formulation for interacting higher spin fields requires a weakening of localization from point- to string-like fields for which the d=s+1 short distance scaling dimension for integer spins is reduced to d=1 and and renormalizable couplings in the sense of power-counting exist for any spin. This new setting leads to a significant conceptual change of the relation of massless couplings with their massless counterpart. Whereas e.g. the renormalizable interactions of s=1 massive vectormesons with s<1 matter falls within the standard field-particle setting, their zero mass limits lead to much less understood phenomena as "infraparticles" and gluon/quark confinement. It is not surprising that such drastic conceptual changes in the area of gauge theories also lead to a radical change concerning the Higgs issue.

A modular localization system as a positioning service for road transport.

In recent times smart devices have attracted a large number of users. Since many of these devices allow position estimation using Global Navigation Satellite Systems (GNSS) signals, a large number of location-based applications and services have emerged, especially in transport systems. However GNSS signals are affected by the environment and are not always present, especially in dense urban environment or indoors. In this work firstly a Modular Localization Algorithm is proposed to allow seamless switching between different positioning modules. This helps us develop a positioning system that is able to provide position estimates in both indoor and outdoor environments without any user interaction. Since the proposed system can run as a service on any smart device, it could allow users to navigate not only in outdoor environments, but also indoors, e.g., underground garages, tunnels etc. Secondly we present the proposal of a 2-phase map reduction algorithm which allows one to significantly reduce the complexity of position estimation processes in case that positioning is performed using a fingerprinting framework. The proposed 2-phase map reduction algorithm can also improve the accuracy of the position estimates by filtering out reference points that are far from the mobile device. Both algorithms were implemented into a positioning system and tested in real world conditions in both indoor and outdoor environments.

The Ongoing Impact of Modular Localization on Particle Theory

Modular localization is the concise conceptual formulation of causal localization in the setting of local quantum physics. Unlike QM it does not refer to individual operators but rather to ensembles of observables which share the same localization region, as a result it explains the probabilistic aspects of QFT in terms of the impure KMS nature arising from the local restriction of the pure vacuum. Whereas it played no important role in the perturbation theory of low spin particles, it becomes indispensible for interactions which involve higher spin $s\geq1$ fields, where is leads to the replacement of the operator (BRST) gauge theory setting in Krein space by a new formulation in terms of stringlocal fields in Hilbert space. The main purpose of this paper is to present new results which lead to a rethinking of important issues of the Standard Model concerning massive gauge theories and the Higgs mechanism. We place these new findings into the broader context of ongoing conceptual changes within QFT which already led to new nonperturbative constructions of models of integrable QFTs. It is also pointed out that modular localization does not support ideas coming from string theory, as extra dimensions and Kaluza-Klein dimensional reductions outside quasiclassical approximations. Apart from hologarphic projections on null-surfaces, holograhic relations between QFT in different spacetime dimensions violate the causal completeness property, this includes in particular the Maldacena conjecture. Last not least, modular localization sheds light onto unsolved problems from QFT's distant past since it reveals that the Einstein-Jordan conundrum is really an early harbinger of the Unruh effect.

Modular localization and the holistic structure of causal quantum theory, a historical perspective

dx.doi.org/10.7437/NF2318-4957/2014.01.002 Abstract Recent insights into the conceptual structure of in QFT (modular localization) led to clarications of old unsolved problems.The oldest one is the Einstein-Jordan conundrum which led Jordan in1925 to the discovery of quantum eld theory. This comparison of fluctuations in subsystems of heat bath systems (Einstein) with those resulting from the restriction of the QFT vacuum state to an open subvolume (Jordan) leads to a perfect analogy; the globally pure vacuum state becomes upon local restriction a strongly impure KMS state. This phenomenon of localization-caused thermal behavior as well as the vacuum-polarization clouds at the causal boundary of the region places localization n QFT into a sharp contrast with quantum mechanics and justies the attribute holstic. In fact it positions the E-J Gedankenexperiment into the same conceptual category as the cosmological constant problem and the Unruh Gedankenexperiment. The holistic structure of QFT resulting from modular localization also leads to a revision of the conceptual origin of the crucial crossing property which entered particle theory at the time of the bootstrap S-matrix approach but suered from incorrect use in the S-matrix settings of the dual model and string theory. The new holistic point of view, which strengthens the autonomous aspect of QFT, also comes with new messages for gauge theory by exposing the clash between Hilbert space structure and and presenting alternative solutions based on the use of stringlocal elds in Hilbert space. Among other things this leads to a radical reformulation of the Englert- Higgs symmetry breaking mechanism.

The ongoing impact of modular localization on particle theory To the memory of Hans-Jurgen Borchers (1926-2011)

dx.doi.org/10.7437/NF2318-4957/2013.01.002 Modular localization is the concise conceptual formulation of causal localizationin the setting of local quantum physics. Unlike QM it does not refer to individualoperators but rather to ensembles of observables which share the same localizationregion; as a result it explains the probabilistic aspects of QFT in terms of the impureKMS nature arising from the local restriction of the pure vacuum. Whereas it playsno important role in perturbation theory, as a result of representing the S-matrixas a relative modular invariant of wedge-localization it becomes indispensable forunderstanding analytic and algebraic properties of on-shell objects as the S-matrixand formfactors.This leads not only to a new critical evaluation of the dual model and string the-ory, but also identifies ideas of embedding and dimensional reduction as inconsistentwith the holistic properties of localization. Instead it reveals the conceptual originof true particle crossing and points the way to a new formulation of Mandelstam&rsquo;son-shell project of the 60s.Modular localization also shows that perturbative calculations in the Krein-space setting can be better done directly in Hilbert space with the help of short-distance lowering string-localized potentials. This points to a vast extension ofrenormalizability for any spin.

Modular Localization and the Foundational Origin of Integrability

The main aim of this work is to relate integrability in QFT with a complete particle interpretation directly to the principle of causal localization, circumventing the standard method of finding sufficiently many conservation laws. Its precise conceptual-mathematical formulation as “modular localization” within the setting of local operator algebras also suggests novel ways of looking at general (non-integrable) QFTs which are not based on quantizing classical field theories. Conformal QFT, which is known to admit no particle interpretation, suggest the presence of a “partial” integrability, referred to as “conformal integrability”. This manifests itself in a “braid-permutation” group structure which contains in particular informations about the anomalous dimensional spectrum. For chiral conformal models this reduces to the braid group as it is represented in Hecke- or Birman-Wenzl-algebras associated to chiral models. Another application of modular localization mentioned in this work is an alternative to the BRST formulation of gauge theories in terms of stringlike vectorpotentials within a Hilbert space setting.

The Einstein-Jordan conundrum and its relation to ongoing foundational research in local quantum physics

We demonstrate the extraordinary modernity of the 1924/25 "Einstein-Jordan fluctuation conundrum", a Gedankenexperiment which led Jordan to his quantization of waves published as a separate section in the famous Born-Heisenberg-Jordan 1926 "Dreim\"annerarbeit". The thermal nature of energy fluctuations caused by the restriction of the QFT vacuum to a subvolume remained unnoticed mainly because it is not present in QM. In order to understand the analogy with Einstein's fluctuation calculation in a thermal black body system, it is important to expose the mechanism which causes a global vacuum state to become impure on a localized subalgebra of QFT. The present work presents the fascinating history behind this problem which culminated in the more recent perception that "causal localization" leads to thermal manifestations. The most appropriate concept which places this property of QFT into the forefront is "modular localization". These new developments in QFT led to a new access to the existence problem for interacting quantum fields whose solution has remained outside the range of renormalized perturbation theory. It also clarifies open problems about the relation of particles and fields in particular about the incompletely understood crossing property. Last not least it leads to a constructive understanding of integrable versus non-integrable QFTs..

Causality and Dispersion Relations and the Role of the S-Matrix in the Ongoing Research

The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent attempts to formulate particle physics as a pure S-matrix project. The feasibility of a pure S-matrix approach are critically analyzed and their serious shortcomings are highlighted. Whereas the conceptual/mathematical demands of renormalized perturbation theory are modest and misunderstandings could easily be corrected, the correct understanding about the origin of the crossing property requires the use of the mathematical theory of modular localization and its relation to the thermal KMS condition. These new concepts, which combine localization, vacuum polarization and thermal properties under the roof of modular theory, will be explained and their potential use in a new constructive (nonperturbative) approach to QFT will be indicated. The S-matrix still plays a predominant role but, different from Heisenberg’s and Mandelstam’s proposals, the new project is not a pure S-matrix approach. The S-matrix plays a new role as a “relative modular invariant”.

An Alternative to the Gauge Theoretic Setting

The standard formulation of quantum gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic quantum theoretical access in the spirit of Wigner’s representation theory shows that there is a fundamental clash between the pointlike localization of zero mass (vector, tensor) potentials and the Hilbert space (positivity, unitarity) structure of QT. The quantization approach has no other way than to stay with pointlike localization and sacrifice the Hilbert space whereas the approach built on the intrinsic quantum concept of modular localization keeps the Hilbert space and trades the conflict creating pointlike generation with the tightest consistent localization: semiinfinite spacelike string localization. Whereas these potentials in the presence of interactions stay quite close to associated pointlike field strengths, the interacting matter fields to which they are coupled bear the brunt of the nonlocal aspect in that they are string-generated in a way which cannot be undone by any differentiation. The new stringlike approach to gauge theory also revives the idea of a Schwinger-Higgs screening mechanism as a deeper and less metaphoric description of the Higgs spontaneous symmetry breaking and its accompanying tale about “God’s particle” and its mass generation for all the other particles.

Pascual Jordan’s legacy and the ongoing research in quantum field theory⋆

Pascual Jordan's path-breaking role as the protagonist of quantum field theory (QFT) is recalled and his friendly dispute with Dirac's particle-based relativistic quantum theory is presented as the start of the field-particle conundrum which, though in modified form, persists up to this date. Jordan had an intuitive understanding that the existence of a causal propagation with finite propagation speed in a quantum theory led to radically different physical phenomena than those of QM. The conceptional-mathematical understanding for such an approach began to emerge only 30 years later. The strongest link between Jordan's view of QFT and modern "local quantum physics" is the central role of causal locality as the defining principle of QFT as opposed to the Born localization in QM. The issue of causal localization is also the arena where misunderstandings led to a serious derailment of large part of particle theory e.g. the misinterpretation of an infinite component pointlike field resulting from the quantization of the Nambu-Goto Lagrangian as a spacetime quantum string. The new concept of modular localization, which replaces Jordan's causal locality, is especially important to overcome the imperfections of gauge theories for which Jordan was the first to note nonlocal aspects of physical (not Lagrangian) charged fields. Two interesting subjects in which Jordan was far ahead of his contemporaries will be presented in two separate sections.

A Critical Look at 50 Years Particle Theory from the Perspective of the Crossing Property

The crossing property is perhaps the most subtle aspect of the particle-field relation. Although it is not difficult to state its content in terms of certain analytic properties relating different matrixelements of the S-matrix or formfactors, its relation to the localization- and positive energy spectral principles requires a level of insight into the inner workings of QFT which goes beyond anything which can be found in typical textbooks on QFT. This paper presents a recent account based on new ideas derived from "modular localization" including a mathematic appendix on this subject. Its main novel achievement is the proof of the crossing property of formfactors from a two-algebra generalization of the KMS condition. The main content of this article is the presentation of the derailments of particle theory during more than 4 decades: the S-matrix bootstrap, the dual model and its string theoretic extension. Rather than being related to crossing, string theory is the (only known) realization of a dynamic infinite component one-particle wave function space and its associated infinite component field. Here "dynamic" means that, unlike a mere collection of infinitely many irreducible unitary Poincar\'e group representation or free fields, the formalism contains also operators which communicate between the different irreducible Poincar\'e represenations (the levels of the "infinite tower") and set the mass/spin spectrum. Wheras in pre-string times there were unsuccessful attempts to achieve this in analogy to the O(4,2) hydrogen spectrum by the use of higher noncompact groups, the superstring in d=9+1, which uses instead (bosonic/fermionic) oscillators obtained from multicomponent chiral currents is the only known unitary positive energy solution of the dynamical infinite component pointlike localized field project.

Localization and the interface between quantum mechanics, quantum field theory and quantum gravity II: The search of the interface between QFT and QG

The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it has led to a new constructive “outside-inwards approach” in which the pointlike fields and the compactly localized operator algebras which they generate only appear from intersecting much simpler algebras localized in noncompact wedge regions whose generators have extremely mild almost free field behavior. Another consequence of vacuum polarization presented in this essay is the localization entropy near a causal horizon which follows a logarithmically modified area law in which a dimensionless area (the area divided by the square of dR where dR is the thickness of a light-sheet) appears. There are arguments that this logarithmically modified area law corresponds to the volume law of the standard heat bath thermal behavior. We also explain the symmetry enhancing effect of holographic projections onto the causal horizon of a region and show that the resulting infinite dimensional symmetry groups contain the Bondi–Metzner–Sachs group. This essay is the second part of a partitioned longer paper.

Bondi-Metzner-Sachs Symmetry, Holography on Null-surfaces and Area Proportionality of “Light-slice” Entropy

It is shown that certain kinds of behavior, which hitherto were expected to be characteristic for classical gravity and quantum field theory in curved spacetime, as the infinite dimensional Bondi-Metzner-Sachs symmetry, holography on event horizons and an area proportionality of entropy, have in fact an unnoticed presence in Minkowski QFT.This casts new light on the fundamental question whether the volume proportionality of heat bath entropy and the (logarithmically corrected) dimensionless area law obeyed by localization-induced thermal behavior are different geometric parametrizations which share a common primordial algebraic origin. Strong arguments are presented that these two different thermal manifestations can be directly related, this is in fact the main aim of this paper.It will be demonstrated that QFT beyond the Lagrangian quantization setting receives crucial new impulses from holography onto horizons.The present paper is part of a project aimed at elucidating the enormous physical range of “modular localization”. The latter does not only extend from standard Hamiltonian heat bath thermal states to thermal aspects of causal- or event-horizons addressed in this paper. It also includes the recent understanding of the crossing property of formfactors whose intriguing similarity with thermal properties was, although sometimes noticed, only sufficiently understood in the modular setting (Schroer in arXiv:0905.4006 (2009)).