Tracking Multiple Vehicles Using a Variational Radar Model

High-resolution radar sensors are able to resolve multiple detections per object and therefore provide valuable information for vehicle environment perception. For instance, multiple detections allow to infer the size of an object or to more precisely measure the object's motion. Yet, the increased amount of data raises the demands on tracking modules: measurement models that are able to process multiple detections for an object are necessary and measurement-to-object associations become more complex. This paper presents a new variational radar model for tracking vehicles using radar detections and demonstrates how this model can be incorporated into a Random-Finite-Set-based multi-object filter. The measurement model is learned from actual data using variational Gaussian mixtures and avoids excessive manual engineering. In combination with the multiobject tracker, the entire process chain from the raw measurements to the resulting tracks is formulated probabilistically. The presented approach is evaluated on experimental data and it is demonstrated that the data-driven measurement model outperforms a manually designed model.Comment: This is a preprint (i.e. the accepted version) of: A. Scheel and K. Dietmayer, "Tracking Multiple Vehicles Using a Variational Radar Model," in IEEE Transactions on Intelligent Transportation Systems, vol. 20, no. 10, pp. 3721-3736, 2019. Digital Object Identifier 10.1109/TITS.2018.287904

Multistability, local pattern formation, and global collective firing in a small-world network of non-leaky integrate-and-fire neurons

We investigate numerically the collective dynamical behavior of pulse-coupled non-leaky integrate-and-fire-neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for spontaneous firing for each neuron. We study network dynamics evolving from different sets of initial conditions in dependence on coupling strength and rewiring probability. Beside a homogeneous equilibrium state for low coupling strength, we observe different local patterns including cyclic waves, spiral waves, and turbulent-like patterns, which -- depending on network parameters -- interfere with the global collective firing of the neurons. We attribute the various network dynamics to distinct regimes in the parameter space. For the same network parameters different network dynamics can be observed depending on the set of initial conditions only. Such a multistable behavior and the interplay between local pattern formation and global collective firing may be attributable to the spatiotemporal dynamics of biological networks

Quantum Zeno effect in parameter estimation

The quantum Zeno effect freezes the evolution of a quantum system subject to frequent measure- ments. We apply a Fisher information analysis to show that because of this effect, a closed quantum system should be probed as rarely as possible while a dissipative quantum systems should be probed at specifically determined intervals to yield the optimal estimation of parameters governing the sys- tem dynamics. With a Bayesian analysis we show that a few frequent measurements are needed to identify the parameter region within which the Fisher information analysis appliesComment: 9 pages, 8 figure

Input-Output Theory with Quantum Pulses

We present a formalism that accounts for the evolution of quantum states of travelling light pulses incident on and emanating from a local quantum scatterer such as an atom or a cavity. We assume non-dispersive asymptotic propagation of the pulses and Markovian coupling of the stationary system to input and output fields. This permits derivation of a cascaded system master equation where the input and output pulses are treated as single oscillator modes that both couple to the local system. As examples of our theory we analyse reflection by an empty cavity with phase noise, stimulated atomic emission by a quantum light pulse, and formation of a Schr\"odinger-cat state by the dispersive interaction of a coherent pulse and a single atom in a cavity.Comment: 6 pages, 5 figures, supp. mat. with generalization of the theory to multiple input and output mode

A supernova scenario for magnetic fields and rotation measures in galaxies

We present a model for the seeding and evolution of magnetic fields in galaxies by supernovae (SN). SN explosions during galaxy assembly provide seed fields, which are subsequently amplified by compression, shear flows and random motions. Our model explains the origin of microG magnetic fields within galactic structures. We implement our model in the MHD version of the cosmological simulation code Gadget-3 and couple it with a multi-phase description of the interstellar medium. We perform simulations of Milky Way-like galactic halo formation and analyze the distribution and strength of the magnetic field. We investigate the intrinsic rotation measure (RM) evolution and find RM values exceeding 1000 rad/m*m at high redshifts and RM values around 10 rad/m*m at present-day. We compare our simulations to a limited set of observational data points and find encouraging similarities. In our model, galactic magnetic fields are a natural consequence of the very basic processes of star formation and galaxy assembly.Comment: 2 pages, proceedings of IAU symposium 31

Hypothesis testing with a continuously monitored quantum system

In a Bayesian analysis, the likelihood that specific candidate parameters govern the evolution of a quantum system are conditioned on the outcome of measurements which, in turn, cause measurement backaction on the state of the system [M. Tsang, Phys. Rev. Lett. 108, 170502 (2012)]. Specializing to the distinction of two candidate hypotheses, we study the achievements of continuous monitoring of the radiation emitted by a quantum system followed by an optimal projective measurement on its conditioned final state. Our study of the radiative decay of a driven two-level system shows an intricate interplay between the maximum information available from photon counting and homodyne detection and the final projective measurement on the emitter. We compare the results with theory predicting a lower bound for the probability to assign a wrong hypothesis by any combined measurement on the system and its radiative environment.Comment: 8 pages, 5 figure

Bayesian parameter estimation by continuous homodyne detection

We simulate the process of continuous homodyne detection of the radiative emission from a quantum system, and we investigate how a Bayesian analysis can be employed to determine unknown parameters that govern the system evolution. Measurement back-action quenches the system dynamics at all times and we show that the ensuing transient evolution is more sensitive to system parameters than the steady state of the system. The parameter sensitivity can be quantified by the Fisher information, and we investigate numerically and analytically how the temporal noise correlations in the measurement signal contribute to the ultimate sensitivity limit of homodyne detection.Comment: 10 pages, 4 figure

Estimation of atomic interaction parameters by photon counting

Detection of radiation signals is at the heart of precision metrology and sensing. In this article we show how the fluctuations in photon counting signals can be exploited to optimally extract information about the physical parameters that govern the dynamics of the emitter. For a simple two-level emitter subject to photon counting, we show that the Fisher information and the Cram\'er- Rao sensitivity bound based on the full detection record can be evaluated from the waiting time distribution in the fluorescence signal which can, in turn, be calculated for both perfect and imperfect detectors by a quantum trajectory analysis. We provide an optimal estimator achieving that bound.Comment: 9 pages, 7 figure

Multi-state and multi-hypothesis discrimination with open quantum systems

We show how an upper bound for the ability to discriminate any number N of candidates for the Hamiltonian governing the evolution of an open quantum system may be calculated by numerically efficient means. Our method applies an effective master equation analysis to evaluate the pairwise overlaps between candidate full states of the system and its environment pertaining to the Hamiltonians. These overlaps are then used to construct an N -dimensional representation of the states. The optimal positive-operator valued measure (POVM) and the corresponding probability of assigning a false hypothesis may subsequently be evaluated by phrasing optimal discrimination of multiple non-orthogonal quantum states as a semi-definite programming problem. We investigate the structure of the optimal POVM and we provide three realistic examples of hypothesis testing with open quantum systems.Comment: 9 pages, 5 figure

Scheduling on (Un-)Related Machines with Setup Times

We consider a natural generalization of scheduling $n$ jobs on $m$ parallel machines so as to minimize the makespan. In our extension the set of jobs is partitioned into several classes and a machine requires a setup whenever it switches from processing jobs of one class to jobs of a different class. During such a setup, a machine cannot process jobs and the duration of a setup may depend on the machine as well as the class of the job to be processed next. For this problem, we study approximation algorithms for non-identical machines. We develop a polynomial-time approximation scheme for uniformly related machines. For unrelated machines we obtain an $O(\log n + \log m)$-approximation, which we show to be optimal (up to constant factors) unless $NP \subset RP$. We also identify two special cases that admit constant factor approximations