SMC methods to avoid self-resolving for online Bayesian parameter estimation

Abstract—The particle filter is a powerful filtering technique that is able to handle a broad scope of nonlinear problems. However, it has also limitations: a standard particle filter is unable to handle, for instance, systems that include static variables (parameters) to be estimated together with the dynamic states. This limitation is due to the well-known “self-resolving” phenomenon, which is caused by the gradual loss of information that occurs during the resampling steps. In the context of online Bayesian parameter estimation, some approaches to handle this problem have proposed, such as adding artificial dynamics to the parameter model. However, these approaches typically both introduce new parameters (e.g. the intensity of artificial process noise) and inherent biases to the estimation problem. In this paper, we will give a give a look at two Sequential Monte Carlo techniques that do not rely on biasing the system model: the Autonomous Multiple Model particle filter and the Rao-Blackwellized Marginal particle filter. These approaches are not new, but have not been applied yet to the problem of online Bayesian parameter estimation for non-structured models. We will derive suitable adaptations of these methods for this problem and evaluate them using simulations. I

A Bayesian analysis of the mixed labelling phenomenon in two-target tracking

In mulit-target tracking and labelling (MTTL), mixed labelling corresponds to a situation where there is ambiguity in labelling, i.e. in the assignment of labels to locations (where a "location" here means simply an unlabelled single-target state. The phenomenon is well-known in literature, and known to occur in the situation where targets move in close proximity to each other and afterwards separate. The occurrence of mixed labelling has been empirically observed using particle filter implementations of the Bayesian MTTL recursion. In this memorandum, we will instead demonstrate the occurrence of mixed labelling (in the situation of closely spaced targets) using only the Bayesian recursion itself, for a scenario containing two targets and no target births or deaths. We will also show how mixed labelling generally persists after the targets become well-separated, and how mixed labelling might not happen when the unlabelled single-target state contains non-kinematic quantities

A Bayesian solution to multi-target tracking problems with mixed labelling

In Multi-Target Tracking (MTT), the problem of assigning labels to tracks (track labelling) is vastly covered in literature and has been previously formulated using Bayesian recursion. However, the existing literature lacks an appropriate measure of uncertainty related to the assigned labels which has sound mathematical basis and clear practical meaning (to the user). This is especially important in a situation where targets move in close proximity with each other and thereafter separate again. Because, in such a situation it is well-known that there will be confusion on target identities, also known as “mixed labelling‿. In this paper, we provide a mathematical characterization of the labelling uncertainties present in Bayesian multi-target tracking and labelling (MTTL) problems and define measures of labelling uncertainties with clear physical interpretation. The introduced uncertainty measures can be used to find the optimal track label assignment, and evaluate track labelling performance. We also analyze in details the mixed labelling phenomenon in the presence of two targets. In addition, we propose a new Sequential Monte Carlo (SMC) algorithm, the Labelling Uncertainty Aware Particle Filter (LUA-PF), for the multi target tracking and labelling problem that can provide good estimates of the uncertainty measures. We validate this using simulation and show that the proposed method performs much better when compared with the performance of the SIR multi-target SMC filter

Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems

We prove Lieb-Robinson bounds for the dynamics of systems with an infinite dimensional Hilbert space and generated by unbounded Hamiltonians. In particular, we consider quantum harmonic and certain anharmonic lattice systems

Measurement of the π−\pi^- decay width of Λ5^5_\LambdaHe

We have precisely measured $\Lambda \to p\pi^-$ decay width of \5LHe and demonstrated significantly larger $\alpha$ -$\Lambda$ overlap than expected from the central repulsion $\alpha$-$\Lambda$ potential, which is derived from YNG \Lambda$-nucleon interaction.Comment: 4 pages, 3 figure

Flat-Band Ferromagnetism in Organic Polymers Designed by a Computer Simulation

By coupling a first-principles, spin-density functional calculation with an exact diagonalization study of the Hubbard model, we have searched over various functional groups for the best case for the flat-band ferromagnetism proposed by R. Arita et al. [Phys. Rev. Lett. {\bf 88}, 127202 (2002)] in organic polymers of five-membered rings. The original proposal (poly-aminotriazole) has turned out to be the best case among the materials examined, where the reason why this is so is identified here. We have also found that the ferromagnetism, originally proposed for the half-filled flat band, is stable even when the band filling is varied away from the half-filling. All these make the ferromagnetism proposed here more experimentally inviting.Comment: 11 pages, 13figure

Proton asymmetry in non-mesonic weak decay of light hypernuclei

We have obtained the decay asymmetry parameters in non-mesonic weak decay of polarized Lambda-hypernuclei by measuring the proton asymmetry. The polarized Lambda-hypernuclei, 5_Lambda-He, 12_Lambda-C, and 11_Lambda-B, were produced in high statistics via the (pi^+,k^+) reaction at 1.05 GeV/c in the forward angles. Preliminary analysis shows that the decay asymmetry parameters are very small for these s-shell and p-shell hypernuclei.Comment: 4pages, 4figures, International Conference on Hypernuclear and Strange Particle Physics (HYP2003

pi^0 decay branching ratios of 5_Lambda-He and 12_Lambda-C hypernuclei

We precisely measured pi^0 branching ratios of 5_Lambda-He and 12_Lambda-C hypernuclei produced via (pi^+,k^+) reaction. Using these pi^0 branching ratios with the pi^- branching ratios and the lifetimes, we obtained the pi^0 decay widths and the non-mesonic weak decay widths at high statistics with the accuracy of ~5 % (stat) for both hypernuclei.Comment: 4pages, 4figures, International Conference on Hypernuclear and Strange Particle Physics (HYP2003

Nucleon-nucleon coincidence measurement in the non-mesonic weak decay of 5_Lambda-He and 12_Lambda-C hypernuclei

We have measured both yields of neutron-proton and neutron-neutron pairs emitted from the non-mesonic weak decay process of 5_Lambda-He and 12_Lambda-C hypernuclei produced via the (pi^+,K^+) reaction for the first time. We observed clean back-to-back correlation of the np- and nn-pairs in the coincidence spectra for both hypernuclei. The ratio of those back-to-back pair yields, Nnn / Nnp, must be close to the ratio of neutron- and proton-induced decay widths of the decay, Gn(Lambda n -> nn)/Gp(Lambda p -> np). The obtained ratios for each hypernuclei support recent calculations based on short-range interactions.Comment: 4 pages, 1 figure, International Nuclear Physics Conference (INPC 2004), Goteborg, Sweden, June 27 - July 2, 2004, to appear in Nuclear Physics

Time of arrival through interacting environments: Tunneling processes

We discuss the propagation of wave packets through interacting environments. Such environments generally modify the dispersion relation or shape of the wave function. To study such effects in detail, we define the distribution function P_{X}(T), which describes the arrival time T of a packet at a detector located at point X. We calculate P_{X}(T) for wave packets traveling through a tunneling barrier and find that our results actually explain recent experiments. We compare our results with Nelson's stochastic interpretation of quantum mechanics and resolve a paradox previously apparent in Nelson's viewpoint about the tunneling time.Comment: Latex 19 pages, 11 eps figures, title modified, comments and references added, final versio