85 research outputs found
A Nonparametric Adaptive Nonlinear Statistical Filter
We use statistical learning methods to construct an adaptive state estimator
for nonlinear stochastic systems. Optimal state estimation, in the form of a
Kalman filter, requires knowledge of the system's process and measurement
uncertainty. We propose that these uncertainties can be estimated from
(conditioned on) past observed data, and without making any assumptions of the
system's prior distribution. The system's prior distribution at each time step
is constructed from an ensemble of least-squares estimates on sub-sampled sets
of the data via jackknife sampling. As new data is acquired, the state
estimates, process uncertainty, and measurement uncertainty are updated
accordingly, as described in this manuscript.Comment: Accepted at the 2014 IEEE Conference on Decision and Contro
<Contributed Talk 15>An Energy Harvester for Broadband Vibrations
[Date] November 28 (Mon) - December 2 (Fri), 2011: [Place] Kyoto University Clock Tower Centennial Hall, Kyoto, JAPA
Phase noise of oscillators with unsaturated amplifiers
We study the role of amplifier saturation in eliminating feedback noise in self-sustained oscillators. We extend previous works that use a saturated amplifier to quench fluctuations in the feedback magnitude, while simultaneously tuning the oscillator to an operating point at which the resonator nonlinearity cancels fluctuations in the feedback phase. We consider a generalized model which features an amplitude-dependent amplifier gain function. This allows us to determine the total oscillator phase noise in realistic configurations due to noise in both quadratures of the feedback, and to show that it is not necessary to drive the resonator to large oscillation amplitudes in order to eliminate noise in the phase of the feedback
Global Isochrons and Phase Sensitivity of Bursting Neurons
Phase sensitivity analysis is a powerful method for studying (asymptotically periodic) bursting neuron models. One popular way of capturing phase sensitivity is through the computation of isochrons---subsets of the state space that each converge to the same trajectory on the limit cycle. However, the computation of isochrons is notoriously difficult, especially for bursting neuron models. In [W. E. Sherwood and J. Guckenheimer, SIAM J. Appl. Dyn. Syst., 9 (2010), pp. 659--703], the phase sensitivity of the bursting Hindmarsh--Rose model is studied through the use of singular perturbation theory: cross sections of the isochrons of the full system are approximated by those of fast subsystems. In this paper, we complement the previous study, providing a detailed phase sensitivity analysis of the full (three-dimensional) system, including computations of the full (two-dimensional) isochrons. To our knowledge, this is the first such computation for a bursting neuron model. This was made possible thanks to the numerical method recently proposed in [A. Mauroy and I. Mezić, Chaos, 22 (2012), 033112]---relying on the spectral properties of the so-called Koopman operator---which is complemented with the use of adaptive quadtree and octree grids. The main result of the paper is to highlight the existence of a region of high phase sensitivity called the almost phaseless set and to completely characterize its geometry. In particular, our study reveals the existence of a subset of the almost phaseless set that is not predicted by singular perturbation theory (i.e., by the isochrons of fast subsystems). We also discuss how the almost phaseless set is related to empirically observed phenomena such as addition/deletion of spikes and to extrema of the phase response of the system. Finally, through the same numerical method, we show that an elliptic bursting model is characterized by a very high phase sensitivity and other remarkable properties
Effect of Noise on Excursions To and Back From Infinity
The effect of additive white noise on a model for bursting behavior in large
aspect-ratio binary fluid convection is considered. Such bursts are present in
systems with nearly square symmetry and are the result of heteroclinic cycles
involving infinite amplitude states created when the square symmetry is broken.
A combination of numerical results and analytical arguments show how even a
very small amount of noise can have a very large effect on the amplitudes of
successive bursts. Large enough noise can also affect the physical
manifestations of the bursts. Finally, it is shown that related bursts may
occur when white noise is added to the normal form equations for the Hopf
bifurcation with exact square symmetry.Comment: 17 pages, 9 figure
- …