4,884 research outputs found
Minimum Number of Probes for Brain Dynamics Observability
In this paper, we address the problem of placing sensor probes in the brain
such that the system dynamics' are generically observable. The system dynamics
whose states can encode for instance the fire-rating of the neurons or their
ensemble following a neural-topological (structural) approach, and the sensors
are assumed to be dedicated, i.e., can only measure a state at each time. Even
though the mathematical description of brain dynamics is (yet) to be
discovered, we build on its observed fractal characteristics and assume that
the model of the brain activity satisfies fractional-order dynamics.
Although the sensor placement explored in this paper is particularly
considering the observability of brain dynamics, the proposed methodology
applies to any fractional-order linear system. Thus, the main contribution of
this paper is to show how to place the minimum number of dedicated sensors,
i.e., sensors measuring only a state variable, to ensure generic observability
in discrete-time fractional-order systems for a specified finite interval of
time. Finally, an illustrative example of the main results is provided using
electroencephalogram (EEG) data.Comment: arXiv admin note: text overlap with arXiv:1507.0720
Single shot parameter estimation via continuous quantum measurement
We present filtering equations for single shot parameter estimation using
continuous quantum measurement. By embedding parameter estimation in the
standard quantum filtering formalism, we derive the optimal Bayesian filter for
cases when the parameter takes on a finite range of values. Leveraging recent
convergence results [van Handel, arXiv:0709.2216 (2008)], we give a condition
which determines the asymptotic convergence of the estimator. For cases when
the parameter is continuous valued, we develop quantum particle filters as a
practical computational method for quantum parameter estimation.Comment: 9 pages, 5 image
Degenerate Kalman filter error covariances and their convergence onto the unstable subspace
The characteristics of the model dynamics are critical in the performance of (ensemble) Kalman filters. In particular, as emphasized in the seminal work of Anna Trevisan and coauthors, the error covariance matrix is asymptotically supported by the unstable-neutral subspace only, i.e., it is spanned by the backward Lyapunov vectors with nonnegative exponents. This behavior is at the core of algorithms known as assimilation in the unstable subspace, although a formal proof was still missing. This paper provides the analytical proof of the convergence of the Kalman filter covariance matrix onto the unstable-neutral subspace when the dynamics and the observation operator are linear and when the dynamical model is error free, for any, possibly rank-deficient, initial error covariance matrix. The rate of convergence is provided as well. The derivation is based on an expression that explicitly relates the error covariances at an arbitrary time to the initial ones. It is also shown that if the unstable and neutral directions of the model are sufficiently observed and if the column space of the initial covariance matrix has a nonzero projection onto all of the forward Lyapunov vectors associated with the unstable and neutral directions of the dynamics, the covariance matrix of the Kalman filter collapses onto an asymptotic sequence which is independent of the initial covariances. Numerical results are also shown to illustrate and support the theoretical findings
A Framework for Phasor Measurement Placement in Hybrid State Estimation via Gauss-Newton
In this paper, we study the placement of Phasor Measurement Units (PMU) for
enhancing hybrid state estimation via the traditional Gauss-Newton method,
which uses measurements from both PMU devices and Supervisory Control and Data
Acquisition (SCADA) systems. To compare the impact of PMU placements, we
introduce a useful metric which accounts for three important requirements in
power system state estimation: {\it convergence}, {\it observability} and {\it
performance} (COP). Our COP metric can be used to evaluate the estimation
performance and numerical stability of the state estimator, which is later used
to optimize the PMU locations. In particular, we cast the optimal placement
problem in a unified formulation as a semi-definite program (SDP) with integer
variables and constraints that guarantee observability in case of measurements
loss. Last but not least, we propose a relaxation scheme of the original
integer-constrained SDP with randomization techniques, which closely
approximates the optimum deployment. Simulations of the IEEE-30 and 118 systems
corroborate our analysis, showing that the proposed scheme improves the
convergence of the state estimator, while maintaining optimal asymptotic
performance.Comment: accepted to IEEE Trans. on Power System
Efficiency and Sensitivity Analysis of Observation Networks for Atmospheric Inverse Modelling with Emissions
The controllability of advection-diffusion systems, subject to uncertain
initial values and emission rates, is estimated, given sparse and error
affected observations of prognostic state variables. In predictive geophysical
model systems, like atmospheric chemistry simulations, different parameter
families influence the temporal evolution of the system.This renders
initial-value-only optimisation by traditional data assimilation methods as
insufficient. In this paper, a quantitative assessment method on validation of
measurement configurations to optimize initial values and emission rates, and
how to balance them, is introduced. In this theoretical approach, Kalman filter
and smoother and their ensemble based versions are combined with a singular
value decomposition, to evaluate the potential improvement associated with
specific observational network configurations. Further, with the same singular
vector analysis for the efficiency of observations, their sensitivity to model
control can be identified by determining the direction and strength of maximum
perturbation in a finite-time interval.Comment: 30 pages, 10 figures, 5 table
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