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ABSTRACT: This Letter presents offline estimation results for the decay-time constant for an experimental Fabry-Perot optical cavity for cavity ring-down spectroscopy (CRDS). The cavity dynamics are modeled in terms of a low pass filter (LPF) with unity DC gain. This model is used by an extended Kalman filter (EKF) along with the recorded light intensity at the output of the cavity in order to estimate the decay-time constant. The estimation results using the LPF cavity model are compared to those obtained using the quadrature model for the cavity presented in previous work by Kallapur et al. The estimation process derived using the LPF model comprises two states as opposed to three states in the quadrature model. When considering the EKF, this means propagating two states and a (2×2) covariance matrix using the LPF model, as opposed to propagating three states and a (3×3) covariance matrix using the quadrature model. This gives the former model a computational advantage over the latter and leads to faster execution times for the corresponding EKF. It is shown in this Letter that the LPF model for the cavity with two filter states is computationally more efficient, converges faster, and is hence a more suitable method than the three-state quadrature model presented in previous work for real-time estimation of the decay-time constant for the cavity.
Optics Letters 08/2012; 37(15):3018-20. · 3.40 Impact Factor
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ABSTRACT: This article approaches deterministic filtering via an application of the
min-plus linearity of the corresponding dynamic programming operator. This
filter design method yields a set-valued state estimator for discrete-time
nonlinear systems (nonlinear dynamics and output functions). The energy bounds
in the process and the measurement disturbances are modeled using a sum
quadratic constraint. The filtering problem is recast into an optimal control
problem in the form of a Hamilton-Jacobi-Bellman (HJB) equation, the solution
to which is obtained by employing the min-plus linearity property of the
dynamic programming operator. This approach enables the solution to the HJB
equation and the design of the filter without recourse to linearization of the
system dynamics/ output equation.
03/2012;
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ABSTRACT: This paper is concerned with stability conditions for the positive feedback
interconnection of negative imaginary systems. A generalization of the negative
imaginary lemma is derived, which remains true even if the transfer function
has poles on the imaginary axis including the origin. A sufficient condition
for the internal stability of a feedback interconnection for NI systems
including a pole at the origin is given and an illustrative example is
presented to support the result.
07/2011;
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ABSTRACT: This paper discusses the application of a discrete-time extended Kalman filter (EKF) to the problem of estimating the decay time constant for a Fabry-Perot optical cavity for cavity ring-down spectroscopy (CRDS). The data for the estimation process is obtained from a CRDS experimental setup in terms of the light intensity at the output of the cavity. The cavity is held in lock with the input laser frequency by controlling the distance between the mirrors within the cavity by means of a proportional-integral (PI) controller. The cavity is purged with nitrogen and placed under vacuum before chopping the incident light at 25 KHz and recording the light intensity at its output. In spite of beginning the EKF estimation process with uncertainties in the initial value for the decay time constant, its estimates converge well within a small neighborhood of the expected value for the decay time constant of the cavity within a few ring-down cycles. Also, the EKF estimation results for the decay time constant are compared to those obtained using the Levenberg-Marquardt estimation scheme.
Optics Express 03/2011; 19(7):6377-86. · 3.59 Impact Factor
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Proceedings of the IEEE International Conference on Control Applications, CCA 2011, Denver, CO, USA, September 28-30, 2011; 01/2011
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ABSTRACT: This paper develops a robust extended Kalman filter for nonlinear uncertain systems with
a deterministic description of noise and uncertainty. The system state dynamics are formulated in
reverse time and the uncertainties are modeled in terms of sum quadratic constraints. The robust
filtering problem is formulated as a set-valued state estimation problem which is recast into an optimal
control problem. The solution of the resulting Hamilton-Jacobi-Bellman equation is obtained by using a
quadratic approximation. This leads to an approximate information state for the filtering problem which
is computed recursively through a difference Riccati equation derived by linearizing the observation
equation and using a quadratic approximation to the system dynamics. The reduction of the robust
estimator to the standard Kalman filter in the uncertainty-free linear case is also discussed.
18th IFAC World Congress, August 28 - September 2, 2011, Milan, Italy; 01/2011
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Proceedings of the IEEE International Conference on Control Applications, CCA 2010, Yokohama, Japan, September 8-10, 2010; 01/2010
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Proceedings of the IEEE International Conference on Control Applications, CCA 2010, Yokohama, Japan, September 8-10, 2010; 01/2010
