18,077 research outputs found
Trajectory Synthesis for Fisher Information Maximization
Estimation of model parameters in a dynamic system can be significantly
improved with the choice of experimental trajectory. For general, nonlinear
dynamic systems, finding globally "best" trajectories is typically not
feasible; however, given an initial estimate of the model parameters and an
initial trajectory, we present a continuous-time optimization method that
produces a locally optimal trajectory for parameter estimation in the presence
of measurement noise. The optimization algorithm is formulated to find system
trajectories that improve a norm on the Fisher information matrix. A
double-pendulum cart apparatus is used to numerically and experimentally
validate this technique. In simulation, the optimized trajectory increases the
minimum eigenvalue of the Fisher information matrix by three orders of
magnitude compared to the initial trajectory. Experimental results show that
this optimized trajectory translates to an order of magnitude improvement in
the parameter estimate error in practice.Comment: 12 page
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data
While nonlinear stochastic partial differential equations arise naturally in
spatiotemporal modeling, inference for such systems often faces two major
challenges: sparse noisy data and ill-posedness of the inverse problem of
parameter estimation. To overcome the challenges, we introduce a strongly
regularized posterior by normalizing the likelihood and by imposing physical
constraints through priors of the parameters and states. We investigate joint
parameter-state estimation by the regularized posterior in a physically
motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate
reconstruction. The high-dimensional posterior is sampled by a particle Gibbs
sampler that combines MCMC with an optimal particle filter exploiting the
structure of the SEBM. In tests using either Gaussian or uniform priors based
on the physical range of parameters, the regularized posteriors overcome the
ill-posedness and lead to samples within physical ranges, quantifying the
uncertainty in estimation. Due to the ill-posedness and the regularization, the
posterior of parameters presents a relatively large uncertainty, and
consequently, the maximum of the posterior, which is the minimizer in a
variational approach, can have a large variation. In contrast, the posterior of
states generally concentrates near the truth, substantially filtering out
observation noise and reducing uncertainty in the unconstrained SEBM
Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations
The adjoint method, among other sensitivity analysis methods, can fail in
chaotic dynamical systems. The result from these methods can be too large,
often by orders of magnitude, when the result is the derivative of a long time
averaged quantity. This failure is known to be caused by ill-conditioned
initial value problems. This paper overcomes this failure by replacing the
initial value problem with the well-conditioned "least squares shadowing (LSS)
problem". The LSS problem is then linearized in our sensitivity analysis
algorithm, which computes a derivative that converges to the derivative of the
infinitely long time average. We demonstrate our algorithm in several dynamical
systems exhibiting both periodic and chaotic oscillations.Comment: submitted to JCP in revised for
Parameter estimation in kinetic reaction models using nonlinear observers facilitated by model extensions
An essential part of mathematical modelling is the accurate and reliable estimation of model parameters. In biology, the required parameters are particularly difficult to measure due to either shortcomings of the measurement technology or a lack of direct measurements. In both cases, parameters must be estimated from indirect measurements, usually in the form of time-series data. Here, we present a novel approach for parameter estimation that is particularly tailored to biological models consisting of nonlinear ordinary differential equations. By assuming specific types of nonlinearities common in biology, resulting from generalised mass action, Hill kinetics and products thereof, we can take a three step approach: (1) transform the identification into an observer problem using a suitable model extension that decouples the estimation of non-measured states from the parameters; (2) reconstruct all extended states using suitable nonlinear observers; (3) estimate the parameters using the reconstructed states. The actual estimation of the parameters is based on the intrinsic dependencies of the extended states arising from the definitions of the extended variables. An important advantage of the proposed method is that it allows to identify suitable measurements and/or model structures for which the parameters can be estimated. Furthermore, the proposed identification approach is generally applicable to models of metabolic networks, signal transduction and gene regulation
Sampling-based Motion Planning for Active Multirotor System Identification
This paper reports on an algorithm for planning trajectories that allow a
multirotor micro aerial vehicle (MAV) to quickly identify a set of unknown
parameters. In many problems like self calibration or model parameter
identification some states are only observable under a specific motion. These
motions are often hard to find, especially for inexperienced users. Therefore,
we consider system model identification in an active setting, where the vehicle
autonomously decides what actions to take in order to quickly identify the
model. Our algorithm approximates the belief dynamics of the system around a
candidate trajectory using an extended Kalman filter (EKF). It uses
sampling-based motion planning to explore the space of possible beliefs and
find a maximally informative trajectory within a user-defined budget. We
validate our method in simulation and on a real system showing the feasibility
and repeatability of the proposed approach. Our planner creates trajectories
which reduce model parameter convergence time and uncertainty by a factor of
four.Comment: Published at ICRA 2017. Video available at
https://www.youtube.com/watch?v=xtqrWbgep5
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