Search NASA⌕ Search

SEARCH · Search NASA

Results for “Nonlinear filtering”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations

Abstract In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then, we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis.

Mathematics↗
DOE OSTI2019

A direct filter method for parameter estimation

Parameter estimation is an important research topic in data assimilation. In this paper, a novel parameter estimation method is introduced, where the parameter is considered as the state process in a nonlinear filtering problem and the state model that contains the parameter is used to construct a pseudo-observation. This approach is named the direct filter method since nonlinear filtering algorithms are used to estimate the parameter directly without estimating the state model as part of the solution in the nonlinear filtering problem. Numerical experiments are carried out to examine the effectiveness and accuracy of the direct filter method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Nonlinear Ensemble Filtering with Diffusion Models: Application to the Surface Quasigeostrophic Dynamics

The intersection between classical data assimilation methods and novel machine learning techniques has attracted significant interest in recent years. Here, we explore another promising solution in which diffusion models are used to formulate a robust nonlinear ensemble filter for sequential data assimilation. Unlike standard machine learning methods, the proposed ensemble score filter (EnSF) is completely training free and can efficiently generate a set of analysis ensemble members. Here, in this study, we apply the EnSF to a surface quasigeostrophic model and compare its performance against the popular local ensemble transform Kalman filter (LETKF), which makes Gaussian assumptions in the analysis step. Numerical tests demonstrate that EnSF maintains stable performance in the absence of localization and for a variety of experimental settings. We find that while LETKF maintains optimal performance in the case of linear observations of the entire state and a perfect model, EnSF shows improvements over LETKF when nonlinear observations are assimilated and the system is subject to unexpected model errors. A spectral decomposition of the analysis results in this nonlinear observation regime shows that the largest improvements over LETKF occur at large scales (small wavenumbers), where LETKF lacks sufficient ensemble spread. Overall, this initial application of EnSF to a geophysical model of intermediate complexity motivates further development of the algorithm for more realistic problems.

Artificial intelligence↗
DOE OSTI2020

Polar coupling enabled nonlinear optical filtering at MoS 2 /ferroelectric heterointerfaces

Complex oxide heterointerfaces and van der Waals heterostructures present two versatile but intrinsically different platforms for exploring emergent quantum phenomena and designing new functionalities. The rich opportunity offered by the synergy between these two classes of materials, however, is yet to be charted. Here, we report an unconventional nonlinear optical filtering effect resulting from the interfacial polar alignment between monolayer MoS 2 and a neighboring ferroelectric oxide thin film. The second harmonic generation response at the heterointerface is either substantially enhanced or almost entirely quenched by an underlying ferroelectric domain wall depending on its chirality, and can be further tailored by the polar domains. Unlike the extensively studied coupling mechanisms driven by charge, spin, and lattice, the interfacial tailoring effect is solely mediated by the polar symmetry, as well explained via our density functional theory calculations, pointing to a new material strategy for the functional design of nanoscale reconfigurable optical applications.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Higher-order dispersion compensating pulse shaper via amplitude spectral filtering and nonlinear phase accumulation

A method of pulse shaping using spectral filtering, positive chirp, and self-phase modulation to control the accumulated higher-order phase terms of the spectral phase. This pulse shaping method has particular advantage in fiber chirped pulse amplification (FCPA) systems, where there are two effects: (1) an offsetting of the fourth order phase via nonlinear phase accumulation, allowing for a higher Strehl ratio (i.e., a cleaner pulse), higher peak power pulse and (2) enabling power scaling to higher pulse energies without the increased nonlinear phase accumulation leading to pulse breakup. This technique can be used both in a passive system with no amplification to clean up an existing pulse, and in an amplifier system to enable higher performance operation (shorter pulses, cleaner pulses, higher energy pulses).

Domingue, Scott R.↗
DOE OSTI2020

Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows

Reduced rank nonlinear filters are increasingly utilized in data assimilation of geophysical flows, but often require a set of ensemble forward simulations to estimate forecast covariance. On the other hand, predictor-corrector type nudging approaches are still attractive due to their simplicity of implementation when more complex methods need to be avoided. However, optimal estimate of nudging gain matrix might be cumbersome. In this paper, we put forth a fully nonintrusive recurrent neural network approach based on a long short-term memory (LSTM) embedding architecture to estimate the nudging term, which plays a role not only to force the state trajectories to the observations but also acts as a stabilizer. Furthermore, our approach relies on the power of archival data and the trained model can be retrained effectively due to power of transfer learning in any neural network applications. In order to verify the feasibility of the proposed approach, we perform twin experiments using Lorenz 96 system. Our results demonstrate that the proposed LSTM nudging approach yields more accurate estimates than both extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) when only sparse observations are available. With the availability of emerging AI-friendly and modular hardware technologies and heterogeneous computing platforms, we articulate that our simplistic nudging framework turns out to be computationally more efficient than either the EKF or EnKF approaches.

42 ENGINEERING↗
DOE OSTI2023

An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems

We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low accuracy in handling high-dimensional and highly nonlinear problems. EnSF attacks this challenge by exploiting the score-based diffusion model, defined in a pseudo-temporal domain, to characterizing the evolution of the filtering density. EnSF stores the information of the recursively updated filtering density function in the score function, in stead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation that uses mini-batch-based Monte Carlo estimator to directly approximate the score function at any pseudo-spatial-temporal location, which provides sufficient accuracy in solving high-dimensional nonlinear problems as well as saves tremendous amount of time spent on training neural networks. Another essential aspect of EnSF is its analytical update step, gradually incorporating data information into the score function, which is crucial in mitigating the degeneracy issue faced when dealing with very high-dimensional nonlinear filtering problems. High-dimensional Lorenz systems are used to demonstrate the performance of our method. EnSF provides surprisingly impressive performance in reliably tracking extremely high-dimensional Lorenz systems (up to 1,000,000 dimension) with highly nonlinear observation processes, which is a well-known challenging problem for existing filtering methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

RBFNN-based Minimum Entropy Filtering for a Class of Stochastic Nonlinear Systems

This paper presents a novel minimum entropy filter design for a class of stochastic nonlinear systems which are subjected to non-Gaussian noises. Motivated by stochastic distribution control, an output entropy model is developed using RBF neural network while the parameters of the model can be identified by the collected data. Based upon the presented model, the filtering problem has been investigated while the system dynamics have been represented. As the model output is the entropy of the estimation error, the optimal nonlinear filter is obtained based on the Lyapunov design which makes the model output minimum. Moreover, the entropy assignment problem has been discussed as an extension of the presented approach. To verify the presented design procedure, a numerical example is given which illustrates the effectiveness of the presented algorithm. The contributions of this paper can be included as 1) an output entropy model is presented using neural network; 2) a nonlinear filter design algorithm is developed as the main result and 3) a solution of entropy assignment problem is obtained which is an extension of the presented framework.

42 ENGINEERING↗
DOE OSTI2019

Unscented Kalman Filter-based Unbiased Minimum-Variance Estimation for Nonlinear Systems with Unknown Inputs

This paper proposes an unscented Kalman filter (UKF)-based unbiased minimum-variance estimation (UMV) method for the nonlinear system with unknown inputs. By utilizing the statistical linerization, the nonlinear system and measurement functions are transformed into a “linear-like” regression form. The latter preserves the nonlinearity of the system and the measurement models. To this end, the unknown inputs can be estimated by the weighted least-squares. This “linear-like” regression form also allows us to resort to the UMV state estimation framework for the development of new nonlinear filter to handle unknown inputs. Specifically, two approaches have been developed: 1) given the estimated inputs, we derive a filter by minimizing the trace of the state error covariance matrix; 2) without input estimation, we derive the filter by minimizing the trace of the state error covariance matrix subject to a constraint imposed on the gain matrix. We prove that these two approaches provide the same results. Numerical results validate the effectiveness of the proposed method.

Unscented Kalman filter, unbiased minimumvariance ↗
DOE OSTI2020

Dynamic Performance Enhancement for Nonlinear Stochastic Systems Using RBF Driven Nonlinear Compensation with Extended Kalman Filter

In this paper, a novel hybrid control method is proposed to enhance the control performance of the PI based control system for a class of nonlinear and non-Gaussian stochastic dynamic processes with unmeasurable states. Firstly, to enhance the tracking performance of the PI controller where the PI parameters are fixed in many actual control systems, the compensative signal is formed using the extended Kalman filter(EKF) based state estimator and driven by the radial basis function (RBF) neural network based compensator. In addition, the weights of RBF is trained to minimize the entropy criterion of tracking error as the process is subjected to non-Gaussian disturbances. Meanwhile, since the precise statistical property of noises is hard to obtain for many industrial processes, the kernel density estimation (KDE) technique is employed in this paper to estimate the entropy. The convergence of RBF network is discussed and the stability of the resulted closed-loop hybrid control system is analyzed in mean square sense. Finally, a numerical example and a practical system testing are given to illustrate the effectiveness of the proposed control method.

stochastic systems, PI Controller, Entropy, Extend↗
DOE OSTI2020

Filtering adaptive output feedback control for multivariable nonlinear systems with mismatched uncertainties and unmodeled dynamics

This article synthesizes a filtering adaptive output feedback controller for multivariable nonlinear systems with mismatched uncertainties and unmodeled dynamics. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. The unmodeled dynamics are bounded-input bounded-output stable. By adopting an estimation/cancellation strategy, a piecewise constant adaptive law drives the estimation error to zero at every time instant, which yields the adaptive parameters; a disturbance rejection control law is designed to compensate the nonlinear uncertainties within the bandwidth of low-pass filters. The matched uncertainties are cancelled directly by adopting their opposite in the control signal, while a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. A feedforward control law is designed to track a given command. Since the virtual reference system defines the best performance that can be achieved by the closed-loop system, the uniform performance bounds are derived for the states and control signals via comparison. Both numerical and practical examples are provided to illustrate the effectiveness of the proposed filtering adaptive output feedback control architecture, comparisons with the model reference adaptive control demonstrates the superiority of the proposed control method.

filtering adaptive control, mismatched uncertainit↗
DOE OSTI2025

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Nonlinear manipulation of surface plasmons on graphene-TMDC Bragg reflectors

In this study, we benefit from the nonlinear optical tunability of the graphene-transition metal dichalcogenide (G-TMDC) heterostructure and the strong confinement of the electromagnetic fields of surface plasmon polaritons (SPPs) on graphene in order to propose a highly tunable nonlinear optical Bragg reflector. Recently, two-dimensional (2D) TMDCs are the subject of intense researches because of their nonlinear optical properties at near infrared wavelengths which are very intriguing for various optical applications. We choose two kinds of 2D-TMDCs, MoSe{sub 2} and WSe{sub 2}, with the strongest second order optical nonlinearity at near infrared range to properly design the periodic variation of the propagating SPP waves on the graphene layer. We utilize theoretical method of quantum electrostatic heterostructure to compute the dielectric function of graphene-TMDCs. Different nonlinearities of two TMDCs lead to noticeable tuning of the full width at half maximum (FWHM) and the central Bragg wavelength of the reflector which let design various optical devices. We design an add/drop filter, a nonlinear switch, and an AND/OR optical logic gate based on our proposed Bragg reflector. Our finite difference time domain numerical and transfer matrix analytical results reveal that by increment of the optical intensity up to 6 MW/cm{sup 2} which is below the pulse damage threshold of graphene, due to the second order nonlinearity, a 10-nm red-shift in central Bragg wavelength is observed and the 20-nm FWHM at linear regime decreases to 1.5 nm. The SPP intensities of 0.8 MW/cm{sup 2} and 1.53 MW/cm{sup 2} fulfill the requirements for AND and OR logical operations with 57 and 66.51 dB extinction ratios, respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗