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Chaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model error

Colin Grudzien, Alberto Carrassi, Marc Bocquet
2018 Nonlinear Processes in Geophysics  
Analytical results for linear systems explicitly describe the mechanism for the upwelling, and the associated recursive Riccati equation for the forecast error, while nonlinear approximations are explored  ...  Our derivation of the forecast error evolution describes the dynamic upwelling of the unfiltered error from outside of the span of the anomalies into the filtered subspace.  ...  evolution is weakly-nonlinear, the ensemble span will align with the span of the leading backward Lyapunov vectors -therefore the error decomposition in the basis of backward Lyapunov vectors will be  ... 
doi:10.5194/npg-25-633-2018 fatcat:grz6fjsvunh65mxmf7x5lzjdu4

Chaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model error

Colin Grudzien, Alberto Carrassi, Marc Bocquet
2018 Nonlinear Processes in Geophysics Discussions  
Analytical results for linear systems explicitly describe the mechanism for the upwelling, and the associated recursive Riccati equation for the forecast error, while nonlinear approximations are explored  ...  Our derivation of the forecast error evolution describes the dynamic upwelling of the unfiltered error from outside of the span of the anomalies into the filtered subspace.  ...  evolution is weakly-nonlinear, the ensemble span will align with the span of the leading backward Lyapunov vectors -therefore the error decomposition in the basis of backward Lyapunov vectors will be  ... 
doi:10.5194/npg-2018-4 fatcat:alh7abt4wjaf3iotti322q34dy

Dimensionality reduction in neural models: An information-theoretic generalization of spike-triggered average and covariance analysis

Jonathan W. Pillow, Eero P. Simoncelli
2006 Journal of Vision  
and robust, allowing recovery of multiple linear filters from a data set of relatively modest size; (3) it provides an explicit "default" model of the nonlinear stage mapping the filter responses to spike  ...  consistency of spike-triggered average or covariance analysis are met; (5) it can be augmented with additional constraints, such as space-time separability, on the filters.  ...  Movshon for helpful discussions and for providing us with the physiological data shown in this paper. Thanks also to L. Paninski for helpful comments on the manuscript.  ... 
doi:10.1167/6.4.9 pmid:16889478 fatcat:52eiednkira2tno2e3xj7tfe4m

Development of an Efficient Face Recognition System based on Linear and Nonlinear Algorithms

Filani Araoluwa, Adetunmbi Adebayo
2016 International Journal of Computer Applications  
The overall result using 400 images of AT&T database showed that the performance of the linear and nonlinear algorithms can be affected by the number of classes of the images, preprocessing of images,  ...  This paper presents appearance based methods for face recognition using linear and nonlinear techniques.  ...  Then finally project Ф( ) to a lower dimensional space spanned by the eigenvectors Ф in a way similar to Kernel PCA [14] .  ... 
doi:10.5120/ijca2016907932 fatcat:acovwbnsazd45l5ikbpdc7o2pm

Spike-triggered neural characterization

Odelia Schwartz, Jonathan W. Pillow, Nicole C. Rust, Eero P. Simoncelli
2006 Journal of Vision  
Spike-triggered average and covariance analyses can be used to estimate the filters and nonlinear combination rule from extracellular experimental data.  ...  This description may be formalized in a model that operates with a small set of linear filters whose outputs are nonlinearly combined to determine the instantaneous firing rate.  ...  10 Nonlinearity for an LNP model with a single linear filter followed by a point nonlinearity.  ... 
doi:10.1167/6.4.13 pmid:16889482 fatcat:567kgwyfmjfbllwilscwzkjq2a

Advanced Convolutional Neural Networks for Nonlinearity Mitigation in Long-Haul WDM Transmission Systems

Oleg Sidelnikov, Alexey Redyuk, Stylianos Sygletos, Mikhail Fedoruk, Sergei K. Turitsyn
2021 Journal of Lightwave Technology  
We propose a design that includes original initialisation of the weights of the layers by a filter predefined through the training a single-layer convolutional neural network.  ...  We examine application of the proposed convolutional neural network for the nonlinearity compensation using only one sample per symbol and evaluate complexity and performance of the proposed technique.  ...  Accordingly, coefficients with c = s correspond to XPM effects and by analogy with SPM filters we call it XPM-k filters for the spectral channels spaced at k channel spacing.  ... 
doi:10.1109/jlt.2021.3051609 fatcat:kc5e343djrcgzlceh5mwxf4vey

FAST NONLINEAR PROJECTIVE FILTERING IN A DATA STREAM

THOMAS SCHREIBER, MARCUS RICHTER
1999 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering  
We introduce a modified algorithm to perform nonlinear filtering of a time series by locally linear phase space projections.  ...  The data base that represents the phase space structure generated by the data is updated dynamically. This also allows filtering of non-stationary signals and dynamic parameter adjustment.  ...  Also nonlinear filtering procedures were designed to exploit the specific structure generated by deterministic dynamics in phase space.  ... 
doi:10.1142/s0218127499001474 fatcat:xtpwbdhw45e33h4gyhygvhvnie

Heuristic approach for multiple queries of 3D n-finger frictional force closure grasp

Nattee Niparnan, Thanathorn Phoka, Attawith Sudsang
2009 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems  
The condition finds its use as a heuristic for multiple queries force closure test. The heuristic works as a filtering criteria which improves the overall running time of the entire set of queries.  ...  This work proposes a necessary condition for nfinger force closure grasp which considers true quadratic force cone without linearization.  ...  Fig. 1 : 1 Example of vectors that satisfied Proposition 3.1. (a) the vectors do not positively span the space. (b) the vectors positively span the space.  ... 
doi:10.1109/iros.2009.5354481 dblp:conf/iros/NiparnanPS09 fatcat:b2lo2vnqtfdcdeqvm5wazrx6je

Page 1520 of Mathematical Reviews Vol. , Issue 80D [page]

1980 Mathematical Reviews  
Thus, the linear prediction problem can be solved by calculating the orthogonal projection of e™ onto the space spanned by {q,: 0<k <N} and letting Noo.  ...  It is well known that the closed linear subspace of L,(o) spanned by {q,: k=0,1,--- } is the same as that spanned by {e*: 1<0}, where o,(A)=(1+ iA)“.  ... 

On the Kalman Filter error covariance collapse into the unstable subspace

A. Trevisan, L. Palatella
2011 Nonlinear Processes in Geophysics  
Therefore the solution is the same as the solution obtained by confining the assimilation to the space spanned by the Lyapunov vectors with non-negative Lyapunov exponents.  ...  This is due to the collapse into the unstable and neutral tangent subspace of the solution of the full Extended Kalman Filter.  ...  This work has been funded by the Strategic Project: Nowcasting con l'uso di tecnologie GRID e GIS, PS080. Edited by: O. Talagrand  ... 
doi:10.5194/npg-18-243-2011 fatcat:dfk5ld37kra7lba3zi42d7tktm

Partition-based weighted sum filters for image restoration

K.E. Barner, A.M. Sarhan, R.C. Hardie
1999 IEEE Transactions on Image Processing  
Here, we focus on partitioning the observation space utilizing vector quantization and restrict the filtering function within each partition to be linear.  ...  In the general framework, each observation vector is mapped to one of M partitions comprising the observation space, and each partition has an associated filtering function.  ...  However, these nonlinear filters generally offer little or no improvement over linear filters in the case of Gaussian noise.  ... 
doi:10.1109/83.760341 pmid:18267489 fatcat:jpbuxkjjljhatjjr2lyzxliwbu

Page 223 of Journal of Applied Physics Vol. 23, Issue 2 [page]

1952 Journal of Applied Physics  
The converse, however, is true only in the case of linear filters. The basic properties of ideal filters are investigated by the use of function space techniques.  ...  sets in question span disjoint manifolds in the signal space.  ... 

Projection-based approaches for model reduction of weakly nonlinear, time-varying systems

J.R. Phillips
2003 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
The discussion proceeds from linear time-varying, to weakly nonlinear, to nonlinear time-varying analysis, relying generally on perturbational techniques to handle deviations from the linear time-invariant  ...  The main intent is to explore which perturbational techniques work, which do not, and outline some problems that remain to be solved in developing robust, general nonlinear reduction methods.  ...  Definition 1-Krylov Subspace: The Krylov subspace generated by a matrix and vector , of order , is the space spanned by the set of vectors .  ... 
doi:10.1109/tcad.2002.806605 fatcat:johyi6bsubejzeoq5srmopuvoq

Ill-Conditioned Covariance Matrices in the First-Order Two-Step Estimator

James L. Garrison, Penina Axelrad, N. Jeremy Kasdin
1998 Journal of Guidance Control and Dynamics  
A different column space basis vector ¢ would, therefore, be generated for each simulation. This point is further emphasized by the plot in Fig. 6c.  ...  to span the first-step state space.  ... 
doi:10.2514/2.4302 fatcat:uacdl4crgneizn5lldr62rdvci

On the observability codistributions of a nonlinear system

C.De Persis, A. Isidori
2000 Systems & control letters (Print)  
The purpose of this is to introduce the notion of observability codistribution for a nonlinear system, which extends the (dual of the) notion of "unobservability subspace".  ...  Then, we study its properties, which bear important similarities with a number of properties which render the notion of unobservability subspace powerful in the solution of certain design problems.  ...  In fact, in this case, since Ker{dh} ⊂ span{ ∂ ∂x 1 , ∂ ∂x 3 } , the vector field [ψ i , τ ] is trivially zero. In particular, the assumption is satisfied if the g i (x)'s are linear vector fields.  ... 
doi:10.1016/s0167-6911(00)00014-1 fatcat:vm4kdtrjgbbh3jauumt53alcmm
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