Recursive Nonlinear Estimation: A Geometric Approach

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Our experiments confirm that the derived minimum energy filter with higher-order state differential equation copes with higher-order kinematics and is also able to minimize model noise. We also show that the proposed filter is superior to state-of-the-art extended Kalman filters on Lie groups in the case of linear observations and that our method reaches the accuracy of modern visual odometry methods.

Recursive Nonlinear Estimation: A Geometric Approach

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There are various information-geometric model selection criteria, which I want to know more about; I suspect, based purely on this disciplinary prejudice, that they will out-perform coordinate-dependent criteria. I should also mention that statistical physics , while it does no actual statistics , is also very much concerned with probability distributions. Sun-Ichi Amari, who is the leader of a large and impressive Japanese school of information-geometers, has a nice result in, e. I think this throws a very interesting new light on the issue of why we can assume equilibrium corresponds to a state of maximum entropy pace Jaynes, assuming independence is clearly not an innocent way of saying "I really don't know anything more".

I also see, via the Arxiv, that people are starting to think about phase transitions in information-geometric terms, which seems natural in retrospect, though I can't comment further, not having read the papers.

Filtering, State Estimation, and Other Forms of Signal Processing

See also: Exponential Families of Probability Measures , where the geometry is especially nice; Filtering and State Estimation for some papers on differential-geometric ideas in statistical state estimation and signal processing; Partial Identification of Parametric Statistical Models Recommended, big picture: S. Amari, O.

Barndorff-Nielsen, R. Kass, S. Lauritzen, and C.

Kass and Paul W. Myung, Vijay Balasubramanian and M. Dodson, "Neighborhoods of Independence for Random Processes", math.

Recursive Variational Bayesian Dual Estimation for Nonlinear Dynamics and Non-Gaussian Observations

Barndorff-Nielsen and Richard D. Carter, Raviv Raich, William G. Finn, Alfred O. Crooks, "Measuring Thermodynamic Length", Physical Review Letters 99 : ["Thermodynamic length is a metric distance between equilibrium thermodynamic states. Among other interesting properties, this metric asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system.

It is also connected to the Jensen-Shannon divergence, Fisher information, and Rao's entropy differential metric. Dodson and H.

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Wang, "Iterative Approximation of Statistical Distributions and Relation to Information Geometry", Statistical Inference for Stochastic Processes 4 : ["the optimal control of stochastic processes through sensor estimation of probability density functions is given a geometric setting via information theory and the information metric.