19,428 research outputs found
Robust Singular Smoothers For Tracking Using Low-Fidelity Data
Tracking underwater autonomous platforms is often difficult because of noisy,
biased, and discretized input data. Classic filters and smoothers based on
standard assumptions of Gaussian white noise break down when presented with any
of these challenges. Robust models (such as the Huber loss) and constraints
(e.g. maximum velocity) are used to attenuate these issues. Here, we consider
robust smoothing with singular covariance, which covers bias and correlated
noise, as well as many specific model types, such as those used in navigation.
In particular, we show how to combine singular covariance models with robust
losses and state-space constraints in a unified framework that can handle very
low-fidelity data. A noisy, biased, and discretized navigation dataset from a
submerged, low-cost inertial measurement unit (IMU) package, with ultra short
baseline (USBL) data for ground truth, provides an opportunity to stress-test
the proposed framework with promising results. We show how robust modeling
elements improve our ability to analyze the data, and present batch processing
results for 10 minutes of data with three different frequencies of available
USBL position fixes (gaps of 30 seconds, 1 minute, and 2 minutes). The results
suggest that the framework can be extended to real-time tracking using robust
windowed estimation.Comment: 9 pages, 9 figures, to be included in Robotics: Science and Systems
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Deducing the Multi-Trader Population Driving a Financial Market
We previously laid out a framework for predicting financial movements and pockets of predictability by deducing the heterogeneity in the multi-agent population in temrs of trader types playing in an artificial financial market model [7]. This work explores extensions to this basic framework. We allow for more intelligent agents with a richer strategy set, and we no longer constrain the estimate for the heterogeneity over the agents to a probability space. We then introduce a scheme which accounts for models with a wide variety of agent types. We also discuss a mechanism for bias removal on the estimates of the relevant parameters
Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises
Copyright [2002] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, a robust finite-horizon Kalman filter is designed for discrete time-varying uncertain systems with both additive and multiplicative noises. The system under consideration is subject to both deterministic and stochastic uncertainties. Sufficient conditions for the filter to guarantee an optimized upper bound on the state estimation error variance for admissible uncertainties are established in terms of two discrete Riccati difference equations. A numerical example is given to show the applicability of the presented method
Optimization viewpoint on Kalman smoothing, with applications to robust and sparse estimation
In this paper, we present the optimization formulation of the Kalman
filtering and smoothing problems, and use this perspective to develop a variety
of extensions and applications. We first formulate classic Kalman smoothing as
a least squares problem, highlight special structure, and show that the classic
filtering and smoothing algorithms are equivalent to a particular algorithm for
solving this problem. Once this equivalence is established, we present
extensions of Kalman smoothing to systems with nonlinear process and
measurement models, systems with linear and nonlinear inequality constraints,
systems with outliers in the measurements or sudden changes in the state, and
systems where the sparsity of the state sequence must be accounted for. All
extensions preserve the computational efficiency of the classic algorithms, and
most of the extensions are illustrated with numerical examples, which are part
of an open source Kalman smoothing Matlab/Octave package.Comment: 46 pages, 11 figure
Gain-constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays
This is the post-print of the Article. The official published version can be accessed from the link below - Copyright @ 2013 IEEE.This paper is concerned with the gain-constrained recursive filtering problem for a class of time-varying nonlinear stochastic systems with probabilistic sensor delays and correlated noises. The stochastic nonlinearities are described by statistical means that cover the multiplicative stochastic disturbances as a special case. The phenomenon of probabilistic sensor delays is modeled by introducing a diagonal matrix composed of Bernoulli distributed random variables taking values of 1 or 0, which means that the sensors may experience randomly occurring delays with individual delay characteristics. The process noise is finite-step autocorrelated. The purpose of the addressed gain-constrained filtering problem is to design a filter such that, for all probabilistic sensor delays, stochastic nonlinearities, gain constraint as well as correlated noises, the cost function concerning the filtering error is minimized at each sampling instant, where the filter gain satisfies a certain equality constraint. A new recursive filtering algorithm is developed that ensures both the local optimality and the unbiasedness of the designed filter at each sampling instant which achieving the pre-specified filter gain constraint. A simulation example is provided to illustrate the effectiveness of the proposed filter design approach.This work was supported in part by the National Natural Science Foundation of China by Grants 61273156, 61028008, 60825303, 61104125, and 11271103, National 973 Project by Grant 2009CB320600, the Fok Ying Tung Education Fund by Grant 111064, the Special Fund for the Author of National Excellent Doctoral Dissertation of China by Grant 2007B4, the State Key Laboratory of Integrated Automation for the Process Industry (Northeastern University) of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. by Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany
A New Approach to Linear/Nonlinear Distributed Fusion Estimation Problem
Disturbance noises are always bounded in a practical system, while fusion
estimation is to best utilize multiple sensor data containing noises for the
purpose of estimating a quantity--a parameter or process. However, few results
are focused on the information fusion estimation problem under bounded noises.
In this paper, we study the distributed fusion estimation problem for linear
time-varying systems and nonlinear systems with bounded noises, where the
addressed noises do not provide any statistical information, and are unknown
but bounded. When considering linear time-varying fusion systems with bounded
noises, a new local Kalman-like estimator is designed such that the square
error of the estimator is bounded as time goes to . A novel
constructive method is proposed to find an upper bound of fusion estimation
error, then a convex optimization problem on the design of an optimal weighting
fusion criterion is established in terms of linear matrix inequalities, which
can be solved by standard software packages. Furthermore, according to the
design method of linear time-varying fusion systems, each local nonlinear
estimator is derived for nonlinear systems with bounded noises by using Taylor
series expansion, and a corresponding distributed fusion criterion is obtained
by solving a convex optimization problem. Finally, target tracking system and
localization of a mobile robot are given to show the advantages and
effectiveness of the proposed methods.Comment: 9 pages, 3 figure
State-space modeling with correlated measurements with application to small area estimation under benchmark constraints
The problem of Small Area Estimation is how to produce reliable estimates of area (domain) characteristics, when the sizes within the areas are too small to warrant the use of traditional direct survey estimates. This problem is commonly tackled by borrowing information from either neighboring areas and/or from previous surveys, using appropriate time series/cross-sectional models. In order to protect against possible model breakdowns and for other reasons, it is often required to benchmark the model dependent estimates to the corresponding direct survey estimates in larger areas, for which the survey estimates are sufficiently accurate. The benchmarking process defines another way of borrowing information across the areas.This article shows how benchmarking can be implemented with the state-space models used by the Bureau of Labor Statistics in the U.S. for the production of the monthly employment and unemployment estimates at the state level. The computation of valid estimators for the variances of the benchmarked estimators requires joint modeling of the direct estimators in several states, which in turn requires the development of a filtering algorithm for state-space models with correlated measurement errors. No such algorithm has been developed so far. The application of the proposed procedure is illustrated using real unemployment series
Variable Splitting Methods for Constrained State Estimation in Partially Observed Markov Processes
In this paper, we propose a class of efficient, accurate, and general methods
for solving state-estimation problems with equality and inequality constraints.
The methods are based on recent developments in variable splitting and
partially observed Markov processes. We first present the generalized framework
based on variable splitting, then develop efficient methods to solve the
state-estimation subproblems arising in the framework. The solutions to these
subproblems can be made efficient by leveraging the Markovian structure of the
model as is classically done in so-called Bayesian filtering and smoothing
methods. The numerical experiments demonstrate that our methods outperform
conventional optimization methods in computation cost as well as the estimation
performance.Comment: 3 figure
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