10,868 research outputs found
A Nonparametric Adaptive Nonlinear Statistical Filter
We use statistical learning methods to construct an adaptive state estimator
for nonlinear stochastic systems. Optimal state estimation, in the form of a
Kalman filter, requires knowledge of the system's process and measurement
uncertainty. We propose that these uncertainties can be estimated from
(conditioned on) past observed data, and without making any assumptions of the
system's prior distribution. The system's prior distribution at each time step
is constructed from an ensemble of least-squares estimates on sub-sampled sets
of the data via jackknife sampling. As new data is acquired, the state
estimates, process uncertainty, and measurement uncertainty are updated
accordingly, as described in this manuscript.Comment: Accepted at the 2014 IEEE Conference on Decision and Contro
Dynamic Estimation of Rigid Motion from Perspective Views via Recursive Identification of Exterior Differential Systems with Parameters on a Topological Manifold
We formulate the problem of estimating the motion of a rigid object viewed under perspective projection as the identification of a dynamic model in Exterior Differential form with parameters on a topological manifold.
We first describe a general method for recursive identification of nonlinear implicit systems using prediction error criteria. The parameters are allowed to move slowly on some topological (not necessarily smooth) manifold. The basic recursion is solved in two different ways: one is based on a simple extension of the traditional Kalman Filter to nonlinear and implicit measurement constraints, the other may be regarded as a generalized "Gauss-Newton" iteration, akin to traditional Recursive Prediction Error Method techniques in linear identification. A derivation of the "Implicit Extended Kalman Filter" (IEKF) is reported in the appendix.
The ID framework is then applied to solving the visual motion problem: it indeed is possible to characterize it in terms of identification of an Exterior Differential System with parameters living on a C0 topological manifold, called the "essential manifold". We consider two alternative estimation paradigms. The first is in the local coordinates of the essential manifold: we estimate the state of a nonlinear implicit model on a linear space. The second is obtained by a linear update on the (linear) embedding space followed by a projection onto the essential manifold. These schemes proved successful in performing the motion estimation task, as we show in experiments on real and noisy synthetic image sequences
Active Classification for POMDPs: a Kalman-like State Estimator
The problem of state tracking with active observation control is considered
for a system modeled by a discrete-time, finite-state Markov chain observed
through conditionally Gaussian measurement vectors. The measurement model
statistics are shaped by the underlying state and an exogenous control input,
which influence the observations' quality. Exploiting an innovations approach,
an approximate minimum mean-squared error (MMSE) filter is derived to estimate
the Markov chain system state. To optimize the control strategy, the associated
mean-squared error is used as an optimization criterion in a partially
observable Markov decision process formulation. A stochastic dynamic
programming algorithm is proposed to solve for the optimal solution. To enhance
the quality of system state estimates, approximate MMSE smoothing estimators
are also derived. Finally, the performance of the proposed framework is
illustrated on the problem of physical activity detection in wireless body
sensing networks. The power of the proposed framework lies within its ability
to accommodate a broad spectrum of active classification applications including
sensor management for object classification and tracking, estimation of sparse
signals and radar scheduling.Comment: 38 pages, 6 figure
Optimal State Estimation with Measurements Corrupted by Laplace Noise
Optimal state estimation for linear discrete-time systems is considered.
Motivated by the literature on differential privacy, the measurements are
assumed to be corrupted by Laplace noise. The optimal least mean square error
estimate of the state is approximated using a randomized method. The method
relies on that the Laplace noise can be rewritten as Gaussian noise scaled by
Rayleigh random variable. The probability of the event that the distance
between the approximation and the best estimate is smaller than a constant is
determined as function of the number of parallel Kalman filters that is used in
the randomized method. This estimator is then compared with the optimal linear
estimator, the maximum a posteriori (MAP) estimate of the state, and the
particle filter
Recursive Motion Estimation on the Essential Manifold
Visual motion estimation can be regarded as estimation of the state of a system of difference equations with unknown inputs defined on a manifold. Such a system happens to be "linear", but it is defined on a space (the so called "Essential manifold") which is not a linear (vector) space.
In this paper we will introduce a novel perspective for viewing the motion estimation problem which results in three original schemes for solving it. The first consists in "flattening the space" and solving a nonlinear estimation problem on the flat (euclidean) space.
The second approach consists in viewing the system as embedded in a larger euclidean space (the smallest of the embedding spaces), and solving at each step a linear estimation problem on a linear space, followed by a "projection" on the manifold (see fig. 5).
A third "algebraic" formulation of motion estimation is inspired by the structure of the problem in local coordinates (flattened space), and consists in a double iteration for solving an "adaptive fixed-point" problem (see fig. 6).
Each one of these three schemes outputs motion estimates together with the joint second order statistics of the estimation error, which can be used by any structure from motion module which incorporates motion error [20, 23] in order to estimate 3D scene structure.
The original contribution of this paper involves both the problem formulation, which gives new insight into the differential geometric structure of visual motion estimation, and the ideas generating the three schemes. These are viewed within a unified framework. All the schemes have a strong theoretical motivation and exhibit accuracy, speed of convergence, real time operation and flexibility which are superior to other existing schemes [1, 20, 23].
Simulations are presented for real and synthetic image sequences to compare the three schemes against each other and highlight the peculiarities of each one
Computational tools for multi-linked flexible structures
A software module which designs and tests controllers and filters in Kalman Estimator form, based on a polynomial state-space model is discussed. The user-friendly program employs an interactive graphics approach to simplify the design process. A variety of input methods are provided to test the effectiveness of the estimator. Utilities are provided which address important issues in filter design such as graphical analysis, statistical analysis, and calculation time. The program also provides the user with the ability to save filter parameters, inputs, and outputs for future use
Regression analysis with missing data and unknown colored noise: application to the MICROSCOPE space mission
The analysis of physical measurements often copes with highly correlated
noises and interruptions caused by outliers, saturation events or transmission
losses. We assess the impact of missing data on the performance of linear
regression analysis involving the fit of modeled or measured time series. We
show that data gaps can significantly alter the precision of the regression
parameter estimation in the presence of colored noise, due to the frequency
leakage of the noise power. We present a regression method which cancels this
effect and estimates the parameters of interest with a precision comparable to
the complete data case, even if the noise power spectral density (PSD) is not
known a priori. The method is based on an autoregressive (AR) fit of the noise,
which allows us to build an approximate generalized least squares estimator
approaching the minimal variance bound. The method, which can be applied to any
similar data processing, is tested on simulated measurements of the MICROSCOPE
space mission, whose goal is to test the Weak Equivalence Principle (WEP) with
a precision of . In this particular context the signal of interest is
the WEP violation signal expected to be found around a well defined frequency.
We test our method with different gap patterns and noise of known PSD and find
that the results agree with the mission requirements, decreasing the
uncertainty by a factor 60 with respect to ordinary least squares methods. We
show that it also provides a test of significance to assess the uncertainty of
the measurement.Comment: 12 pages, 4 figures, to be published in Phys. Rev.
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