649 research outputs found
A New Reduction Scheme for Gaussian Sum Filters
In many signal processing applications it is required to estimate the
unobservable state of a dynamic system from its noisy measurements. For linear
dynamic systems with Gaussian Mixture (GM) noise distributions, Gaussian Sum
Filters (GSF) provide the MMSE state estimate by tracking the GM posterior.
However, since the number of the clusters of the GM posterior grows
exponentially over time, suitable reduction schemes need to be used to maintain
the size of the bank in GSF. In this work we propose a low computational
complexity reduction scheme which uses an initial state estimation to find the
active noise clusters and removes all the others. Since the performance of our
proposed method relies on the accuracy of the initial state estimation, we also
propose five methods for finding this estimation. We provide simulation results
showing that with suitable choice of the initial state estimation (based on the
shape of the noise models), our proposed reduction scheme provides better state
estimations both in terms of accuracy and precision when compared with other
reduction methods
A low-order automatic domain splitting approach for nonlinear uncertainty mapping
This paper introduces a novel method for the automatic detection and handling
of nonlinearities in a generic transformation. A nonlinearity index that
exploits second order Taylor expansions and polynomial bounding techniques is
first introduced to rigorously estimate the Jacobian variation of a nonlinear
transformation. This index is then embedded into a low-order automatic domain
splitting algorithm that accurately describes the mapping of an initial
uncertainty set through a generic nonlinear transformation by splitting the
domain whenever some imposed linearity constraints are non met. The algorithm
is illustrated in the critical case of orbital uncertainty propagation, and it
is coupled with a tailored merging algorithm that limits the growth of the
domains in time by recombining them when nonlinearities decrease. The low-order
automatic domain splitting algorithm is then combined with Gaussian mixtures
models to accurately describe the propagation of a probability density
function. A detailed analysis of the proposed method is presented, and the
impact of the different available degrees of freedom on the accuracy and
performance of the method is studied
Multi-modal filtering for non-linear estimation
Multi-modal densities appear frequently in time series and practical applications. However, they are not well represented by common state estimators, such as the Extended Kalman Filter and the Unscented Kalman Filter, which additionally suffer from the fact that uncertainty is often not captured sufficiently well. This can result in incoherent and divergent tracking performance. In this paper, we address these issues by devising a non-linear filtering algorithm where densities are represented by Gaussian mixture models, whose parameters are estimated in closed form. The resulting method exhibits a superior performance on nonlinear benchmarks. © 2014 IEEE
Enhanced GMM-based Filtering with Measurement Update Ordering and Innovation-based Pruning
The Gaussian mixture model (GMM) has been extensively investigated in nonlinear/non-Gaussian filtering problems. This paper presents two enhancements for GMM-based nonlinear filtering techniques, namely, the adaptive ordering of the measurement update and normalized innovation square (NIS)-based mixture component management. The first technique selects the order of measurement update by maximizing the marginal measurement likelihood to improve performance. The second approach takes the filtering history of a mixture component into account and prunes those components with NIS larger than a threshold to eliminate their impact on the filtering posterior. The advantage of the proposed enhancements is illustrated via simulations that consider source tracking using the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements received at two unmanned aerial vehicles (UAVs). A GMM-cubature quadrature Kalman filter (CQKF) is implemented and its performances with different measurement update and mixture component management strategies are compared. The superior performance obtained via the use of the two proposed techniques is demonstrated
Multi-modal filtering for non-linear estimation
Multi-modal densities appear frequently in time series and practical applications. However, they are not well represented by common state estimators, such as the Extended Kalman Filter and the Unscented Kalman Filter, which additionally suffer from the fact that uncertainty is often not captured sufficiently well. This can result in incoherent and divergent tracking performance. In this paper, we address these issues by devising a non-linear filtering algorithm where densities are represented by Gaussian mixture models, whose parameters are estimated in closed form. The resulting method exhibits a superior performance on nonlinear benchmarks
Single camera pose estimation using Bayesian filtering and Kinect motion priors
Traditional approaches to upper body pose estimation using monocular vision
rely on complex body models and a large variety of geometric constraints. We
argue that this is not ideal and somewhat inelegant as it results in large
processing burdens, and instead attempt to incorporate these constraints
through priors obtained directly from training data. A prior distribution
covering the probability of a human pose occurring is used to incorporate
likely human poses. This distribution is obtained offline, by fitting a
Gaussian mixture model to a large dataset of recorded human body poses, tracked
using a Kinect sensor. We combine this prior information with a random walk
transition model to obtain an upper body model, suitable for use within a
recursive Bayesian filtering framework. Our model can be viewed as a mixture of
discrete Ornstein-Uhlenbeck processes, in that states behave as random walks,
but drift towards a set of typically observed poses. This model is combined
with measurements of the human head and hand positions, using recursive
Bayesian estimation to incorporate temporal information. Measurements are
obtained using face detection and a simple skin colour hand detector, trained
using the detected face. The suggested model is designed with analytical
tractability in mind and we show that the pose tracking can be
Rao-Blackwellised using the mixture Kalman filter, allowing for computational
efficiency while still incorporating bio-mechanical properties of the upper
body. In addition, the use of the proposed upper body model allows reliable
three-dimensional pose estimates to be obtained indirectly for a number of
joints that are often difficult to detect using traditional object recognition
strategies. Comparisons with Kinect sensor results and the state of the art in
2D pose estimation highlight the efficacy of the proposed approach.Comment: 25 pages, Technical report, related to Burke and Lasenby, AMDO 2014
conference paper. Code sample: https://github.com/mgb45/SignerBodyPose Video:
https://www.youtube.com/watch?v=dJMTSo7-uF
Nonlinear Filtering based on Log-homotopy Particle Flow : Methodological Clarification and Numerical Evaluation
The state estimation of dynamical systems based on measurements is an ubiquitous problem. This is relevant in applications like robotics, industrial manufacturing, computer vision, target tracking etc. Recursive Bayesian methodology can then be used to estimate the hidden states of a dynamical system. The procedure consists of two steps: a process update based on solving the equations modelling the state evolution, and a measurement update in which the prior knowledge about the system is improved based on the measurements. For most real world systems, both the evolution and the measurement models are nonlinear functions of the system states. Additionally, both models can also be perturbed by random noise sources, which could be non-Gaussian in their nature. Unlike linear Gaussian models, there does not exist any optimal estimation scheme for nonlinear/non-Gaussian scenarios. This thesis investigates a particular method for nonlinear and non-Gaussian data assimilation, termed as the log-homotopy based particle flow. Practical filters based on such flows have been known in the literature as Daum Huang filters (DHF), named after the developers. The key concept behind such filters is the gradual inclusion of measurements to counter a major drawback of single step update schemes like the particle filters i.e. namely the degeneracy. This could refer to a situation where the likelihood function has its probability mass well seperated from the prior density, and/or is peaked in comparison. Conventional sampling or grid based techniques do not perform well under such circumstances and in order to achieve a reasonable accuracy, could incur a high processing cost. DHF is a sampling based scheme, which provides a unique way to tackle this challenge thereby lowering the processing cost. This is achieved by dividing the single measurement update step into multiple sub steps, such that particles originating from their prior locations are graduated incrementally until they reach their final locations. The motion is controlled by a differential equation, which is numerically solved to yield the updated states. DH filters, even though not new in the literature, have not been fully explored in the detail yet. They lack the in-depth analysis that the other contemporary filters have gone through. Especially, the implementation details for the DHF are very application specific. In this work, we have pursued four main objectives. The first objective is the exploration of theoretical concepts behind DHF. Secondly, we build an understanding of the existing implementation framework and highlight its potential shortcomings. As a sub task to this, we carry out a detailed study of important factors that affect the performance of a DHF, and suggest possible improvements for each of those factors. The third objective is to use the improved implementation to derive new filtering algorithms. Finally, we have extended the DHF theory and derived new flow equations and filters to cater for more general scenarios. Improvements in the implementation architecture of a standard DHF is one of the key contributions of this thesis. The scope of the applicability of DHF is expanded by combining it with other schemes like the Sequential Markov chain Monte Carlo and the tensor decomposition based solution of the Fokker Planck equation, resulting in the development of new nonlinear filtering algorithms. The standard DHF, using improved implementation and the newly derived algorithms are tested in challenging simulated test scenarios. Detailed analysis have been carried out, together with the comparison against more established filtering schemes. Estimation error and the processing time are used as important performance parameters. We show that our new filtering algorithms exhibit marked performance improvements over the traditional schemes
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