Conditional Posterior Cramer-Rao Lower Bound and Distributed Target Tracking in Sensor Networks

Sequential Bayesian estimation is the process of recursively estimating the state of a dynamical system observed in the presence of noise. Posterior Cramer-Rao lower bound (PCRLB) sets a performance limit onany Bayesian estimator for the given dynamical system. The PCRLBdoes not fully utilize the existing measurement information to give anindication of the mean squared error (MSE) of the estimator in the future. In many practical applications, we are more concerned with the value of the bound in the future than in the past. PCRLB is an offline bound, because it averages out the very useful measurement information, which makes it an off-line bound determined only by the system dynamical model, system measurement model and the prior knowledge of the system state at the initial time. This dissertation studies the sequential Bayesian estimation problem and then introduces the notation of conditional PCRLB, which utilizes the existing measurement information up to the current time, and sets the limit on the MSE of any Bayesian estimators at the next time step. This work has two emphases: firstly, we give the mathematically rigorous formulation of the conditional PCRLB as well as the approximate recursive version of conditional PCRLB for nonlinear, possibly non-Gaussian dynamical systems. Secondly, we apply particle filter techniques to compute the numerical values of the conditional PCRLB approximately, which overcomes the integration problems introduced by nonlinear/non-Gaussian systems. Further, we explore several possible applications of the proposed bound to find algorithms that provide improved performance. The primary problem of interest is the sensor selection problem for target tracking in sensor networks. Comparisons are also made between the performance of sensor selection algorithm based on the proposed bound and the existing approaches, such as information driven, nearest neighbor, and PCRLB with renewal strategy, to demonstrate the superior performances of the proposed approach. This dissertation also presents a bandwidth-efficient algorithm for tracking a target in sensor networks using distributed particle filters. This algorithm distributes the computation burden for target tracking over the sensor nodes. Each sensor node transmits a compressed local tracking result to the fusion center by a modified expectationmaximization (EM) algorithm to save the communication bandwidth. The fusion center incorporates the compressed tracking results to give the estimate of the target state. Finally, the target tracking problem in heterogeneous sensor networks is investigated extensively. Extended Kalman Filter and particle filter techniques are implemented and compared for tracking a maneuvering

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Probabilistic Approach to Robust Wearable Gaze Tracking

Creative Commons Attribution License (CC BY 4.0)This paper presents a method for computing the gaze point using camera data captured with a wearable gaze tracking device. The method utilizes a physical model of the human eye, ad- vanced Bayesian computer vision algorithms, and Kalman filtering, resulting in high accuracy and low noise. Our C++ implementation can process camera streams with 30 frames per second in realtime. The performance of the system is validated in an exhaustive experimental setup with 19 participants, using a self-made device. Due to the used eye model and binocular cam- eras, the system is accurate for all distances and invariant to device movement. We also test our system against a best-in-class commercial device which is outperformed for spatial accuracy and precision. The software and hardware instructions as well as the experimental data are pub- lished as open source.Peer reviewe

Joint Estimation and Control for Multi-Target Passive Monitoring with an Autonomous UAV Agent

This work considers the problem of passively monitoring multiple moving targets with a single unmanned aerial vehicle (UAV) agent equipped with a direction-finding radar. This is in general a challenging problem due to the unobservability of the target states, and the highly non-linear measurement process. In addition to these challenges, in this work we also consider: a) environments with multiple obstacles where the targets need to be tracked as they manoeuvre through the obstacles, and b) multiple false-alarm measurements caused by the cluttered environment. To address these challenges we first design a model predictive guidance controller which is used to plan hypothetical target trajectories over a rolling finite planning horizon. We then formulate a joint estimation and control problem where the trajectory of the UAV agent is optimized to achieve optimal multi-target monitoring

Probabilistic Framework for Sensor Management

A probabilistic sensor management framework is introduced, which maximizes the utility of sensor systems with many different sensing modalities by dynamically configuring the sensor system in the most beneficial way. For this purpose, techniques from stochastic control and Bayesian estimation are combined such that long-term effects of possible sensor configurations and stochastic uncertainties resulting from noisy measurements can be incorporated into the sensor management decisions

Approximate Gaussian Conjugacy: Parametric Recursive Filtering Under Nonlinearity, Multimodal, Uncertainty, and Constraint, and Beyond

This is a post-peer-review, pre-copyedit version of an article published in Frontiers of Information Technology & Electronic Engineering. The final authenticated version is available online at: https://doi.org/10.1631/FITEE.1700379Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

A marginalised particle filter with variational inference for non‐linear state‐space models with Gaussian mixture noise

This work proposes a marginalised particle filter with variational inference for non‐linear state‐space models (SSMs) with Gaussian mixture noise. A latent variable indicating the component of the Gaussian mixture considered at each time instant is introduced to specify the measurement mode of the SSM. The resulting joint posterior distribution of the state vector, the mode variable and the parameters of the Gaussian mixture noise is marginalised with respect to the noise variables. The marginalised posterior distribution of the state and mode is then approximated by using an appropriate marginalised particle filter. The noise parameters conditionally on each particle system of the state and mode variable are finally updated by using variational Bayesian inference. A simulation study is conducted to compare the proposed method with state‐of‐the‐art approaches in the context of positioning in urban canyons using global navigation satellite systems

Statistical modelling and analysis of traffic: a dynamic approach

In both developed and emerging-economies, major cities continue to experience increasing traffic congestion. To address this issue, complex Traffic Management Systems (TMS) are employed in recent years to help manage traffic. These systems fuse traffic-surveillance-related information from a variety of sensors deployed across traffic networks. A TMS requires real-time information to make effective control decisions and to deliver trustworthy information to users, such as travel time, congestion level, etc. There are three fundamental inputs required by TMS, namely, traffic volume, vehicular speed, and traffic density. Using conventional traffic loop detectors one can directly measure flow and velocity. However, traffic density is more difficult to measure. The situation becomes more difficult for multi-lane motorways due to drivers lane-change behaviour. This research investigates statistical modelling and analysis of traffic flow. It contributes to the literature of transportation and traffic management and research in several aspects. First, it takes into account lane-changes in traffic modelling through incorporating a Markov chain model to describe the drivers lane-change behaviour. Secondly, the lane change probabilities between two adjacent lanes are not assumed to be fixed but rather they depend on the current traffic condition. A discrete choice model is used to capture drivers lane choice behaviour. The drivers choice probabilities are modelled by several traffic-condition related attributes such as vehicle time headway, traffic density and speed. This results in a highly nonlinear state equation for traffic density. To address the issue of high nonlinearity of the state space model, the EKF and UKF is used to estimate the traffic density recursively. In addition, a new transformation approach has been proposed to transform the observation equation from a nonlinear form to a linear one so that the potential approximation in the EKF & UKF can be avoided. Numerical studies have been conducted to investigate the performance of the developed method. The proposed method outperformed the existing methods for traffic density estimation in simulation studies. Furthermore, it is shown that the computational cost for updating the estimate of traffic densities for a multi-lane motorway is kept at a minimum so that online applications are feasible in practice. Consequently the traffic densities can be monitored and the relevant information can be fed into the traffic management system of interest

Perceptually inspired image estimation and enhancement

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Brain and Cognitive Sciences, 2009.Includes bibliographical references (p. 137-144).In this thesis, we present three image estimation and enhancement algorithms inspired by human vision. In the first part of the thesis, we propose an algorithm for mapping one image to another based on the statistics of a training set. Many vision problems can be cast as image mapping problems, such as, estimating reflectance from luminance, estimating shape from shading, separating signal and noise, etc. Such problems are typically under-constrained, and yet humans are remarkably good at solving them. Classic computational theories about the ability of the human visual system to solve such under-constrained problems attribute this feat to the use of some intuitive regularities of the world, e.g., surfaces tend to be piecewise constant. In recent years, there has been considerable interest in deriving more sophisticated statistical constraints from natural images, but because of the high-dimensional nature of images, representing and utilizing the learned models remains a challenge. Our techniques produce models that are very easy to store and to query. We show these techniques to be effective for a number of applications: removing noise from images, estimating a sharp image from a blurry one, decomposing an image into reflectance and illumination, and interpreting lightness illusions. In the second part of the thesis, we present an algorithm for compressing the dynamic range of an image while retaining important visual detail. The human visual system confronts a serious challenge with dynamic range, in that the physical world has an extremely high dynamic range, while neurons have low dynamic ranges.(cont.) The human visual system performs dynamic range compression by applying automatic gain control, in both the retina and the visual cortex. Taking inspiration from that, we designed techniques that involve multi-scale subband transforms and smooth gain control on subband coefficients, and resemble the contrast gain control mechanism in the visual cortex. We show our techniques to be successful in producing dynamic-range-compressed images without compromising the visibility of detail or introducing artifacts. We also show that the techniques can be adapted for the related problem of "companding", in which a high dynamic range image is converted to a low dynamic range image and saved using fewer bits, and later expanded back to high dynamic range with minimal loss of visual quality. In the third part of the thesis, we propose a technique that enables a user to easily localize image and video editing by drawing a small number of rough scribbles. Image segmentation, usually treated as an unsupervised clustering problem, is extremely difficult to solve. With a minimal degree of user supervision, however, we are able to generate selection masks with good quality. Our technique learns a classifier using the user-scribbled pixels as training examples, and uses the classifier to classify the rest of the pixels into distinct classes. It then uses the classification results as per-pixel data terms, combines them with a smoothness term that respects color discontinuities, and generates better results than state-of-art algorithms for interactive segmentation.by Yuanzhen Li.Ph.D