Distributed implementations of the particle filter with performance bounds

The focus of the thesis is on developing distributed estimation algorithms for systems with nonlinear dynamics. Of particular interest are the agent or sensor networks (AN/SN) consisting of a large number of local processing and observation agents/nodes, which can communicate and cooperate with each other to perform a predefined task. Examples of such AN/SNs are distributed camera networks, acoustic sensor networks, networks of unmanned aerial vehicles, social networks, and robotic networks. Signal processing in the AN/SNs is traditionally centralized and developed for systems with linear dynamics. In the centralized architecture, the participating nodes communicate their observations (either directly or indirectly via a multi-hop relay) to a central processing unit, referred to as the fusion centre, which is responsible for performing the predefined task. For centralized systems with linear dynamics, the Kalman filter provides the optimal approach but suffers from several drawbacks, e.g., it is generally unscalable and also susceptible to failure in case the fusion centre breaks down. In general, no analytic solution can be determined for systems with nonlinear dynamics. Consequently, the conventional Kalman filter cannot be used and one has to rely on numerical approaches. In such cases, the sequential Monte Carlo approaches, also known as the particle filters, are widely used as approximates to the Bayesian estimators but mostly in the centralized configuration. Recently there has been a growing interest in distributed signal processing algorithms where: (i) There is no fusion centre; (ii) The local nodes do not have (require) global knowledge of the network topology, and; (iii) Each node exchanges data only within its local neighborhood. Distributed estimation have been widely explored for estimation/tracking problems in linear systems. Distributed particle filter implementations for nonlinear systems are still in their infancy and are the focus of this thesis. In the first part of this thesis, four different consensus-based distributed particle filter implementations are proposed. First, a constrained sufficient statistic based distributed implementation of the particle filter (CSS/DPF) is proposed for bearing-only tracking (BOT) and joint bearing/range tracking problems encountered in a number of applications including radar target tracking and robot localization. Although the number of parallel consensus runs in the CSS/DPF is lower compared to the existing distributed implementations of the particle filter, the CSS/DPF still requires a large number of iterations for the consensus runs to converge. To further reduce the consensus overhead, the CSS/DPF is extended to distributed implementation of the unscented particle filter, referred to as the CSS/DUPF, which require a limited number of consensus iterations. Both CSS/DPF and CSS/DUPF are specific to BOT and joint bearing/range tracking problems. Next, the unscented, consensus-based, distributed implementation of the particle filter (UCD /DPF) is proposed which is generalizable to systems with any dynamics. In terms of contributions, the UCD /DPF makes two important improvements to the existing distributed particle filter framework: (i) Unlike existing distributed implementations of the particle filter, the UCD /DPF uses all available global observations including the most recent ones in deriving the proposal distribution based on the distributed UKF, and; (ii) Computation of the global estimates from local estimates during the consensus step is based on an optimal fusion rule. Finally, a multi-rate consensus/fusion based framework for distributed implementation of the particle filter, referred to as the CF /DPF, is proposed. Separate fusion filters are designed to consistently assimilate the local filtering distributions into the global posterior by compensating for the common past information between neighbouring nodes. The CF /DPF offers two distinct advantages over its counterparts. First, the CF /DPF framework is suitable for scenarios where network connectivity is intermittent and consensus can not be reached between two consecutive observations. Second, the CF /DPF is not limited to the Gaussian approximation for the global posterior density. Numerical simulations verify the near-optimal performance of the proposed distributed particle filter implementations. The second half of the thesis focuses on the distributed computation of the posterior Cramer-Rao lower bounds (PCRLB). The current PCRLB approaches assume a centralized or hierarchical architecture. The exact expression for distributed computation of the PCRLB is not yet available and only an approximate expression has recently been derived. Motivated by the distributed adaptive resource management problems with the objective of dynamically activating a time-variant subset of observation nodes to optimize the network's performance, the thesis derives the exact expression, referred to as the dPCRLB, for computing the PCRLB for any AN/SN configured in a distributed fashion. The dPCRLB computational algorithms are derived for both the off-line conventional (non-conditional) PCRLB determined primarily from the state model, observation model, and prior knowledge of the initial state of the system, and the online conditional PCRLB expressed as a function of past history of the observations. Compared to the non-conditional dPCRLB, its conditional counterpart provides a more accurate representation of the estimator's performance and, consequently, a better criteria for sensor selection. The thesis then extends the dPCRLB algorithms to quantized observations. Particle filter realizations are used to compute these bounds numerically and quantify their performance for data fusion problems through Monte-Carlo simulations

Convergence of Distributed Flooding and Its Application for Distributed Bayesian Filtering

Distributed flooding is a fundamental information sharing method to get network consensus via peer-to-peer communication. However, a unified consensus-oriented formulation of the algorithm and its convergence performance are not yet explicitly available in the literature. To fill this void in this paper, set-theoretic flooding rules are defined by encapsulating the information of interest in finite sets (one set per node), namely distributed set-theoretic information flooding (DSIF). This leads to a new type of consensus referred to as ”collecting consensus” which aims to ensure that all nodes get the same information. Convergence and optimality analyses are provided based on a consistent measure of the degree of consensus (DoC) of the network. Compared with the prevailing averaging consensus, the proposed DSIF protocol benefits from avoiding repeated use of any information and offering the highest converging efficiency for network consensus while being exposed to increasing node-storage requirements against communication iterations and higher communication load. The protocol has been advocated for distributed nonlinear Bayesian filtering, where each node operates a separate particle filter, and the collecting consensus is pursued on the sensor data alone or jointly with intermediate local estimates. Simulations are provided in detail to demonstrate the theoretical findings

Modeling brain connectivity dynamics in functional Magnetic Resonance Imaging via Particle Filtering

Interest in the studying of functional connections in the brain has grown considerably in the last decades, as many studies have pointed out that alterations in the interaction among brain areas can play a role as markers of neurological diseases. Most studies in this field treat the brain network as a system of connections stationary in time, but dynamic features of brain connectivity can provide useful information, both on physiology and pathological conditions of the brain. In this paper, we propose the application of a computational methodology, named Particle Filter (PF), to study non-stationarities in brain connectivity in functional Magnetic Resonance Imaging (fMRI). The PF algorithm estimates time-varying hidden parameters of a first-order linear time-varying Vector Autoregressive model (VAR) through a Sequential Monte Carlo strategy. On simulated time series, the PF approach effectively detected and enabled to follow time-varying hidden parameters and it captured causal relationships among signals. The method was also applied to real fMRI data, acquired in presence of periodic tactile or visual stimulations, in different sessions. On these data, the PF estimates were consistent with current knowledge on brain functioning. Most importantly, the approach enabled to detect statistically significant modulations in the cause-effect relationship between brain areas, which correlated with the underlying visual stimulation pattern presented during the acquisition

Computational intelligence approaches to robotics, automation, and control [Volume guest editors]

No abstract available