Motivated by non-linear, non-Gaussian, distributed multi-sensor/agent navigation and tracking applications, we propose a multi-rate consensus/fusion based framework for distributed implementation of the particle filter (CF/DPF). The CF/DPF framework is based on running localized particle filters to estimate the overall state vector at each observation node. 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. A third contribution of the paper is the derivation of the exact expression for computing the posterior Cramér-Rao lower bound (PCRLB) for the distributed architecture based on a recursive procedure involving the local Fisher information matrices (FIM) of the distributed estimators. The performance of the CF/DPF algorithm closely follows the centralized particle filter approaching the PCRLB at the signal to noise ratios that we tested. IEEEkeywords: Consensus algorithms, Data fusion, Distributed estimation, Multi-sensor tracking, Nonlinear systems, and Particle filters. I. INTRODUCTION The paper focuses on distributed estimation and tracking algorithms for non-linear, non-Gaussian, data fusion problems in networked systems. Distributed state estimation has been the center of attention recently both for linear [5]-[10] and non-linear systems [11]-[32] with widespread applications such as autonomous navigation of unmanned aerial vehicles (UAV) [13], localization in robotics [15], tracking/localization in underwater sensor networks [16], distributed state estimation for power distribution 2 networks [14], and bearings-only target tracking [17]. A major problem in distributed estimation networks is unreliable communication (especially in large and multi-hop networks), which results in communication delays and information loss. Referred to as intermittent network connectivity [33], [34], this issue has been investigated broadly in the context of the Kalman filter [33], [34]. Such methods are, however, limited to linear systems and have not yet been extended to non-linear systems. The paper addresses this gap. Distributed Estimation: Traditionally, state estimation algorithms have been largely centralized with participating nodes communicating their raw observations (either directly or indirectly via a multi-hop relay) to the fusion centre: a central processing unit responsible for computing the overall estimate. Although optimal, such centralized approaches are unscalable and susceptible to failure in case the fusion centre breaks down. The alternative is to apply distributed estimation algorithms, where: (i) There is no fusion center; (ii) The...
In this paper, we propose a consensus-based, distributed implementation of the unscented particle filter (CD/UPF) that extends the distributed Kalman filtering framework to non-linear, distributed dynamical systems with non-Gaussian excitations. Compared to the existing distributed implementations of the particle filter, the CD/UPF offers two advantages. First, it uses all available local observations including the most recent ones in deriving the proposal distribution. Second, computation of global estimates from local estimates during the consensus step is based on an optimal fusion rule. In our bearingonly tracking simulations, the performance of the proposed CD/UPF is virtually indistinguishable from its centralized counterpart.
We i n vestigate the properties of block matrices with block banded inverses to derive e cient matrix inversion algorithms for such matrices. In particular, we d e r i v e the following: (1) a recursive algorithm to invert a full matrix whose inverse is structured as a block tridiagonal matrix (2) a recursive algorithm to compute the inverse of a structured block tridiagonal matrix. These algorithms are exact. They reduce the computational complexity respectively by two and one orders of magnitude over the direct inversion of the associated matrices. We apply these algorithms to develop a computationally e cient approximate implementation of the Kalman-Bucy lter (KBf) that we refer to as the local KBf. The computational e ort of the local KBf is reduced by a factor of I 2 over the exact KBf while exhibiting near-optimal performance.
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