Luigi Chisci

C. Fantacci, B. -N. Vo, B. -T. Vo et al.

This paper addresses distributed multi-object tracking over a network of heterogeneous and geographically dispersed nodes with sensing, communication and processing capabilities. The main contribution is an approach to distributed multi-object estimation based on labeled Random Finite Sets (RFSs) and dynamic Bayesian inference, which enables the development of two novel consensus tracking filters, namely a Consensus Marginalized $δ$-Generalized Labeled Multi-Bernoulli and Consensus Labeled Multi-Bernoulli tracking filter. The proposed algorithms provide fully distributed, scalable and computationally efficient solutions for multi-object tracking. Simulation experiments via Gaussian mixture implementations confirm the effectiveness of the proposed approach on challenging scenarios.

Lin Gao, Giorgio Battistelli, Luigi Chisci

Generalized covariance intersection (GCI) has been effective in fusing multiobject densities from multiple agents for multitarget tracking and mapping purposes. From an information-theoretic viewpoint, it has been shown that GCI fusion essentially minimizes the weighted information gain (WIG) from local densities to the fused one. In this paper, the interest is in the fusion rule that dually minimizes the weighted information loss (WIL) and it turns out that such a fusion rule is consistent with the so-called linear opinion pool (LOP). However, the LOP cannot be directly applied to multiobject fusion since the resulting fused multiobject density (FMD), in general, no longer belongs to the same family of the local ones, thus it cannot be utilized as prior information for the next recursion in the context of Bayesian multiobject filtering. In order to overcome such a difficulty, the principle of minimizing WIL is further exploited in that the optimal FMD in the same family of the local ones is looked for. Implementation issues relative to the proposed minimum WIL (MWIL) fusion rule are discussed. Finally, the performance of the MWIL rule is assessed via simulation experiments concerning distributed multitarget tracking over a wireless sensor network.

Nicola Forti, Giorgio Battistelli, Luigi Chisci et al.

This paper deals with secure state estimation of cyber-physical systems subject to switching (on/off) attack signals and injection of fake packets (via either packet substitution or insertion of extra packets). The random set paradigm is adopted in order to model, via Random Finite Sets (RFSs), the switching nature of both system attacks and the injection of fake measurements. The problem of detecting an attack on the system and jointly estimating its state, possibly in the presence of fake measurements, is then formulated and solved in the Bayesian framework for systems with and without direct feedthrough of the attack input to the output. This leads to the analytical derivation of a hybrid Bernoulli filter (HBF) that updates in real-time the joint posterior density of a Bernoulli attack RFS and of the state vector. A closed-form Gaussian-mixture implementation of the proposed hybrid Bernoulli filter is fully derived in the case of invertible direct feedthrough. Finally, the effectiveness of the developed tools for joint attack detection and secure state estimation is tested on two case-studies concerning a benchmark system for unknown input estimation and a standard IEEE power network application.

Lin Gao, Giorgio Battistelli, Luigi Chisci et al.

This paper addresses distributed registration of a sensor network for multitarget tracking. Each sensor gets measurements of the target position in a local coordinate frame, having no knowledge about the relative positions (referred to as drift parameters) and azimuths (referred to as orientation parameters) of its neighboring nodes. The multitarget set is modeled as an independent and identically distributed (i.i.d.) cluster random finite set (RFS), and a consensus cardinality probability hypothesis density (CPHD) filter is run over the network to recursively compute in each node the posterior RFS density. Then a suitable cost function, xpressing the discrepancy between the local posteriors in terms of averaged Kullback-Leibler divergence, is minimized with respect to the drift and orientation parameters for sensor registration purposes. In this way, a computationally feasible optimization approach for joint sensor registraton and multitarget tracking is devised. Finally, the effectiveness of the proposed approach is demonstrated through simulation experiments on both tree networks and networks with cycles, as well as with both linear and nonlinear sensors.

Giorgio Battistelli, Luigi Chisci, Lin Gao et al.

The aim of this paper is to devise a strategy that is able to reduce communication bandwidth and, consequently, energy consumption in the context of distributed state estimation over a peer-to-peer sensor network. Specifically, a distributed Bayes filter with event-triggered communication is developed by enforcing each node to transmit its local information to the neighbors only when the Kullback-Leibler divergence between the current local posterior and the one predictable from the last transmission exceeds a preset threshold. The stability of the proposed eventtriggered distributed Bayes filter is proved in the linear-Gaussian (Kalman filter) case. The performance of the proposed algorithm is also evaluated through simulation experiments concerning a target tracking application.

Giorgio Battistelli, Luigi Chisci, Nicola Forti et al.

The paper deals with decentralized state estimation for spatially distributed systems described by linear partial differential equations from discrete in-space-and-time noisy measurements provided by sensors deployed over the spatial domain of interest. A fully scalable approach is pursued by decomposing the domain into overlapping subdomains assigned to different processing nodes interconnected to form a network. Each node runs a local finite-dimensional Kalman filter which exploits the finite element approach for spatial discretization and the parallel Schwarz method to iteratively enforce consensus on the estimates and covariances over the boundaries of adjacent subdomains. Stability of the proposed distributed consensus-based finite element Kalman filter is mathematically proved and its effectiveness is demonstrated via simulation experiments concerning the estimation of a bi-dimensional temperature field.

Matteo Tesori, Giorgio Battistelli, Luigi Chisci

This paper introduces a framework based on linear splines for 2-dimensional extended object tracking and classification. Unlike state of the art models, linear splines allow to represent extended objects whose contour is an arbitrarily complex curve. An exact likelihood is derived for the case in which noisy measurements can be scattered from any point on the contour of the extended object, while an approximate Monte Carlo likelihood is provided for the case wherein scattering points can be anywhere, i.e. inside or on the contour, on the object surface. Exploiting such likelihood to measure how well the observed data fit a given shape, a suitable estimator is developed. The proposed estimator models the extended object in terms of a kinematic state, providing object position and orientation, along with a shape vector, characterizing object contour and surface. The kinematic state is estimated via a nonlinear Kalman filter, while the shape vector is estimated via a Bayesian classifier so that classification is implicitly solved during shape estimation. Numerical experiments are provided to assess, compared to state of the art extended object estimators, the effectiveness of the proposed one.

Lin Gao, Giorgio Battistelli, Luigi Chisci et al.

In this paper, consensus-based Kalman filtering is extended to deal with the problem of joint target tracking and sensor self-localization in a distributed wireless sensor network. The average weighted Kullback-Leibler divergence, which is a function of the unknown drift parameters, is employed as the cost to measure the discrepancy between the fused posterior distribution and the local distribution at each sensor. Further, a reasonable approximation of the cost is proposed and an online technique is introduced to minimize the approximated cost function with respect to the drift parameters stored in each node. The remarkable features of the proposed algorithm are that it needs no additional data exchanges, slightly increased memory space and computational load comparable to the standard consensus-based Kalman filter. Finally, the effectiveness of the proposed algorithm is demonstrated through simulation experiments on both a tree network and a network with cycles as well as for both linear and nonlinear sensors.