Giorgio Battistelli

Suqi Li, Wei Yi, Reza Hoseinnezhad et al.

This paper considers the problem of the distributed fusion of multi-object posteriors in the labeled random finite set filtering framework, using Generalized Covariance Intersection (GCI) method. Our analysis shows that GCI fusion with labeled multi-object densities strongly relies on label consistencies between local multi-object posteriors at different sensor nodes, and hence suffers from a severe performance degradation when perfect label consistencies are violated. Moreover, we mathematically analyze this phenomenon from the perspective of Principle of Minimum Discrimination Information and the so called yes-object probability. Inspired by the analysis, we propose a novel and general solution for the distributed fusion with labeled multi-object densities that is robust to label inconsistencies between sensors. Specifically, the labeled multi-object posteriors are firstly marginalized to their unlabeled posteriors which are then fused using GCI method. We also introduce a principled method to construct the labeled fused density and produce tracks formally. Based on the developed theoretical framework, we present tractable algorithms for the family of generalized labeled multi-Bernoulli (GLMB) filters including $δ$-GLMB, marginalized $δ$-GLMB and labeled multi-Bernoulli filters. The robustness and efficiency of the proposed distributed fusion algorithm are demonstrated in challenging tracking scenarios via numerical experiments.

Guchong Li, Giorgio Battistelli, Wei Yi et al.

Distributed multi-target tracking (DMTT) is addressed for sensors having different fields of view (FoVs). The proposed approach is based on the idea of fusing the posterior Probability Hypotheses Densities (PHDs) generated by the sensors on the basis of the local measurements. An efficient and robust distributed fusion algorithm combining the Generalized Covariance Intersection (GCI) rule with a suitable Clustering Algorithm (CA) is proposed. The CA is used to decompose each posterior PHD into well-separated components (clusters). For the commonly detected targets, an efficient parallelized GCI fusion strategy is proposed and analyzed in terms of $L_1$ error. For the remaining targets, a suitable compensation strategy is adopted so as to counteract the GCI sensitivity to independent detections while reducing the occurrence of false targets. Detailed implementation steps using a Gaussian Mixture (GM) representation of the PHDs are provided. Numerical experiments clearly confirms the effectiveness of the proposed CA-GCI fusion algorithm.

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.

Giorgio Battistelli, Luigi Chisci, Stefano Gherardini

The paper addresses state estimation for linear discrete-time systems with binary (threshold) measurements. A Moving Horizon Estimation (MHE) approach is followed and different estimators, characterized by two different choices of the cost function to be minimized and/or by the possible inclusion of constraints, are proposed. Specifically, the cost function is either quadratic, when only the information pertaining to the threshold-crossing instants is exploited, or piece-wise quadratic, when all the available binary measurements are taken into account. Stability results are provided for the proposed MHE algorithms in the presence of unknown but bounded disturbances and measurement noises. Performance of the proposed techniques is also assessed by means of a simulation example.

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 addresses state estimation for discrete-time systems with binary (threshold) measurements by following a Maximum A posteriori Probability (MAP) approach and exploiting a Moving Horizon (MH) approximation of the MAP cost-function. It is shown that, for a linear system and noise distributions with log-concave probability density function, the proposed MH-MAP state estimator involves the solution, at each sampling interval, of a convex optimization problem. Application of the MH-MAP estimator to dynamic estimation of a diffusion field given pointwise-in-time-and-space binary measurements of the field is also illustrated and, finally, simulation results relative to this application are shown to demonstrate the effectiveness of the proposed approach.

Giorgio Battistelli, Pietro Tesi

We consider the problem of classifying trajectories generated by dynamical systems. We investigate a model-based approach, the common approach in control engineering, and a data-driven approach based on Support Vector Machines, a popular method in the area of machine learning. The analysis points out connections between the two approaches and their relative merits.

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.

Ángel F. García-Fernández, Giorgio Battistelli

This paper presents the distributed Poisson multi-Bernoulli (PMB) filter based on the generalised covariance intersection (GCI) fusion rule for distributed multi-object filtering. Since the exact GCI fusion of two PMB densities is intractable, we derive a principled approximation. Specifically, we approximate the power of a PMB density as an unnormalised PMB density, which corresponds to an upper bound of the PMB density. Then, the GCI fusion rule corresponds to the normalised product of two unnormalised PMB densities. We show that the result is a Poisson multi-Bernoulli mixture (PMBM), which can be expressed in closed form. Future prediction and update steps in each filter preserve the PMBM form, which can be projected back to a PMB density before the next fusion step. Experimental results show the benefits of this approach compared to other distributed multi-object filters.

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.

Giulia Vezzani, Ugo Pattacini, Giorgio Battistelli et al.

This paper addresses 6-DOF (degree-of-freedom) tactile localization, i.e. the pose estimation of tridimensional objects given tactile measurements. This estimation problem is fundamental for the operation of autonomous robots that are often required to manipulate and grasp objects whose pose is a-priori unknown. The nature of tactile measurements, the strict time requirements for real-time operation and the multimodality of the involved probability distributions pose remarkable challenges and call for advanced nonlinear filtering techniques. Following a Bayesian approach, this paper proposes a novel and effective algorithm, named Memory Unscented Particle Filter (MUPF), which solves the 6-DOF localization problem recursively in real-time by only exploiting contact point measurements. MUPF combines a modified particle filter that incorporates a sliding memory of past measurements to better handle multimodal distributions, along with the unscented Kalman filter that moves the particles towards regions of the search space that are more likely with the measurements. The performance of the proposed MUPF algorithm has been assessed both in simulation and on a real robotic system equipped with tactile sensors (i.e., the iCub humanoid robot). The experiments show that the algorithm provides accurate and reliable localization even with a low number of particles and, hence, is compatible with real-time requirements.