Alessio Benavoli

Brief paper: Data-driven communication for state estimation with sensor networks

This paper deals with the problem of estimating the state of a discrete-time linear stochastic dynamical system on the basis of data collected from multiple sensors subject to a limitation on the communication rate from the sensors. More specifically, the attention is devoted to a centralized sensor network consisting of: (1) multiple remote nodes which collect measurements of the given system, compute state estimates at the full measurement rate and transmit data (either raw measurements or estimates) at a reduced communication rate; (2) a fusion node that, based on received data, provides an estimate of the system state at the full rate. Local data-driven transmission strategies are considered and issues related to the stability and performance of such strategies are investigated. Simulation results confirm the effectiveness of the proposed strategies.

Knowledge-based system for multi-target tracking in a littoral environment

The paper addresses how to efficiently exploit the knowledge-base (KB), e.g. environmental maps and characteristics of the targets, in order to gain improved performance in the tracking of multiple targets via measurements provided by a ship-borne radar operating in a littoral environment. In this scenario, the nonhomogeneity of the surveillance region makes the conventional tracking systems (not using the KB) very sensitive to false alarms and/or missed detections. It is demonstrated that an effective use of the KB can be exploited at various levels of the tracking algorithms so as to significantly reduce the number of false alarms, missed detections, and false tracks and improve true target track life. The KB is exploited at two different levels. First, some key parameters of the tracking system are made dependent upon the track location, e.g., sea, land, coast, meteo zones (i.e., zones affected by meteorological phenomena) etc. Second, modifications are introduced to cope with a priori identified regions nit hi high clutter density (e.g. littoral areas, roads, meteo zones etc.). To evaluate the behavior of the proposed knowledge-based tracking systems, extensive results are presented using both simulated and real radar data

Robust Filtering Through Coherent Lower Previsions

The classical filtering problem is re-examined to take into account imprecision in the knowledge about the probabilistic relationships involved. Imprecision is modeled in this paper by closed convex sets of probabilities. We derive a solution of the state estimation problem under such a framework that is very general: it can deal with any closed convex set of probability distributions used to characterize uncertainty in the prior, likelihood, and state transition models. This is made possible by formulating the theory directly in terms of coherent lower previsions, that is, of the lower envelopes of the expectations obtained from the set of distributions. The general solution is specialized to two particular classes of coherent lower previsions. The first consists of a family of Gaussian distributions whose means are only known to belong to an interval. The second is the so-called linear-vacuous mixture model, which is a family made of convex combinations of a known nominal distribution (e.g., a Gaussian) with arbitrary distributions. For the latter case, we empirically compare the proposed estimator with the Kalman filter. This shows that our solution is more robust to the presence of modelling errors in the system and that, hence, appears to be a more realistic approach than the Kalman filter in such a case.

An approach to threat assessment based on evidential networks

The paper develops an information fusion system that aims at supporting a commanders decision making by providing an assessment of threat, that is an estimate of the extent to which an enemy platform poses a threat based on evidence about its intent and capability. Threat is modelled in the framework of the valuation-based system (VBS), by a network of entities and relationships between them. The uncertainties in the relationships are represented by belief functions as defined in the theory of evidence. Hence the resulting network for reasoning is referred to as an evidential network. Local computations in the evidential network are carried out by inward propagation on the underlying joint binary tree. This allows the dynamic nature of the external evidence, which drives the evidential network, to be taken into account by recomputing only the affected paths in the joint binary tree.

Review: Fibonacci sequence, golden section, Kalman filter and optimal control

A connection between the Kalman filter and the Fibonacci sequence is developed. More precisely it is shown that, for a scalar random walk system in which the two noise sources (process and measurement noise) have equal variance, the Kalman filters estimate turns out to be a convex linear combination of the a priori estimate and of the measurements with coefficients suitably related to the Fibonacci numbers. It is also shown how, in this case, the steady-state Kalman gain as well as the predicted and filtered covariances are related to the golden ratio @f=(5+1)/2. Furthermore, it is shown that, for a generic scalar system, there exist values of its key parameters (i.e. system dynamics and ratio of process-to-measurement noise variances) for which the previous connection is preserved. Finally, by exploiting the duality principle between control and estimation, similar connections with the linear quadratic control problem are outlined.

Tracking of a Ballistic Missile with A-Priori Information

The paper addresses the problem of estimating the launch and impact points of a ballistic target from radar measurements. The problem has been faced under different hypotheses on the available prior knowledge. The proposed approach combines a nonlinear batch estimator with a recursive MM (multiple model) particle filter in order to attain the estimation goal. Extensive simulations assess the achievable estimation performance.

State estimation with remote sensors and intermittent transmissions

Abstract This paper deals with the problem of estimating the state of a discrete-time linear stochastic dynamical system on the basis of data collected from multiple sensors subject to a limitation on the communication rate from the remote sensor units. The optimal probabilistic measurement-independent strategy for deciding when to transmit estimates from each sensor is derived. Simulation results show that the derived strategy yields certain advantages in terms of worst-case time-averaged performance with respect to periodic strategies when coordination among sensors is not possible.

Hard-constrained versus soft-constrained parameter estimation

The paper aims at contrasting two different ways of incorporating a priori information in parameter estimation, i.e., hard-constrained and soft-constrained estimation. Hard-constrained estimation can be interpreted, in the Bayesian framework, as maximum a posteriori probability (MAP) estimation with uniform prior distribution over the constraining set, and amounts to a constrained least-squares (LS) optimization. Novel analytical results on the statistics of the hard-constrained estimator are presented for a linear regression model subject to lower and upper bounds on a single parameter. This analysis allows to quantify the mean squared error (MSE) reduction implied by constraints and to see how this depends on the size of the constraining set compared with the confidence regions of the unconstrained estimator. Contrastingly, soft-constrained estimation can be regarded as MAP estimation with Gaussian prior distribution and amounts to a less computationally demanding unconstrained LS optimization with a cost suitably modified by the mean and covariance of the Gaussian distribution. Results on the design of the prior covariance of the soft-constrained estimator for optimal MSE performance are also given. Finally, a practical case-study concerning a line fitting estimation problem is presented in order to validate the theoretical results derived in the paper as well as to compare the performance of the hard-constrained and soft-constrained approaches under different settings

Performance Measures and MHT for Tracking Move-Stop-Move Targets with MTI Sensors

We consider the problem of tracking ground-based vehicles with moving target indicator (MTI) sensors. MTI sensors can only detect a target if the magnitude of the range-rate exceeds the minimum detectable velocity, and as a result targets typically exhibit evasive move-stop-move (MSM) behavior in order to avoid detection. Further complexity is added by the fact that the environment is cluttered, resulting in both missed detections and spurious false measurements. A key problem is then to distinguish between a missed detection of a moving target and a lack of a detection due to the target stopping (or moving at low velocity). In this paper, we provide a novel framework for calculating performance measures (which are not necessarily bounds) for this problem. Our approach unifies state-of-the-art posterior Cramér-Rao lower bound (PCRLB) approaches for dealing with manoeuvring targets (namely, the best-fitting Gaussian approach) and cluttered environments (the measurement sequence conditioning approach). Our approach is also able to exploit the correlation between the number of measurements at each sampling time and the target motion model. Furthermore, we are able to show that established PCRLB methodologies are special cases of this unifying approach. We therefore provide a general technique for calculating performance bounds/measures for target tracking that can be applied to a broad range of problems. We also introduce a multiple hypothesis tracker (MHT) implementation for this problem. In simulations, the MHT is shown to accurately track the target, and provided that the probability of detection is close to unity, the new performance measure is an extremely accurate predictor of the localization performance of the MHT. If the probability of detection is lower, and except when employing a short scanback, the MHT performance is significantly better than the measure. In such cases the true limit of performance is the measure calculated by assuming the correct motion model, and data association hypotheses are known. The MHT filter is also shown to maintain track of the target in a high percentage of simulations, even with a scanback of just a few time steps. Therefore if track maintenance is the most important requirement, the employment of long scanbacks is not essential. We conclude that our PCRLB-like measure and MHT implementation provide effective approaches for performance prediction and target tracking, respectively, in the challenging MTI domain.

A probabilistic interpretation of set-membership filtering

Set-membership estimation is usually formulated in the context of set-valued calculus and no probabilistic calculations are necessary. In this paper, we show that set-membership estimation can be equivalently formulated in the probabilistic setting by employing sets of probability measures. Inference in set-membership estimation is thus carried out by computing expectations with respect to the updated set of probability measures P as in the probabilistic case. In particular, it is shown that inference can be performed by solving a particular semi-infinite linear programming problem, which is a special case of the truncated moment problem in which only the zero-th order moment is known (i.e., the support). By writing the dual of the above semi-infinite linear programming problem, it is shown that, if the nonlinearities in the measurement and process equations are polynomial and if the bounding sets for initial state, process and measurement noises are described by polynomial inequalities, then an approximation of this semi-infinite linear programming problem can efficiently be obtained by using the theory of sum-of-squares polynomial optimization. We then derive a smart greedy procedure to compute a polytopic outer-approximation of the true membership-set, by computing the minimum-volume polytope that outer-bounds the set that includes all the means computed with respect to P.