An Application of Evidential Networks to Threat Assessment

Decision makers operating in modern defence theatres need to comprehend and reason with huge quantities of potentially uncertain and imprecise data in a timely fashion. An automatic information fusion system is developed which aims at supporting a commander's decision making by providing a threat assessment, 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 by a network of entities and relationships between them, while the uncertainties in the relationships are represented by belief functions as defined in the theory of evidence. To support the implementation of the threat assessment functionality, an efficient valuation-based reasoning scheme, referred to as an evidential network, is developed. To reduce computational overheads, the scheme performs local computations in the network by applying an inward propagation algorithm to the underlying binary join 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 binary join tree.     

Performance measure for Markovian switching systems using best-fitting Gaussian distributions

This paper considers the theoretical posterior Cramer-Rao lower bound (PCRLB) for the case of tracking a manoeuvring target with Markovian switching dynamics. In a recent article [2] it was proposed to calculate the PCRLB conditional on the manoeuvre sequence and then determine the bound as a weighted average, giving an unconditional PCRLB. However, we demonstrate that this approach can produce an overly optimistic lower bound, because the sequence of manoeuvres is implicitly assumed known. Motivated by this, we develop a general approach and derive a closed-form estimate of the PCRLB in the case of Markovian switching systems. The basis of the approach is to, at each time step, replace the multi-modal prior target probability density function (pdf) with a best-fitting Gaussian (BFG) approximation. We present a recursive formula for calculating the mean and covariance of this Gaussian distribution, and demonstrate how the covariance increases as a result of the potential manoeuvres. We are then able to calculate the PCRLB for this BFG model using an existing Riccati-like recursion. Because of the BFG approximation, we are no longer guaranteed a bound and so we refer to our estimate as an "error performance measure" rather than a bound. The presented approach is applied both to filtering and smoothing cases. The simulation results indicate a very close agreement between the proposed performance measure and the error performance of an interacting multiple model estimator.     

Target classification approach based on the belief function theory

A theoretical framework is presented for target classification based on the belief theory on the continuous space. The proposed approach is applicable when class-conditioned densities of feature/attribute measurements are known only partially, as subjective models of a potential "betting" behaviour. Prior class probabilities may also be unknown. Numerical examples are provided to illustrate how the proposed approach is more cautious in decision making and produces very different results from those obtained using the Bayesian classifier.     

Tracking a ballistic target: comparison of several nonlinear filters

This paper studies the problem of tracking a ballistic object in the reentry phase by processing radar measurements. A suitable (highly nonlinear) model of target motion is developed and the theoretical Cramer-Rao lower bounds (CRLB) of estimation error are derived. The estimation performance (error mean and standard deviation; consistency test) of the following nonlinear filters is compared: the extended Kalman filter (EKF), the. statistical linearization, the particle filtering, and the unscented Kalman filter (UKF). The simulation results favor the EKF; it combines the statistical efficiency with a modest computational load. This conclusion is valid when the target ballistic coefficient is a priori known.