On Undetected Error Probability of Binary Matrix Ensembles

In this paper, an analysis of the undetected error probability of ensembles of binary matrices is presented. The ensemble called the Bernoulli ensemble whose members are considered as matrices generated from i.i.d. Bernoulli source is mainly considered here. The main contributions of this work are (i) derivation of the error exponent of the average undetected error probability and (ii) closed form expressions for the variance of the undetected error probability. It is shown that the behavior of the exponent for a sparse ensemble is somewhat different from that for a dense ensemble. Furthermore, as a byproduct of the proof of the variance formula, simple covariance formula of the weight distribution is derived.Comment: 9 pages, a part of the paper was submitted to ISIT 200

A second-order PHD filter with mean and variance in target number

The Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filters are popular solutions to the multi-target tracking problem due to their low complexity and ability to estimate the number and states of targets in cluttered environments. The PHD filter propagates the first-order moment (i.e. mean) of the number of targets while the CPHD propagates the cardinality distribution in the number of targets, albeit for a greater computational cost. Introducing the Panjer point process, this paper proposes a second-order PHD filter, propagating the second-order moment (i.e. variance) of the number of targets alongside its mean. The resulting algorithm is more versatile in the modelling choices than the PHD filter, and its computational cost is significantly lower compared to the CPHD filter. The paper compares the three filters in statistical simulations which demonstrate that the proposed filter reacts more quickly to changes in the number of targets, i.e., target births and target deaths, than the CPHD filter. In addition, a new statistic for multi-object filters is introduced in order to study the correlation between the estimated number of targets in different regions of the state space, and propose a quantitative analysis of the spooky effect for the three filters

Extended Object Tracking: Introduction, Overview and Applications

This article provides an elaborate overview of current research in extended object tracking. We provide a clear definition of the extended object tracking problem and discuss its delimitation to other types of object tracking. Next, different aspects of extended object modelling are extensively discussed. Subsequently, we give a tutorial introduction to two basic and well used extended object tracking approaches - the random matrix approach and the Kalman filter-based approach for star-convex shapes. The next part treats the tracking of multiple extended objects and elaborates how the large number of feasible association hypotheses can be tackled using both Random Finite Set (RFS) and Non-RFS multi-object trackers. The article concludes with a summary of current applications, where four example applications involving camera, X-band radar, light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are highlighted.Comment: 30 pages, 19 figure

Assessment of Response Surface Models using Independent Confirmation Point Analysis

This paper highlights various advantages that confirmation-point residuals have over conventional model design-point residuals in assessing the adequacy of a response surface model fitted by regression techniques to a sample of experimental data. Particular advantages are highlighted for the case of design matrices that may be ill-conditioned for a given sample of data. The impact of both aleatory and epistemological uncertainty in response model adequacy assessments is considered