Emmanuel Delande

Regional Variance for Multi-Object Filtering

Recent progress in multi-object filtering has led to algorithms that compute the first-order moment of multi-object distributions based on sensor measurements. The number of targets in arbitrarily selected regions can be estimated using the first-order moment. In this work, we introduce explicit formulae for the computation of the second-order statistic on the target number. The proposed concept of regional variance quantifies the level of confidence on target number estimates in arbitrary regions and facilitates information-based decisions. We provide algorithms for its computation for the probability hypothesis density (PHD) and the cardinalized probability hypothesis density (CPHD) filters. We demonstrate the behaviour of the regional statistics through simulation examples.

Performance metric in closed-loop sensor management for stochastic populations

Methods for sensor control are crucial for modern surveillance and sensing systems to enable efficient allocation and prioritisation of resources. The framework of partially observed Markov decision processes enables decisions to be made based on data received by the sensors within an information-theoretic context. This work addresses the problem of closed-loop sensor management in a multi-target surveillance context where each target is assumed to move independently of other targets. Analytic expressions of the information gain are obtained, for a class of exact multi-target tracking filters are obtained and based on the Rényi divergence. The proposed method is sufficiently general to address a broad range of sensor management problems through the application-specific reward function defined by the operator.

PHD filtering with localised target number variance

Mahler’s Probability Hypothesis Density (PHD filter), proposed in 2000, addresses the challenges of the multipletarget detection and tracking problem by propagating a mean density of the targets in any region of the state space. However, when retrieving some local evidence on the target presence becomes a critical component of a larger process - e.g. for sensor management purposes - the local target number is insufficient unless some confidence on the estimation of the number of targets can be provided as well. In this paper, we propose a first implementation of a PHD filter that also includes an estimation of localised variance in the target number following each update step; we then illustrate the advantage of the PHD filter + variance on simulated data from a multiple-target scenario.

Joint estimation of telescope drift and space object tracking

With the proliferation of low-cost CCD-based sensors used on telescopes by amateur astronomers, there is potential to exploit these within an infrastructure for space surveillance. Observations may be corrupted by an undesirable drift of the telescope due to mount jittering and uncompensated diurnal motion of stars. This work presents an approach for drift compensation based on a joint estimation of the sensor drift and the states of the objects and stars observed by the telescope. It exploits a recent development in multi-object estimation, known as the single-cluster Probability Hypothesis Density filter, that was designed for group tracking. The sensor drift is obtained by estimating the collective motion of the stars, which is in turn used to correct the estimation of moving objects. The proposed method is illustrated on simulated and real data.

Sensor Management with Regional Statistics for the PHD Filter

This paper investigates a sensor management scheme that aims at minimising the regional variance in the number of objects present in regions of interest whilst performing multi-target filtering with the PHD filter. The experiments are conducted in a simulated environment with groups of targets moving through a scene in order to inspect the behaviour of the manager. The results demonstrate that computing the variance in the number of objects in different regions provides a viable means of increasing situational awareness where complete coverage is not possible. A discussion follows, highlighting the limitations of the PHD filter and discussing the applicability of the proposed method to alternative available approaches in multi-object filtering.

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 multitarget 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 (SO-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 modeling choices than the PHD filter, and its computational cost is significantly lower compared to the CPHD filter. This 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 multiobject 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.

The CPHD Filter With Target Spawning

In its classical form, the cardinalized probability hypothesis density (CPHD) filter does not model the appearance of new targets through spawning, yet there are applications for which spawning models more appropriately account for newborn objects when compared to spontaneous birth models. In this paper, we propose a principled derivation of the CPHD filter prediction step including spontaneous birth and spawning. A Gaussian Mixture implementation of the CPHD filter with spawning is then presented, illustrated with three applicable spawning models on a simulated scenario involving two parent targets spawning a total of five objects.

A Tractable Forward– Backward CPHD Smoother

To circumvent the intractability of the usual Cardinalized Probability Hypothesis Density (CPHD) smoother, we present an approximate scheme where the population of targets born until and after the starting time of the smoothing are estimated separately and where smoothing is only applied to the estimate of the former population. The approach is illustrated through the implementation of a tractable approximation of the usual CPHD smoother.

A spherical co-ordinate space parameterisation for orbit estimation

An interesting challenge in orbital estimation problems for space surveillance using optical sensors is that, since both the orbital mechanics and the sensor observation process are non-linear, the standard filtering solutions such as Kalman filters are inapplicable and lead to divergent results. Naïve particle filtering solutions also fail since they require many particles to accurately represent the posterior distribution. However, since the sensor observation noise is modelled as a multivariate Gaussian distribution, it may be expected that the same single-object probability distributions, once projected into the augmented sensor space (a full spherical frame centred on the sensor), assume a simpler form that can be approximated by a multivariate Gaussian distribution. In this paper, a sequential Monte Carlo filter is proposed for the orbital object estimation problem, which exploits the structure of the measurement likelihood probability by introducing a proposal distribution based on a linear Kalman filter update.

Novel Multi-Object Filtering Approach for Space Situational Awareness

Surveillance activities with ground-based assets in the context of space situational awareness are particularly challenging. The observation process is indeed hindered by short observation arcs, li...