Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> 23. Stochastic Geometry and its Applications. By D. Stoyan, W. S. Kendall and J. Mecke. ISBN 0 471 90519 4. Wiley, 1987. 345p. £23.50. (Wiley Series in Probability and Mathematical Statistics. A co‐production with Akademie‐Verlag, GDR.) <s> BIB001 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT. <s> BIB002 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> This tutorial summarizes the motivations, concepts, techniques, and applications of finite-set statistics (FISST), a system-level, "top-down" direct generalization of ordinary single-sensor, single-target engineering statistics to the multisensor, multitarget realm. FISST provides powerful new conceptual and computational methods for dealing with multisensor, multitarget, and multi-evidence data fusion problems. The paper begins with a broad-brush overview of the basic concepts of FISST. It describes how conventional single-sensor, single-target formal Bayesian modeling is carefully extended to general data fusion problems. We examine a simple example: joint detection and tracking of a possibly non-existent maneuvering target in heavy clutter. The tutorial concludes with a commentary on certain criticisms of FISST. <s> BIB003 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> Random finite sets (RFSs) are natural representations of multitarget states and observations that allow multisensor multitarget filtering to fit in the unifying random set framework for data fusion. Although the foundation has been established in the form of finite set statistics (FISST), its relationship to conventional probability is not clear. Furthermore, optimal Bayesian multitarget filtering is not yet practical due to the inherent computational hurdle. Even the probability hypothesis density (PHD) filter, which propagates only the first moment (or PHD) instead of the full multitarget posterior, still involves multiple integrals with no closed forms in general. This article establishes the relationship between FISST and conventional probability that leads to the development of a sequential Monte Carlo (SMC) multitarget filter. In addition, an SMC implementation of the PHD filter is proposed and demonstrated on a number of simulated scenarios. Both of the proposed filters are suitable for problems involving nonlinear nonGaussian dynamics. Convergence results for these filters are also established. <s> BIB004 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> A new recursive algorithm is proposed for jointly estimating the time-varying number of targets and their states from a sequence of observation sets in the presence of data association uncertainty, detection uncertainty, noise, and false alarms. The approach involves modelling the respective collections of targets and measurements as random finite sets and applying the probability hypothesis density (PHD) recursion to propagate the posterior intensity, which is a first-order statistic of the random finite set of targets, in time. At present, there is no closed-form solution to the PHD recursion. This paper shows that under linear, Gaussian assumptions on the target dynamics and birth process, the posterior intensity at any time step is a Gaussian mixture. More importantly, closed-form recursions for propagating the means, covariances, and weights of the constituent Gaussian components of the posterior intensity are derived. The proposed algorithm combines these recursions with a strategy for managing the number of Gaussian components to increase efficiency. This algorithm is extended to accommodate mildly nonlinear target dynamics using approximation strategies from the extended and unscented Kalman filters <s> BIB005 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> This comprehensive resource provides you with an in-depth understanding of finite-set statistics (FISST) - a recently developed method which unifies much of information fusion under a single probabilistic, in fact Bayesian, paradigm. The book helps you master FISST concepts, techniques, and algorithms, so you can use FISST to address real-world challenges in the field. You learn how to model, fuse, and process highly disparate information sources, and detect and track non-cooperative individual/platform groups and conventional non-cooperative targets. You find a rigorous Bayesian unification for many aspects of expert systems theory. Moreover, the book presents systematic integral and differential calculus for multisource-multitarget problems, providing a methodology for devising rigorous new techniques. This accessible and detailed book is supported with over 3,000 equations, 90 clear examples, 70 explanatory figures, and 60 exercises with solutions. <s> BIB006 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of this filter based on propagation of a first-order multitarget moment called the probability hypothesis density (PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which remains first-order in the states of individual targets, but which is higher-order in target number. In this paper we show that this is indeed possible. We derive a closed-form cardinalized PHD (CPHD) filter, which propagates not only the PHD but also the entire probability distribution on target number. <s> BIB007 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> The Gaussian mixture probability hypothesis density (PHD) filter was proposed recently for jointly estimating the time-varying number of targets and their states from a sequence of sets of observations without the need for measurement-to-track data association. It was shown that, under linear-Gaussian assumptions, the posterior intensity at any point in time is a Gaussian mixture. This paper proves uniform convergence of the errors in the algorithm and provides error bounds for the pruning and merging stages. In addition, uniform convergence results for the extended Kalman PHD Filter are given, and the unscented Kalman PHD Filter implementation is discussed <s> BIB008 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> A multisensor multitarget intensity filter is derived for N sensors. The multitarget process is assumed to be a Poisson point process, as are the sensor measurement sets. The sensor data are pooled, but sensor labels are retained. The likelihood function of the pooled data is obtained via the Poisson point process models. The Bayes information updated point process is not Poisson, but it is shown that all its single target marginal probability densities are identical. The Bayes posterior density is approximated by the product of its marginal densities. The marginal single target density is scaled to obtain the intensity of the Poisson point process approximation. The fused multisensor multitarget intensity filter is the average of the sensor intensity filters, provided sensor coverages are identical. The filter for non-identical sensor coverages is also described. <s> BIB009 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> This paper presents a novel and mathematically rigorous Bayes' recursion for tracking a target that generates multiple measurements with state dependent sensor field of view and clutter. Our Bayesian formulation is mathematically well-founded due to our use of a consistent likelihood function derived from random finite set theory. It is established that under certain assumptions, the proposed Bayes' recursion reduces to the cardinalized probability hypothesis density (CPHD) recursion for a single target. A particle implementation of the proposed recursion is given. Under linear Gaussian and constant sensor field of view assumptions, an exact closed-form solution to the proposed recursion is derived, and efficient implementations are given. Extensions of the closed-form recursion to accommodate mild nonlinearities are also given using linearization and unscented transforms. <s> BIB010 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> The probability hypothesis density (PHD) and cardinalized PHD (CPHD) filters were introduced in 2000 and 2006, respectively, as approximations of the full multitarget Bayes detection and tracking filter. Both filters are based on the “standard” multitarget measurement model that underlies most multitarget tracking theory. This paper is one of a series of theoretical studies that address PHD and CPHD filters for nonstandard multitarget measurement models. In this paper I derive the measurement-update equations for a PHD filter that presumes a Poisson model for extended targets due to Gilholm, Godsill, Maskell, and Salmond. <s> BIB011 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> It is shown analytically that the multitarget multiBernoulli (MeMBer) recursion, proposed by Mahler, has a significant bias in the number of targets. To reduce the cardinality bias, a novel multiBernoulli approximation to the multi-target Bayes recursion is derived. Under the same assumptions as the MeMBer recursion, the proposed recursion is unbiased. In addition, a sequential Monte Carlo (SMC) implementation (for generic models) and a Gaussian mixture (GM) implementation (for linear Gaussian models) are proposed. The latter is also extended to accommodate mildly nonlinear models by linearization and the unscented transform. <s> BIB012 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> Poisson Point Processes provides an overview of non-homogeneous and multidimensional Poisson point processes and their numerous applications, written particularly for non-specialists. Readers will find constructive mathematical methods, and applications ranging from emission and transmission computed tomography to multiple target tracking and distributed sensor detection, all written from an engineering perspective. <s> BIB013 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> Recent research into multi-object filtering for non-standard targets introduced alternative approaches for target group representation. In these approaches a measurement model (likelihood) was suggested that led to a representation of the measurements as a spatial point process, namely a Poisson point process. In this paper we take a more traditional approach to extended target tracking. We assume a 'standard' measurement model (at most one measurement generated from a target point), but represent the target group (extended targets) as a spatial cluster process, in particular an independent cluster process with a fixed distribution on the component (daughter) process. With this assumption we are able to derive approximate measurement-update equations for the first order moment density of the extended object Bayes filter in a number of scenarios. Such approximations are Bayes optimal and provide estimates for the number of clusters (extended targets) and their locations. <s> BIB014 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> In most of the existing probability hypothesis density (PHD) filters, the clutter is modeled as a Poisson random finite set (RFS) with a known intensity. The clutter intensity is characterized as a product of the average number of clutter (false alarm) points per scan and the probability density of clutter spatial distribution. The PHD filter is generalized to the problem of multi-target tracking (MTT) in clutter with an unknown intensity. In the proposed approach, the unknown clutter intensity is first estimated for the PHD filter. Estimation of the clutter intensity involves the estimation of the average clutter number per scan and the estimation of the clutter density. The clutter density is estimated as finite mixture models (FMM) via either expectation maximum (EM) or Markov chain Monte Carlo (MCMC) algorithm. Then, the estimated intensity is used directly in the PHD filter to perform multi-target detecting and tracking. Monte Carlo (MC) simulation results show that the proposed approach outperforms the naive PHD filter of assuming uniform clutter distribution significantly especially when the nominal clutter model is obviously different from the ground truth. <s> BIB015 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> In a previous conference paper the first author addressed the problem of devising CPHD and PHD filters ::: that are capable of multitarget detection and tracking in unknown, dynamically changing clutter. That paper ::: assumed that the clutter process is Poisson with an intensity function that is a finite mixture with unknown ::: parameters. The measurement-update equations for these CPHD/PHD filters involved combinatorial sums over ::: all partitions of the current measurement-set. This paper describes an approach that avoids combinatorial sums ::: and is therefore potentially computationally tractable. Clutter is assumed to be a binomial i.i.d. cluster process ::: with unknown parameters. Given this, three different and successively more tractable CPHD/PHD filters are ::: derived, all capable of multitarget track-before-detect capability. The first assumes that the entire intensity ::: function of the clutter process is unknown. The second and third assume that the clutter spatial distribution is ::: known but that the clutter rate (number of clutter returns per scan) is unknown. <s> BIB016 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> In this paper, we describe models and algorithms for detection and tracking of group and individual targets. We develop two novel group dynamical models within a continuous time setting using stochastic differential equations (SDE) that aim to mimic behavioural properties of groups. We also describe a possible way of modeling interactions between closely spaced targets using repulsive forces. These can be combined with a group structure transition model to create realistic evolving group models. We use a Markov chain Monte Carlo (MCMC)-particles algorithm to perform sequential inference. Computer simulations demonstrate the ability of the algorithm to detect and track targets within groups as well as to infer the correct group structure over time. The group tracking model is also applied to two sets of real ground moving target indicator (GMTI) radar data with group targets. The results show significant improvement in tracking accuracy over tracking without group models. <s> BIB017 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> In Bayesian multi-target filtering we have to contend with two notable sources of uncertainty, clutter and detection. Knowledge of parameters such as clutter rate and detection profile are of critical importance in multi-target filters such as the probability hypothesis density (PHD) and Cardinalized PHD (CPHD) filters. Naive application of the CPHD (and PHD) filter with mismatches in clutter and detection model parameters results in biased estimates. In this paper we show how to use the CPHD (and PHD) filter in unknown clutter rate and detection profile. <s> BIB018 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> Poisson point processes (PPP's) are very useful theoretical models for diverse applications. One of those is multi-target tracking of an unknown number of targets, leading to the intensity filter (iFilter) as a generalization of the probability hypothesis density (PHD) filter. This article develops a sequential Monte Carlo (SMC) implementation of the iFilter. In theory it was shown that the iFilter can estimate a clutter model from the measurements and thus does not need it as a-priori knowledge, like the PHD filter does. Our studies show that this property holds not only in simulations but also in real world applications. In addition it can be shown, that the performance of the PHD filter decreases substantially if the a-priori knowledge of the clutter intensity is chosen incorrectly. <s> BIB019 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> In many group target tracking scenarios, a collection of targets move in a correlated manner as part of a formation, such as a convoy of vehicles. The focus of this paper is in the estimation of the evolution over time of a single-group of targets, referred to as a single-cluster, based on a sequence of partial observation sets. Based on Finite Set Statistics, the paper presents a first-moment recursion for a single-group filter and an analytic solution under linear-Gaussian assumptions. The method is demonstrated on simulated data in a cluttered environment. <s> BIB020 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> We comment on the errors in the formulation of Theorem 1 given in Extended Target Tracking Using a Gaussian-Mixture PHD Filter by K. Granstrom, C. Lundquist, and U. Orguner, and give a correct formulation. <s> BIB021 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> The standard formulation of the probability hypothesis density (PHD) and cardinalised PHD (CPHD) filters assumes that the target birth intensity is known a priori. In situations where the targets can appear anywhere in the surveillance volume this is clearly inefficient, since the target birth intensity needs to cover the entire state space. This paper presents a new extension of the PHD and CPHD filters, which distinguishes between the persistent and the newborn targets. This extension enables us to adaptively design the target birth intensity at each scan using the received measurements. Sequential Monte-Carlo (SMC) implementations of the resulting PHD and CPHD filters are presented and their performance studied numerically. The proposed measurement-driven birth intensity improves the estimation accuracy of both the number of targets and their spatial distribution. <s> BIB022 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> Bernoulli filters are a class of exact Bayesian filters for non-linear/non-Gaussian recursive estimation of dynamic systems, recently emerged from the random set theoretical framework. The common feature of Bernoulli filters is that they are designed for stochastic dynamic systems which randomly switch on and off. The applications are primarily in target tracking, where the switching process models target appearance or disappearance from the surveillance volume. The concept, however, is applicable to a range of dynamic phenomena, such as epidemics, pollution, social trends, etc. Bernoulli filters in general have no analytic solution and are implemented as particle filters or Gaussian sum filters. This tutorial paper reviews the theory of Bernoulli filters as well as their implementation for different measurement models. The theory is backed up by applications in sensor networks, bearings-only tracking, passive radar/sonar surveillance, visual tracking, monitoring/prediction of an epidemic and tracking using natural language statements. More advanced topics of smoothing, multi-target detection/tracking, parameter estimation and sensor control are briefly reviewed with pointers for further reading. <s> BIB023 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> Multi-target tracking is a common problem with many applications. In most of these the expected number of targets is not known a priori, so that it has to be estimated from the measured data. Poisson point processes (PPPs) are a very useful theoretical model for diverse applications. One of those is multi-target tracking of an unknown number of targets, leading to the intensity filter (iFilter) and the probability hypothesis density (PHD) filter. This chapter presents a sequential Monte Carlo (SMC) implementation of the iFilter. In theory it was shown that the iFilter can estimate a clutter model from the measurements and thus does not need it as a priori knowledge, like the PHD filter does. Our studies show that this property holds not only in simulations but also in real world applications. In addition it can be shown that the performance of the PHD filter decreases substantially if the a priori knowledge of the clutter intensity is chosen incorrectly. <s> BIB024 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> In extended/group target tracking, where the extensions of the targets are estimated, target spawning and combination events might have significant implications on the extensions. This paper investigates target spawning and combination events for the case that the target extensions are modeled in a random matrix framework. The paper proposes functions that should be provided by the tracking filter in such a scenario. The results, which are obtained by a gamma Gaussian inverse Wishart implementation of an extended target probability hypothesis density filter, confirms that the proposed functions improve the performance of the tracking filter for spawning and combination events. <s> BIB025 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Group tracking using random finite sets <s> In Bayesian multi-target filtering knowledge of parameters such as clutter intensity and detection probability profile are of critical importance. Significant mismatches in clutter and detection model parameters results in biased estimates. In this paper we propose a multi-target filtering solution that can accommodate non-linear target models and an unknown non-homogeneous clutter and detection profile. Our solution is based on the multi-target multi-Bernoulli filter that adaptively learns non-homogeneous clutter intensity and detection probability while filtering. <s> BIB026
In the Bayesian estimation framework the states and measurements are treated as realizations of random variables. In the random sets statistics (RSS), known also as Finite Set Statistics (FISST)  the targets states and the measurements are considered as random sets with unknown numbers. The number of elements in a random finite set is called the set cardinality. The FISST provides an elegant framework for statistical solutions to the group tracking problems. The FISST affords to detect, identify, track and classify groups of targets. It is a natural framework to deal with interval, stochastic and data association uncertainties. The FISST avoids the direct data association and hence the combinatorial problems due to data association which is one of its major advantages. For group tracking a hierarchical layer of objects is envisaged, with the lowest layer being the individual target. Such a randomset filtering approach for tracking groups of targets was proposed in  . In conventional tracking, the target state space is treated as a hidden layer, where the observation space is visible. For group tracking, the group targets are further treated as a doubly or twicehidden layer, and each group target is a random collection of some of the targets in the first hidden layer. In FISST the PHD has the same meaning as the intensity function of a Poisson point process. It is the first moment in point process theory BIB006 BIB007  BIB004  BIB023 . The PHD is also regarded as the first-order statistical moment, or expectation, of the multitarget posterior density. Similarly to the Kalman filter where the mean and variance of the posterior state are recursively propagated, the PHD filter propagates the PHD function by using similar steps prediction and update, however by means of a different and more complicated procedure. The integral over the PHD in a region gives the expected number of targets in that region. Hence, the estimated states of the targets can be inferred from the peaks of the PHD. The number of objects belonging to groups varies in time and the number of measurements at each time step does not necessarily match the number of targets due to missed detections and clutter. This is the rationale behind considering the states and the measurements as random finite sets. A random finite set  is simply a random variable which values are unordered random sets. The multi-target evolution and observation models are considered under the following assumptions: (i) Each target evolves and generates observations independently of one another; (ii) The birth random finite set and the surviving random finite sets are independent of each other; (iii) The clutter random finite set is of Poisson type and independent of target originated measurements; (iv) The prior and predicted multi-target sets are with a Poisson distribution. Instead of working with pdfs, the PHD filter updates recursively the intensities for the prediction and measurement update, respectively v k|k−1 and v k|k : (22) where f k|k−1 (X|ζ ) is the group transition density at time k, p S,k (ζ ) is the group survival probability and γ k (X) is the intensity of spontaneous birth. The update equation is given by Detected targets , (23) where g k (z k |X k ) is the group measurement likelihood, p D,k is the probability of group detection, and κ k (z k ) is the intensity of clutter measurements. The first part of (23) corresponds to non-detected targets and the second term of (23) to the detected targets. Practical implementations of the PHD filter include two main implementations: the SMC solutions BIB004 and Gaussian mixtures BIB005  BIB021 BIB008  . The SMC implementation of the PHD filter approximates the set integrals by propagating a large set of weighted particles over time. The sum of the weights of the particles represents the expected number of targets since the integral over the PHD is the expected number of targets. An improved SMC PHD approach is proposed in BIB022 which adapts the target birth intensity at each processing step using the received measurements. The alternative GM PHD implementation approximates the PHD with a mixture of Gaussian distributions and uses Kalman filters or their nonlinear variants such as Unscented Kalman filters BIB002 . Various approaches are proposed to deal with the unknown number of targets within each group, such as using the birthdeath model BIB017 and estimate the unknown number of targets within each group or the Cardinality PHD (CPHD) filter which estimates the number of targets jointly with the kinematic states. In BIB018 a step further is done where the cardinality number is estimated with the states, together with the clutter noise parameters and probability of detection. This is a general formulation affording to resolve state and parameter estimation problems simultaneously. The relation between the underlying group shape and entity concentrations is represented via intensity functions BIB006 . The intensity function indicates how entities are situated in the state space (i.e., the peaks correspond to the most dense regions in the state space). This is illustrated in Fig. 8 . The top left and middle figures show the intensity functions of two and three groups, respectively, depending on x and y coordinates of the group center. The middle row figures show the groups, represented by ellipses. The last row shows the intensity function in which each peak corresponds to a group. Group splitting and merging are illustrated in the right panels. These are reflected in the changes of the number of peaks of the intensity functions. In BIB009 BIB013 BIB019 BIB024 a different approach is proposed based on the Poisson Point Processes (PPPs). However, the algorithm in essence is similar to the PHD filter. FISST BIB006 BIB010 and cluster point processes  BIB001 are natural mathematical frameworks for analyzing group target motions and extended targets. In general, a cluster process is described as a superposition of point processes. The cluster centers can form parent point processes and their associated component points can form daughter point processes. This layering process can continue upwards, forming groups of groups. In principle such a formulation is general enough to deal with multiple layers of interactions. The multi-group multi-target multi-sensor density can then incorporate group dynamics and group likelihoods. While this is general, it will be a challenge to model the actual interactions between groups of groups. In BIB014 a first-moment approximation of group PHD filter is derived for group object tracking, which is similar to the original PHD filter for single targets. The target group is represented as a spatial cluster process, with the daughter process as an independent cluster process with a fixed distribution. In this group PHD filter, instead of using a typical Poisson observation process for the targets in a group, a more standard observation model of at most one measurement from a target is utilized. An analytical solution to a single group PHD filter is presented in BIB020 , under linear Gaussian assumptions. The RSS approach for extended objects BIB006 BIB011 and group targets modeling remains attractive due to the mathematical rigor offered by the framework. In  a box-PHD filter is developed and its computational efficiency shown compared with the PHD filter. However, producing suitable first-moment approximations for complex group target interactions and scenarios still continues to be a challenge BIB006  BIB025 . The parameters of the PHD filter such as probability of detection, survival probabilities and measurement noise parameters, can be estimated jointly with the object states as it is recently shown in BIB018 BIB015 . The work BIB018 is an important step in dealing with parameter uncertainties which are commonly subject to tuning in each application. Another important class of the FISS framework is represented by the multi-target multi-Bernoulli filters BIB003 BIB006 BIB023 BIB016 BIB012 BIB026 . Unlike the PHD and CPHD filters which propagate moments and cardinality distributions, the multi-Bernoulli filter propagates the parameters of a multi-Bernoulli distribution that approximate the posterior multi-target density BIB026 . An advantage of the multiBernoulli filter over the SMC PHD filter is that it does not require the additional clustering step for multi-target state estimation which the PHD filter has.