Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Generic particle filters <s> An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples, which are updated and propagated by the algorithm. The method is not restricted by assumptions of linear- ity or Gaussian noise: it may be applied to any state transition or measurement model. A simula- tion example of the bearings only tracking problem is presented. This simulation includes schemes for improving the efficiency of the basic algorithm. For this example, the performance of the bootstrap filter is greatly superior to the standard extended Kalman filter. <s> BIB001 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Generic particle filters <s> A lift loader includes a substantially rectangular platform or carrier having each of its four corners connected, by a ball joint, to a respective endless chain, with the chains being trained around sprockets rotatably mounted on a supporting frame including an upper section adjustable vertically relatively to a lower section. The chains are in two sets, each including a pair of laterally spaced endless chains, and each set of chains is trained around a respective set of pairs of laterally spaced sprockets. A motor drives all four endless chains in synchronism with each other along an endless path including a carrier lifting and lowering run, a carrier return run and a pair of vertically spaced horizontal runs. A goods loading station is provided at one end of one horizontal run and a goods discharge station is provided at the opposite end of the other horizontal run. Each carrier is longitudinally flexible and includes a pair of laterally spaced link chains comprising support links articulatedly interconnected by intermediate links, transversely extending juxtaposed support plates each secured on a respective pair of support links, and keeper links insertable between adjacent support links to prevent relative pivoting of the support plates, the keeper links being spring biased to retracted positions. Adjacent the goods loading and discharge stations, the then flexible carrier is convexly curved about support rollers, "opening" the support links, and guide rails engage the keeper links as the carrier reaches the goods loading station to insert the keeper links between the then "open" support links to prevent the support links from "closing" whereby to maintain the carrier with a horizontally planar orientation during its travel along the lifting and lowering run. As the carrier passes the goods discharge station, the support links again "open" providing for retraction of the spring biased keeper links so that the carrier is again flexible during its passage along the return run. Chain take-up means are provided to compensate the endless chains for any adjustment in the relative height of the supporting frame. <s> BIB002 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Generic particle filters <s> Recent developments have demonstrated that particle filtering is an emerging and powerful methodology, using Monte Carlo methods, for sequential signal processing with a wide range of applications in science and engineering. It has captured the attention of many researchers in various communities, including those of signal processing, statistics and econometrics. Based on the concept of sequential importance sampling and the use of Bayesian theory, particle filtering is particularly useful in dealing with difficult nonlinear and non-Gaussian problems. The underlying principle of the methodology is the approximation of relevant distributions with random measures composed of particles (samples from the space of the unknowns) and their associated weights. First, we present a brief review of particle filtering theory; and then we show how it can be used for resolving many problems in wireless communications. We demonstrate its application to blind equalization, blind detection over flat fading channels, multiuser detection, and estimation and detection of space-time codes in fading channels. <s> BIB003 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Generic particle filters <s> Collectively moving object clusters are of particular interest in certain applications and have to be tracked as separate aggregated entities consisting of an unknown number of individuals. Tracking of convoys or large vehicles in wide area ground surveillance are practically important examples (GMTI: Ground Moving Target Indicator). In standard tracking algorithms, the objects of interest are usually considered as point source objects; i. e. compared to the sensor resolution their spatial extension is neglected. Due to the increasing resolution capabilities of modern sensors, however, different scattering centers of an extended object cam cause distinct detections. In this sense also collectively moving object groups can be considered as extended objects. Due to the resulting data association and resolution conflicts. any attempt of tracking individual objects within the group is no longer reasonable. In this paper ellipsoidal object extensions are modeled by random matrices, which are treated as additional state variables to be estimated. An important aspect is the incorporation of context information into the Bayesian data processing formalism. We here consider kinematical constraints such as road maps and sensor specific characteristics such as Doppler-blindness. <s> BIB004 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Generic particle filters <s> In algorithms for tracking and sensor data fusion the targets to be observed are usually considered as point source objects; i.e., compared with the sensor resolution their extension is neglected. Due to the increasing resolution capabilities of modern sensors, however, this assumption is often no longer valid as different scattering centers of an object can cause distinct detections when passing the signal processing chain. Examples of extended targets are found in short-range applications (littoral surveillance, autonomous weapons, or robotics). A collectively moving target group can also be considered as an extended target. This point of view is the more appropriate, the smaller the mutual distances between the individual targets are. Due to the resulting data association and resolution conflicts any attempt of tracking the individual objects within the group seems to be no longer reasonable. With simulated sensor data produced by a partly unresolvable aircraft formation the addressed phenomena are illustrated and an approximate Bayesian solution to the resulting tracking problem is proposed. Ellipsoidal object extensions are modeled by random matrices, which are treated as additional state variables to be estimated or tracked. We expect that the resulting tracking algorithms are also relevant for tracking large, collectively moving target swarms. <s> BIB005 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Generic particle filters <s> Optimal estimation problems for non-linear non-Gaussian state-space models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. recursively as observations become available, and are now routinely used in fields as diverse as computer vision, econometrics, robotics and navigation. The objective of this tutorial is to provide a complete, up-to-date survey of this field as of 2008. Basic and advanced particle methods for filtering as well as smoothing are presented. <s> BIB006 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Generic particle filters <s> The particle filter (PF) was introduced in 1993 as a numerical approximation to the nonlinear Bayesian filtering problem, and there is today a rather mature theory as well as a number of successful applications described in literature. This tutorial serves two purposes: to survey the part of the theory that is most important for applications and to survey a number of illustrative positioning applications from which conclusions relevant for the theory can be drawn. The theory part first surveys the nonlinear filtering problem and then describes the general PF algorithm in relation to classical solutions based on the extended Kalman filter (EKF) and the point mass filter (PMF). Tuning options, design alternatives, and user guidelines are described, and potential computational bottlenecks are identified and remedies suggested. Finally, the marginalized (or Rao-Blackwellized) PF is overviewed as a general framework for applying the PF to complex systems. The application part is more or less a stand-alone tutorial without equations that does not require any background knowledge in statistics or nonlinear filtering. It describes a number of related positioning applications where geographical information systems provide a nonlinear measurement and where it should be obvious that classical approaches based on Kalman filters (KFs) would have poor performance. All applications are based on real data and several of them come from real-time implementations. This part also provides complete code examples. <s> BIB007 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Generic particle filters <s> The task of tracking extended objects or (partly) unresolvable group targets raises new challenges for both data association and track maintenance. Extended objects may give rise to more than one detection per opportunity where the scattering centers may vary from scan to scan. On the other end, group targets (i. e., a number of closely spaced targets moving in a coordinated fashion) often will not cause as many detections as there are individual targets in the group due to limited sensor resolution capabilities. In both cases, tracking and data association under the one target-one detection assumption are no longer applicable. This paper deals with the problem of maintaining a track for an extended object or group target with varying number of detections. Herein, object extension is represented by a random symmetric positive definite matrix. A recently published Bayesian approach to tackling this problem is analyzed and discussed. From there, a new approach is derived that is expected to overcome some of the weaknesses the Bayesian approach suffers from in certain applications. <s> BIB008
The aim of SMC methods, known also as particle filters BIB001 BIB002 BIB006 BIB007  BIB003  is to represent with "particles" the posterior state probability density function given the sensor measurements, p(x k |Z 0:k ), where Z 0:k = {z 0 , . . . , z k } is the observation history up to time k. Two major stages can be distinguished: prediction and update. During prediction, each particle (point mass representation of the probability density) is modified according to the state model, including the addition of random noise in order to simulate the effect of the noise on the state. In the measurement update stage, each particle's weight is re-evaluated based on the new data. Hence, during the prediction step the "cloud of particles" is usually spread/expanded due to the system noise, whereas the measurement update step contributes particles to concentrate around the system states. Hence, the weighted particles {x are propagated through the motion model (1) and updated next upon the measurement arrival, based on the measurement equation (2) . An inherent problem with particle filters (PFs) is degeneracy, the case when only one particle has a significant weight and the others are close to zero. The sampling importance resampling (SIR) SMC avoids the degeneracy by adding an extra resampling step. An estimate of the measure of degeneracy at time k is given as BIB002 . If the number N eff of efficient particles is below a user defined threshold N threshold , the resampling procedure introduces variety in the particles, and can help to avoid degeneracy by eliminating particles with small weights and replicating particles with larger weights. The algorithm of the generic PF is summarized in Table 1 . The estimate of the variable of interest is obtained by a weighted sum of particles. Table 1 Generic particle filter algorithm. [{x  Different proposal distributions have been used in the SMC framework -the most common transition prior or more advanced priors using the latest measurements, MCMC steps and others such as conjugate priors (e.g. inverse Wishart distribution BIB004 BIB005 BIB008 