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EURASIP Journal on Applied Signal Processing 2004:15, 2239–2241c© 2004 Hindawi Publishing CorporationEditorialPetar M. Djuric´Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY 11794, USAEmail: djuric@ece.sunysb.eduSimon J. GodsillDepartment of Engineering, University of Cambridge, Cambridge CB2 1PZ, UKEmail: sjg@eng.cam.ac.ukArnaud DoucetDepartment of Engineering, University of Cambridge, Cambridge CB2 1PZ, UKEmail: ad2@eng.cam.ac.ukIn most problems of sequential signal processing, measuredor received data are processed in real time. Typically, the dataare modeled by state-space models with linear or nonlinearunknowns and noise sources that are assumed either Gaus-sian or non-Gaussian. When the models describing the dataare linear and the noise is Gaussian, the optimal solution isthe renowned Kalman filter. For models that deviate fromlinearity and Gaussianity, many diﬀerent methods exist, ofwhich the best known perhaps is the extended Kalman filter.About a decade ago, Gordon et al. published an article onnonlinear and non-Gaussian state estimation that capturedmuch attention of the signal processing community [1]. Thearticle introduced a method for sequential signal processingbased onMonte Carlo sampling and showed that the methodmay have profound potential. Not surprisingly, it has inciteda great deal of research, which has contributed to making se-quential signal processing by Monte Carlo methods one ofthe most prominent developments in statistical signal pro-cessing in the recent years.The underlying idea of the method is the approximationof posterior densities by discrete randommeasures. Themea-sures are composed of samples from the states of the un-knowns and of weights associated with the samples. The sam-ples are usually referred to as particles, and the process ofupdating the random measures with the arrival of new dataas particle filtering. One may view particle filtering as explo-ration of the space of unknowns with random grids whosenodes are the particles. With the acquisition of new data, therandom grids evolve and their nodes are assigned weightsto approximate optimally the desired densities. The assign-ment of new weights is carried out recursively and is basedon Bayesian importance sampling theory.The beginnings of particle filtering can be traced back tothe late 1940s and early 1950s, which were followed in the lastfifty years with sporadic outbreaks of intense activity [2]. Al-though its implementation is computationally intensive, thewidespread availability of fast computers and the amenabilityof the particle filtering methods for parallel implementationmake them very attractive for solving diﬃcult signal process-ing problems.The papers of the special issue may be arranged into fourgroups, that is, papers on (1) general theory, (2) applica-tions of particle filtering to target tracking, (3) applicationsof particle filtering to communications, and (4) applicationsof particle filtering to speech andmusic processing. In this is-sue, we do not have tutorials on particle filtering, and instead,we refer the reader to some recent references [3, 4, 5, 6].General theoryIn the first paper, “Global sampling for sequential fil-tering over discrete state space,” Cheung-Mon-Chan andMoulines study conditionally Gaussian linear state-spacemodels, which, when conditioned on a set of indicator vari-ables taking values in a finite set, become linear and Gaus-sian. In this paper, the authors propose a global sampling al-gorithm for such filters and compare them with other state-of-the-art implementations.Guo et al. in “Multilevel mixture Kalman filter” pro-pose a new Monte Carlo sampling scheme for implement-ing the mixture Kalman filter. The authors use a multilevelstructure of the space for the indicator variables and drawsamples in a multilevel fashion. They begin with samplingfrom the highest-level space and follow up by drawing sam-ples from associate subspaces from lower-level spaces. They2240 EURASIP Journal on Applied Signal Processingdemonstrate the method on examples fromwireless commu-nication.In the third paper, “Resampling algorithms for particlefilters: A computational complexity perspective,” Bolic´ et al.propose and analyze new resampling algorithms for particlefilters that are suitable for real-time implementation. By de-creasing the number of operations and memory access, thealgorithms reduce the complexity of both hardware and DSPrealization. The performance of the algorithms is evaluatedon particle filters applied to bearings-only tracking and jointdetection and estimation in wireless communications.In “A new class of particle filters for random dynamic sys-tems with unknown statistics,” Mı´guez et al. propose a newclass of particle filtering methods that do not assume explicitmathematical forms of the probability distributions of thenoise in the system. This implies simpler, more robust, andmore flexible particle filters than the standard particle filters.The performance of these filters is shown on autonomouspositioning of a vehicle in a 2-dimensional space.Finally, in “A particle filtering approach to change de-tection for nonlinear systems,” Azimi-Sadjadi and Krish-naprasad present a particle filtering method for change de-tection in stochastic systems with nonlinear dynamics basedon a statistic that allows for recursive computation of likeli-hood ratios. They use the method in an Inertial NavigationSystem/Global Positioning System application.Applications in communicationsIn “Particle filtering for joint symbol and code delay esti-mation in DS spread spectrum systems in multipath envi-ronment,” Punskaya et al. develop receivers based on severalalgorithms that involve both deterministic and randomizedschemes. They test their method against other deterministicand stochastic procedures by means of extensive simulations.In the second paper, “Particle filtering equalizationmethod for a satellite communication channel,” Se´ne´calet al. propose a particle filtering method for inline andblind equalization of satellite communication channels andrestoration of the transmitted messages. The performance ofthe algorithms is presented by bit error rates as functions ofsignal-to-noise ratio.Bertozzi et al. in “Channel tracking using particle filter-ing in unresolvable multipath environments,” propose a newtiming error detector for timing tracking loops of Rake re-ceivers in spread spectrum systems. In their scheme, the de-lays of each path of the frequency-selective channels are esti-mated jointly. Their simulation results demonstrate that theproposed scheme has better performance than the one basedon conventional early-late gate detectors in indoor scenarios.Applications to target trackingIn “Joint tracking of manoeuvring targets and classificationof their manoeuvrability,” by Maskell, semi-Markov modelsare used to describe the behavior of maneuvering targets. Theauthor proposes an architecture that allows particle filters tobe robust and eﬃcient when they jointly track and classifytargets. He also shows that with his approach, one can classifytargets on the basis of their maneuverability.In the other paper, “Bearings-only tracking of manoeu-vring targets using particle filters,” Arulampalam et al. inves-tigate the problem of bearings-only tracking of maneuveringtargets. They formulate the problem in the framework of amultiple-model tracking problem in jump Markov systemsand propose three diﬀerent particle filters. They conduct ex-tensive simulations and show that their filters outperform thetrackers based on standard interacting multiple models.Applications to speech andmusicIn “Time-varying noise estimation for speech enhancementand recognition using sequential Monte Carlo method,” Yaoand Lee develop particle filters for sequential estimation oftime-varying mean vectors of noise power in the log-spectraldomain, where the noise parameters evolve according to arandom walk model. The authors demonstrate the perfor-mance of the proposed filters in automated speech recogni-tion and speech enhancement, respectively.Hainsworth and Macleod in “Particle filtering applied tomusical tempo tracking” aim at estimating the time-varyingtempo process in musical audio analysis. They present twoalgorithms for generic beat tracking that can be used acrossa variety of musical styles. The authors have tested the algo-rithms on a large database and have discussed existing prob-lems and directions for further improvement of the currentmethods.In summary, this special issue provides some inter-esting theoretical developments in particle filtering theoryand novel applications in communications, tracking, andspeech/music signal processing. We hope that these paperswill not only be of immediate use to practitioners and the-oreticians but will also instigate further development in thefield. Lastly, we thank the authors for their contributions andthe reviewers for their valuable comments and criticism.Petar M. Djuric´Simon J. GodsillArnaud DoucetREFERENCES[1] N. J. Gordon, D. J. Salmond, and A. F. M. Smith, “Novel ap-proach to nonlinear/non-Gaussian Bayesian state estimation,”IEE Proceedings Part F: Radar and Signal Processing, vol. 140,no. 2, pp. 107–113, 1993.[2] J. S. Liu, Monte Carlo Strategies in Scientific Computing,Springer, New York, NY, USA, 2001.[3] A. Doucet, N. de Freitas, and N. Gordon, Eds., SequentialMonte Carlo Methods in Practice, Springer, New York, USA,2001.[4] A. Doucet, S. J. Godsill, and C. Andrieu, “On sequential MonteCarlo sampling methods for Bayesian filtering,” Stat. Comput.,vol. 10, no. 3, pp. 197–208, 2000.[5] P. M. Djuric´ and S. J. Godsill, Eds., “Special issue on MonteCarlo methods for statistical signal processing,” IEEE Trans.Signal Processing, vol. 50, no. 2, 2002.[6] P. M. Djuric´, J. H. Kotecha, J. Zhang, et al., “Particle filtering,”IEEE Signal ProcessingMagazine, vol. 20, no. 5, pp. 19–38, 2003.Editorial 2241Petar M. Djuric´ received his B.S. and M.S.degrees in electrical engineering from theUniversity of Belgrade in 1981 and 1986, re-spectively, and his Ph.D. degree in electricalengineering from the University of RhodeIsland in 1990. From 1981 to 1986, he was aResearch Associate with the Institute of Nu-clear Sciences, Vinca, Belgrade. Since 1990,he has been with Stony Brook University,where he is a Professor in the Department ofElectrical and Computer Engineering. He works in the area of sta-tistical signal processing, and his primary interests are in the theoryof modeling, detection, estimation, and time series analysis and itsapplication to a wide variety of disciplines including wireless com-munications and biomedicine.Simon J. Godsill is a Reader in statisti-cal signal processing in the Departmentof Engineering, Cambridge University. Heis an Associate Editor for IEEE Transac-tions on Signal Processing and the Jour-nal of Bayesian Analysis, and is a Mem-ber of IEEE Signal Processing Theory andMethods Committee. He has research inter-ests in Bayesian and statistical methods forsignal processing, Monte Carlo algorithmsfor Bayesian problems, modelling and enhancement of audio andmusical signals, tracking, and genomic signal processing. He haspublished extensively in journals, books, and conferences. He hascoedited in 2002 a special issue of IEEE Transactions on SignalProcessing on Monte Carlo methods in signal processing and or-ganized many conference sessions on related themes.Arnaud Doucet was born in France on the2nd of November 1970. He graduated fromInstitut National des Telecommunicationsin June 1993 and obtained his Ph.D. degreefrom Universite´ Paris-Sud Orsay in Decem-ber 1997. From January 1998 to February2001 he was a research associate in Cam-bridge University. From March 2001 to Au-gust 2002, he was a Senior Lecturer in theDepartment of Electrical Engineering, Mel-bourne University, Australia. Since September 2002, he has been aUniversity Lecturer in information engineering at Cambridge Uni-versity. His research interests include simulation-based methodsand their applications to Bayesian statistics and control.

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