Pub Date : 2006-09-01DOI: 10.1109/NSSPW.2006.4378821
Gustaf Hendeby, R. Karlsson, F. Gustafsson, N. Gordon
Performance for filtering problems is usually measured using the second-order moment. For non-Gaussian applications, this measure is not always sufficient. In this paper, the Kull-back divergence is extensively used to compare estimated distributions. Several estimation techniques are compared, and methods with ability to express non-Gaussian posterior distributions are shown to give superior performance over classical second-order moment based estimators.
{"title":"Performance Issues in Non-Gaussian Filtering Problems","authors":"Gustaf Hendeby, R. Karlsson, F. Gustafsson, N. Gordon","doi":"10.1109/NSSPW.2006.4378821","DOIUrl":"https://doi.org/10.1109/NSSPW.2006.4378821","url":null,"abstract":"Performance for filtering problems is usually measured using the second-order moment. For non-Gaussian applications, this measure is not always sufficient. In this paper, the Kull-back divergence is extensively used to compare estimated distributions. Several estimation techniques are compared, and methods with ability to express non-Gaussian posterior distributions are shown to give superior performance over classical second-order moment based estimators.","PeriodicalId":388611,"journal":{"name":"2006 IEEE Nonlinear Statistical Signal Processing Workshop","volume":"361 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115895892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-09-01DOI: 10.1109/NSSPW.2006.4378831
M. Clark, R. Vinter
In this paper a new algorithm is proposed for tracking problems, in which the state evolves according to a linear difference equation and the measurement is a nonlinear function of a noise corrupted version of the state. The algorithm recursively generates Gaussian approximations of the conditional distribution of the target state given the current and past measurements. It differs from other `moment matching' algorithms, such as the extended Kalman filter and its refinements, because it is based on an exact calculation of the mean and covariance of the updated conditional distribution. A special case of the algorithm, applicable to bearings-only tracking problems, is called the shifted Rayleigh filter. Simulations indicate that the shifted Rayleigh filter can match the accuracy of high order particle filters while significantly reducing the computational burden, even in some scenarios where the extended Kalman filter gives poor estimates or fails altogether. It is expected that the new algorithms will offer similar advantages for other kinds of tracking algorithms, including those involving range-only measurements.
{"title":"A New Class of Moment Matching Filters for Nonlinear Tracking and Estimation Problems","authors":"M. Clark, R. Vinter","doi":"10.1109/NSSPW.2006.4378831","DOIUrl":"https://doi.org/10.1109/NSSPW.2006.4378831","url":null,"abstract":"In this paper a new algorithm is proposed for tracking problems, in which the state evolves according to a linear difference equation and the measurement is a nonlinear function of a noise corrupted version of the state. The algorithm recursively generates Gaussian approximations of the conditional distribution of the target state given the current and past measurements. It differs from other `moment matching' algorithms, such as the extended Kalman filter and its refinements, because it is based on an exact calculation of the mean and covariance of the updated conditional distribution. A special case of the algorithm, applicable to bearings-only tracking problems, is called the shifted Rayleigh filter. Simulations indicate that the shifted Rayleigh filter can match the accuracy of high order particle filters while significantly reducing the computational burden, even in some scenarios where the extended Kalman filter gives poor estimates or fails altogether. It is expected that the new algorithms will offer similar advantages for other kinds of tracking algorithms, including those involving range-only measurements.","PeriodicalId":388611,"journal":{"name":"2006 IEEE Nonlinear Statistical Signal Processing Workshop","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117154715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-09-01DOI: 10.1109/NSSPW.2006.4378824
Jeroen D. Hol, Thomas B. Schon, F. Gustafsson
In this paper a comparison is made between four frequently encountered resampling algorithms for particle filters. A theoretical framework is introduced to be able to understand and explain the differences between the resampling algorithms. This facilitates a comparison of the algorithms with respect to their resampling quality and computational complexity. Using extensive Monte Carlo simulations the theoretical results are verified. It is found that systematic resampling is favourable, both in terms of resampling quality and computational complexity.
{"title":"On Resampling Algorithms for Particle Filters","authors":"Jeroen D. Hol, Thomas B. Schon, F. Gustafsson","doi":"10.1109/NSSPW.2006.4378824","DOIUrl":"https://doi.org/10.1109/NSSPW.2006.4378824","url":null,"abstract":"In this paper a comparison is made between four frequently encountered resampling algorithms for particle filters. A theoretical framework is introduced to be able to understand and explain the differences between the resampling algorithms. This facilitates a comparison of the algorithms with respect to their resampling quality and computational complexity. Using extensive Monte Carlo simulations the theoretical results are verified. It is found that systematic resampling is favourable, both in terms of resampling quality and computational complexity.","PeriodicalId":388611,"journal":{"name":"2006 IEEE Nonlinear Statistical Signal Processing Workshop","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117166696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The quantization based filtering method (see [1], [2]) is a grid based approximation method for solving nonlinear filtering problems with discrete time observations. It relies on off-line preprocessing of some signal grids in order to construct fast recursive schemes for filter approximation. We give here an improvement of this method by taking advantage of the stationary quantizer property. The key ingredient is the use of vanishing correction terms to describe schemes based on piecewise linear approximations. Convergence results are given and comparison with sequential Monte Carlo methods is made.
{"title":"Quantization Based Filtering Method using First Order Approximation and Comparison with the Particle Filtering Approach","authors":"A. Sellami","doi":"10.1137/060652580","DOIUrl":"https://doi.org/10.1137/060652580","url":null,"abstract":"The quantization based filtering method (see [1], [2]) is a grid based approximation method for solving nonlinear filtering problems with discrete time observations. It relies on off-line preprocessing of some signal grids in order to construct fast recursive schemes for filter approximation. We give here an improvement of this method by taking advantage of the stationary quantizer property. The key ingredient is the use of vanishing correction terms to describe schemes based on piecewise linear approximations. Convergence results are given and comparison with sequential Monte Carlo methods is made.","PeriodicalId":388611,"journal":{"name":"2006 IEEE Nonlinear Statistical Signal Processing Workshop","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125766643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-09-01DOI: 10.1109/NSSPW.2006.4378857
M. Ekman, N. Bergman
In this paper the tracking of ground targets using acoustic sensors, distributed in a wireless sensor network, is studied. Since only acoustic sensors are utilized in the study the tracking problem can be regarded as a bearings-only application. The solution to the problem is given within the Bayesian recursive framework, where a sequential Monte Carlo method to the ground target tracking problem is developed. The classical sampling importance resampling (SIR) scheme is redesigned to also track multiple targets. The approach for solving the data association problem is based on hypothesis calculations according to the joint probabilistic data association (JPDA) method. Validation and evaluation of the tracking algorithms are performed using simulated data as well as real data extracted from a ground sensor network.
{"title":"Ground Target Tracking with Acoustic Sensors using Particle Filters and Statistical Data Association","authors":"M. Ekman, N. Bergman","doi":"10.1109/NSSPW.2006.4378857","DOIUrl":"https://doi.org/10.1109/NSSPW.2006.4378857","url":null,"abstract":"In this paper the tracking of ground targets using acoustic sensors, distributed in a wireless sensor network, is studied. Since only acoustic sensors are utilized in the study the tracking problem can be regarded as a bearings-only application. The solution to the problem is given within the Bayesian recursive framework, where a sequential Monte Carlo method to the ground target tracking problem is developed. The classical sampling importance resampling (SIR) scheme is redesigned to also track multiple targets. The approach for solving the data association problem is based on hypothesis calculations according to the joint probabilistic data association (JPDA) method. Validation and evaluation of the tracking algorithms are performed using simulated data as well as real data extracted from a ground sensor network.","PeriodicalId":388611,"journal":{"name":"2006 IEEE Nonlinear Statistical Signal Processing Workshop","volume":"134 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127591010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-09-01DOI: 10.1109/NSSPW.2006.4378838
W. Y. Leong, D. Mandic
A novel approach which extends blind source separation (BSS) of one or group of sources to the case of post-nonlinear mixtures is proposed. This is achieved by an adaptive algorithm in which the cost function jointly estimates the kurtosis and a measure of nonlinearity. Next, Kalman filtering is applied to blindly extract the signal of interest. The analysis of the proposed approach is conducted for the case of smooth post-nonlinear mixing and simulations are provided to illustrate both the quantitative and qualitative performance of the proposed algorithm.
{"title":"Blind Sequential Extraction of Post-Nonlinearly Mixed Sources using Kalman Filtering","authors":"W. Y. Leong, D. Mandic","doi":"10.1109/NSSPW.2006.4378838","DOIUrl":"https://doi.org/10.1109/NSSPW.2006.4378838","url":null,"abstract":"A novel approach which extends blind source separation (BSS) of one or group of sources to the case of post-nonlinear mixtures is proposed. This is achieved by an adaptive algorithm in which the cost function jointly estimates the kurtosis and a measure of nonlinearity. Next, Kalman filtering is applied to blindly extract the signal of interest. The analysis of the proposed approach is conducted for the case of smooth post-nonlinear mixing and simulations are provided to illustrate both the quantitative and qualitative performance of the proposed algorithm.","PeriodicalId":388611,"journal":{"name":"2006 IEEE Nonlinear Statistical Signal Processing Workshop","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130084126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-09-01DOI: 10.1109/NSSPW.2006.4378856
H. Kulatunga, V. Kadirkamanathan
A high-order multiple model approach is proposed for linear equalization and detection problem in ISI wireless channels. This paper is based on the high-order interacting multiple model (HIMM) algorithm and gives a Bayesian statistical description of the algorithm itself and its application to joint sequence estimation.
{"title":"High-Order Multiple Model Channel and Sequence Estimation","authors":"H. Kulatunga, V. Kadirkamanathan","doi":"10.1109/NSSPW.2006.4378856","DOIUrl":"https://doi.org/10.1109/NSSPW.2006.4378856","url":null,"abstract":"A high-order multiple model approach is proposed for linear equalization and detection problem in ISI wireless channels. This paper is based on the high-order interacting multiple model (HIMM) algorithm and gives a Bayesian statistical description of the algorithm itself and its application to joint sequence estimation.","PeriodicalId":388611,"journal":{"name":"2006 IEEE Nonlinear Statistical Signal Processing Workshop","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130273785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-09-01DOI: 10.1109/NSSPW.2006.4378849
P. Closas, J. Fernández-Rubio, C. F. Prades
Sequential Monte Carlo (SMC) methods are studied to deal with multivariate optimization problems arising from Maximum Likelihood (ML) estimation approaches. We compare results to those obtained by other methods, showing faster convergence and improved robustness when local optimums are present in the cost function to optimize. This paper presents a SMC method to obtain ML estimates in general multivariate state-spaces where a closed-form solution cannot be obtained, reporting computer simulation results for a particular application.
{"title":"Particle Filtering Applied to Robust Multivariate Likelihood Optimization in the Absence of a Closed-Form Solution","authors":"P. Closas, J. Fernández-Rubio, C. F. Prades","doi":"10.1109/NSSPW.2006.4378849","DOIUrl":"https://doi.org/10.1109/NSSPW.2006.4378849","url":null,"abstract":"Sequential Monte Carlo (SMC) methods are studied to deal with multivariate optimization problems arising from Maximum Likelihood (ML) estimation approaches. We compare results to those obtained by other methods, showing faster convergence and improved robustness when local optimums are present in the cost function to optimize. This paper presents a SMC method to obtain ML estimates in general multivariate state-spaces where a closed-form solution cannot be obtained, reporting computer simulation results for a particular application.","PeriodicalId":388611,"journal":{"name":"2006 IEEE Nonlinear Statistical Signal Processing Workshop","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133714579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-09-01DOI: 10.1109/NSSPW.2006.4378808
Efthymios Tsakonas, N. Sidiropoulos, A. Swami
We consider the problem of tracking the frequency and complex amplitude of a time-varying (TV) harmonic signal using particle filtering (PF) tools. Similar to previous PF approaches to TV spectral analysis, we assume that the frequency and complex amplitude evolve according to a Gaussian AR(1) model; but we concentrate on the important special case of a single TV harmonic. For this case, we show that the optimal importance function (that minimizes the variance of the particle weights) can be computed in closed form. We also develop a suitable procedure to sample from the optimal importance function. The end result is a custom PF solution that is more efficient than generic ones, and can be used in a broad range of important applications that postulate a single TV harmonic component, e.g., TV Doppler estimation in communications and radar.
{"title":"Time-Frequency Analysis using Particle Filtering: Closed-Form Optimal Importance Function and Sampling Procedure for a Single Time-Varying Harmonic","authors":"Efthymios Tsakonas, N. Sidiropoulos, A. Swami","doi":"10.1109/NSSPW.2006.4378808","DOIUrl":"https://doi.org/10.1109/NSSPW.2006.4378808","url":null,"abstract":"We consider the problem of tracking the frequency and complex amplitude of a time-varying (TV) harmonic signal using particle filtering (PF) tools. Similar to previous PF approaches to TV spectral analysis, we assume that the frequency and complex amplitude evolve according to a Gaussian AR(1) model; but we concentrate on the important special case of a single TV harmonic. For this case, we show that the optimal importance function (that minimizes the variance of the particle weights) can be computed in closed form. We also develop a suitable procedure to sample from the optimal importance function. The end result is a custom PF solution that is more efficient than generic ones, and can be used in a broad range of important applications that postulate a single TV harmonic component, e.g., TV Doppler estimation in communications and radar.","PeriodicalId":388611,"journal":{"name":"2006 IEEE Nonlinear Statistical Signal Processing Workshop","volume":"217 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134023418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-09-01DOI: 10.1109/NSSPW.2006.4378826
S. Liverani, A. Papavasiliou
We propose a particle filter for the estimation of a partially observed Markov chain that has a non dynamic component. Such systems arise when we include unknown parameters or when we decompose non ergodic systems to their ergodic classes. Our main assumption is that the value of the non dynamic component determines the limiting distribution of the observation process. In such cases, we do not want to resample the particles that correspond to the non dynamic component of the Markov chain. Instead, we take a weighted average of particle filters corresponding to different values of the non dynamic component. The computation of the weights is based on entropy and the number of particles corresponding to each particle filter is proportional to the weights.
{"title":"Entropy Based Adaptive Particle Filter","authors":"S. Liverani, A. Papavasiliou","doi":"10.1109/NSSPW.2006.4378826","DOIUrl":"https://doi.org/10.1109/NSSPW.2006.4378826","url":null,"abstract":"We propose a particle filter for the estimation of a partially observed Markov chain that has a non dynamic component. Such systems arise when we include unknown parameters or when we decompose non ergodic systems to their ergodic classes. Our main assumption is that the value of the non dynamic component determines the limiting distribution of the observation process. In such cases, we do not want to resample the particles that correspond to the non dynamic component of the Markov chain. Instead, we take a weighted average of particle filters corresponding to different values of the non dynamic component. The computation of the weights is based on entropy and the number of particles corresponding to each particle filter is proportional to the weights.","PeriodicalId":388611,"journal":{"name":"2006 IEEE Nonlinear Statistical Signal Processing Workshop","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131307702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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