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\n\n \n \n \n \n \n Sequential Estimation of Hidden ARMA Processes by Particle Filtering - Part I.\n \n \n \n\n\n \n Urteaga, I.; and Djurić, P. M.\n\n\n \n\n\n\n
IEEE Transactions on Signal Processing, 65(2): 482–493. 2016.\n
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@Article{j-Urteaga2016,\n author = {I{\\~n}igo Urteaga and Petar M. Djuri\\'{c}},\n title = {{Sequential Estimation of Hidden {ARMA} Processes by Particle Filtering - {P}art {I}}},\n journal = {IEEE Transactions on Signal Processing},\n year = {2016},\n volume = {65},\n number = {2},\n pages = {482--493},\n issn = {1053-587X},\n abstract = {This paper is Part I of a series of two papers where we address sequential estimation of wide-sense stationary autoregressive moving average (ARMA) state processes by particle filtering. In Part I, we present estimation methods for ARMA processes of known model order, where the parameters are first known and then unknown. The driving noise of the ARMA process is Gaussian with unknown variance. We derive the transition density of the ARMA state for settings that correspond to different assumptions of a priori knowledge. Instead of estimating all the unknown parameters of the model, we treat them by Rao-Blackwellization. We propose a particle filtering method, with appropriate variations according to available information, for sequential estimation of the unknown state as it evolves with time. We demonstrate the performance of the proposed methods by extensive computer simulations.},\n doi = {10.1109/TSP.2016.2598309},\n keywords = {Atmospheric measurements;Autoregressive processes;Computational modeling;Estimation;Geophysical measurements;Particle measurements;Signal processing;ARMA processes;Rao-Blackwellization;known model order;nonlinear models;particle filtering},\n owner = {iurteaga},\n timestamp = {2015-10-05},\n}\n\n
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\n This paper is Part I of a series of two papers where we address sequential estimation of wide-sense stationary autoregressive moving average (ARMA) state processes by particle filtering. In Part I, we present estimation methods for ARMA processes of known model order, where the parameters are first known and then unknown. The driving noise of the ARMA process is Gaussian with unknown variance. We derive the transition density of the ARMA state for settings that correspond to different assumptions of a priori knowledge. Instead of estimating all the unknown parameters of the model, we treat them by Rao-Blackwellization. We propose a particle filtering method, with appropriate variations according to available information, for sequential estimation of the unknown state as it evolves with time. We demonstrate the performance of the proposed methods by extensive computer simulations.\n
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\n\n \n \n \n \n \n Sequential Estimation of Hidden ARMA Processes by Particle Filtering - Part II.\n \n \n \n\n\n \n Urteaga, I.; and Djurić, P. M.\n\n\n \n\n\n\n
IEEE Transactions on Signal Processing, 65(2): 494–504.. 2016.\n
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@Article{j-Urteaga2016a,\n author = {I{\\~n}igo Urteaga and Petar M. Djuri\\'{c}},\n title = {{Sequential Estimation of Hidden {ARMA} Processes by Particle Filtering - {P}art {II}}},\n journal = {IEEE Transactions on Signal Processing},\n year = {2016},\n volume = {65},\n number = {2},\n pages = {494--504.},\n issn = {1053-587X},\n abstract = {This is Part II of a series of two papers where we address sequential estimation of wide-sense stationary autoregressive moving average (ARMA) state processes by particle filtering. In Part I, we considered a state-space model where the state was an ARMA process of known order and where the parameters of the process could be known or unknown. In this paper, we extend our work from Part I by considering the same type of models, with the added complexity that the ARMA processes are now of unknown order. Instead of working on a scheme that first tracks the state by operating with different assumed models, and then selects the best model by using a predefined criterion, we present a method that directly estimates the state without the need of knowing the model order.We derive the transition density of the state for unknown ARMA model order, and propose a particle filter based on that density and the empirical Bayesian methodology. We demonstrate the performance of the proposed method with computer simulations and compare it with the methods from Part I.},\n doi = {10.1109/TSP.2016.2598324},\n keywords = {Autoregressive processes;Bayes methods;Computational modeling;Covariance matrices;Estimation;Signal processing;State-space methods;ARMA processes;Rao-Blackwellization;empirical Bayes;nonlinear models;particle filtering;unknown model order},\n owner = {iurteaga},\n timestamp = {2015-10-05},\n}\n\n
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\n This is Part II of a series of two papers where we address sequential estimation of wide-sense stationary autoregressive moving average (ARMA) state processes by particle filtering. In Part I, we considered a state-space model where the state was an ARMA process of known order and where the parameters of the process could be known or unknown. In this paper, we extend our work from Part I by considering the same type of models, with the added complexity that the ARMA processes are now of unknown order. Instead of working on a scheme that first tracks the state by operating with different assumed models, and then selects the best model by using a predefined criterion, we present a method that directly estimates the state without the need of knowing the model order.We derive the transition density of the state for unknown ARMA model order, and propose a particle filter based on that density and the empirical Bayesian methodology. We demonstrate the performance of the proposed method with computer simulations and compare it with the methods from Part I.\n
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