Saikat Saha | INDIAN MARITIME UNIVERSITY (original) (raw)

Papers by Saikat Saha

Research paper thumbnail of A new approach to particle based smoothed marginal MAP

Formal Methods in System Design, 2008

We present here a new method of finding the MAP state estimator from the weighted particles repre... more We present here a new method of finding the MAP state estimator from the weighted particles representation of marginal smoother distribution. This is in contrast to the usual practice, where the particle with the highest weight is selected as the MAP, although the latter is not necessarily the most probable state estimate. The method developed here uses only particles with corresponding filtering and smoothing weights. We apply this estimator for finding the unknown initial state of a dynamical system and addressing the parameter estimation problem.

Research paper thumbnail of Estimating volatility and model parameters of stochastic volatility models with jumps using particle filter

Formal Methods in System Design, 2008

Despite the success of particle filter, there are two factors which cause difficulties in its imp... more Despite the success of particle filter, there are two factors which cause difficulties in its implementation. The first one is the choice of importance functions commonly used in the literature which are far from being optimal. The second one is the combined state and parameter estimation problem. In a widely used Heston model on stochastic volatility in financial literature, we are able to circumvent both these problems. To reflect the most realistic situation, we also include jump in the stochastic volatility model. Numerical results show the effectiveness of the algorithms.

Research paper thumbnail of Marginalized particle filters for Bayesian estimation of Gaussian noise parameters

The particle filter provides a general solution to the nonlinear filtering problem with arbitrari... more The particle filter provides a general solution to the nonlinear filtering problem with arbitrarily accuracy. However, the curse of dimensionality prevents its application in cases where the state dimensionality is high. Further, estimation of stationary parameters is a known challenge in a particle filter framework. We suggest a marginalization approach for the case of unknown noise distribution parameters that avoid both aforementioned problem. First, the standard approach of augmenting the state vector with sensor offsets and scale factors is avoided, so the state dimension is not increased. Second, the mean and covariance of both process and measurement noises are represented with parametric distributions, whose statistics are updated adaptively and analytically using the concept of conjugate prior distributions. The resulting marginalized particle filter is applied to and illustrated with a standard example from literature.

Research paper thumbnail of Gaussian proposal density using moment matching in SMC methods

Statistics and Computing, 2008

In this article we introduce a new Gaussian proposal distribution to be used in conjunction with ... more In this article we introduce a new Gaussian proposal distribution to be used in conjunction with the sequential Monte Carlo (SMC) method for solving non-linear filtering problem. This proposal incorporates all the information about the to be estimated current state from both the available state and observation processes. This makes it more effective than the commonly used state transition density as a proposal, which ignores the recent observation. The introduced proposal is completely characterized by the exact moments obtained from the dynamical system. This is in contrast with recent works where the moments are approximated either numerically or by linearizing the observation model. Because of its Gaussian nature, it is also very easy to implement. We show further that the newly introduced proposal performs better than other similar proposal functions which also incorporate both state and observations.

Research paper thumbnail of Gaussian proposal density using moment matching in SMC methods

Statistics and Computing, 2009

In this article we introduce a new Gaussian proposal distribution to be used in conjunction with ... more In this article we introduce a new Gaussian proposal distribution to be used in conjunction with the sequential Monte Carlo (SMC) method for solving non-linear filtering problems. The proposal, in line with the recent trend, incorporates the current observation. The introduced proposal is characterized by the exact moments obtained from the dynamical system. This is in contrast with recent works where the moments are approximated either numerically or by linearizing the observation model. We show further that the newly introduced proposal performs better than other similar proposal functions which also incorporate both state and observations.

Research paper thumbnail of Exact Moment Matching for Efficient Importance Functions in SMC Methods

Journal of The Optical Society of America B-optical Physics, 2006

In this article we introduce a new proposal distribution to be used in conjunction with the seque... more In this article we introduce a new proposal distribution to be used in conjunction with the sequential Monte Carlo (SMC) method of solving non-linear filtering problem. The proposal distribution incorporates all the information about the to be estimated current state form both the available state and observation processes. This makes it more effective than the state transition density which is more commonly used but ignores the recent observation. Because of its Gaussian nature it is also very easy to implement. We show further that the introduced proposal performs better than other similar importance functions which also incorporate both state and observations.

Research paper thumbnail of On the Monte Carlo marginal MAP estimator for general state space models

IEEE Transactions on Magnetics, 2008

Research paper thumbnail of Non-parametric bayesian measurement noise density estimation in non-linear filtering

In this study, we investigate online Bayesian estimation of the measurement noise density of a gi... more In this study, we investigate online Bayesian estimation of the measurement noise density of a given state space model using particle filters and Dirichlet process mixtures. Dirichlet processes are widely used in statistics for nonparametric density estimation. In the proposed method, the unknown noise is modeled as a Gaussian mixture with unknown number of components. The joint estimation of the

Research paper thumbnail of Parameter estimation in a general state space model from short observation data: A SMC based approach

IEEE Transactions on Aerospace and Electronic Systems, 2009

In this article, we propose a SMC based method for estimating the static parameter of a general s... more In this article, we propose a SMC based method for estimating the static parameter of a general state space model. The proposed method is based on maximizing the joint likelihood of the observation and unknown state sequence with respect to both the unknown parameters and the unknown state sequence. This in turn, casts the problem into simultaneous estimations of state and parameter. We show the efficacy of this method by numerical simulation results.

Research paper thumbnail of Particle filtering with dependent noise

The theory and applications of the particle filter (PF) have developed tremendously during the pa... more The theory and applications of the particle filter (PF) have developed tremendously during the past two decades. However, there appear to be no version of the PF readily applicable to the case of dependent process and measurement noise. This is in contrast to the Kalman filter, where the case of correlated noise is a standard modification. Further, the fact that sampling continuous time models give dependent noise processes is an often neglected fact in literature. We derive the optimal proposal distribution in the PF for general and Gaussian noise processes, respectively. The main result is a modified prediction step. It is demonstrated that the original Bootstrap particle filter gets a particular simple and explicit form for dependent Gaussian noise. Finally, the practical importance of dependent noise is motivated in terms of sampling of continuous time models.

Research paper thumbnail of Particle based MAP state estimation: A comparison

MAP estimation is a good alternative to MMSE for certain applications involving nonlinear non Gau... more MAP estimation is a good alternative to MMSE for certain applications involving nonlinear non Gaussian systems. Recently a new particle filter based MAP estimator has been derived. This new method extracts the MAP directly from the output of a running particle filter. In the recent past, a Viterbi algorithm based MAP sequence estimator has been developed. In this paper, we compare these two methods for estimating the current state and the numerical results show that the former performs better.

Research paper thumbnail of Particle filter based MAP state estimation: a comparison

IEEE Transactions on Aerospace and Electronic Systems, 2009

MAP estimation is a good alternative to MMSE for certain applications involving nonlinear non Gau... more MAP estimation is a good alternative to MMSE for certain applications involving nonlinear non Gaussian systems. Recently a new particle filter based MAP estimator has been derived. This new method extracts the MAP directly from the output of a running particle filter. In the recent past, a Viterbi algorithm based MAP sequence estimator has been developed. In this paper, we compare these two methods for estimating the current state and the numerical results show that the former performs better.

Research paper thumbnail of On parameter estimation of stochastic volatility models from stock data using particle filter - Application to AEX index

International Journal of Innovative Computing Information and Control, 2009

We consider the problem of estimating stochastic volatility from stock data. The estimation of th... more We consider the problem of estimating stochastic volatility from stock data. The estimation of the volatility process of the Heston model is not in the usual framework of the filtering theory. Discretizing the continuous Heston model to the discrete-time one, we can derive the ...

Research paper thumbnail of A new approach to particle based smoothed marginal MAP

Formal Methods in System Design, 2008

We present here a new method of finding the MAP state estimator from the weighted particles repre... more We present here a new method of finding the MAP state estimator from the weighted particles representation of marginal smoother distribution. This is in contrast to the usual practice, where the particle with the highest weight is selected as the MAP, although the latter is not necessarily the most probable state estimate. The method developed here uses only particles with corresponding filtering and smoothing weights. We apply this estimator for finding the unknown initial state of a dynamical system and addressing the parameter estimation problem.

Research paper thumbnail of Estimating volatility and model parameters of stochastic volatility models with jumps using particle filter

Formal Methods in System Design, 2008

Despite the success of particle filter, there are two factors which cause difficulties in its imp... more Despite the success of particle filter, there are two factors which cause difficulties in its implementation. The first one is the choice of importance functions commonly used in the literature which are far from being optimal. The second one is the combined state and parameter estimation problem. In a widely used Heston model on stochastic volatility in financial literature, we are able to circumvent both these problems. To reflect the most realistic situation, we also include jump in the stochastic volatility model. Numerical results show the effectiveness of the algorithms.

Research paper thumbnail of Marginalized particle filters for Bayesian estimation of Gaussian noise parameters

The particle filter provides a general solution to the nonlinear filtering problem with arbitrari... more The particle filter provides a general solution to the nonlinear filtering problem with arbitrarily accuracy. However, the curse of dimensionality prevents its application in cases where the state dimensionality is high. Further, estimation of stationary parameters is a known challenge in a particle filter framework. We suggest a marginalization approach for the case of unknown noise distribution parameters that avoid both aforementioned problem. First, the standard approach of augmenting the state vector with sensor offsets and scale factors is avoided, so the state dimension is not increased. Second, the mean and covariance of both process and measurement noises are represented with parametric distributions, whose statistics are updated adaptively and analytically using the concept of conjugate prior distributions. The resulting marginalized particle filter is applied to and illustrated with a standard example from literature.

Research paper thumbnail of Gaussian proposal density using moment matching in SMC methods

Statistics and Computing, 2008

In this article we introduce a new Gaussian proposal distribution to be used in conjunction with ... more In this article we introduce a new Gaussian proposal distribution to be used in conjunction with the sequential Monte Carlo (SMC) method for solving non-linear filtering problem. This proposal incorporates all the information about the to be estimated current state from both the available state and observation processes. This makes it more effective than the commonly used state transition density as a proposal, which ignores the recent observation. The introduced proposal is completely characterized by the exact moments obtained from the dynamical system. This is in contrast with recent works where the moments are approximated either numerically or by linearizing the observation model. Because of its Gaussian nature, it is also very easy to implement. We show further that the newly introduced proposal performs better than other similar proposal functions which also incorporate both state and observations.

Research paper thumbnail of Gaussian proposal density using moment matching in SMC methods

Statistics and Computing, 2009

In this article we introduce a new Gaussian proposal distribution to be used in conjunction with ... more In this article we introduce a new Gaussian proposal distribution to be used in conjunction with the sequential Monte Carlo (SMC) method for solving non-linear filtering problems. The proposal, in line with the recent trend, incorporates the current observation. The introduced proposal is characterized by the exact moments obtained from the dynamical system. This is in contrast with recent works where the moments are approximated either numerically or by linearizing the observation model. We show further that the newly introduced proposal performs better than other similar proposal functions which also incorporate both state and observations.

Research paper thumbnail of Exact Moment Matching for Efficient Importance Functions in SMC Methods

Journal of The Optical Society of America B-optical Physics, 2006

In this article we introduce a new proposal distribution to be used in conjunction with the seque... more In this article we introduce a new proposal distribution to be used in conjunction with the sequential Monte Carlo (SMC) method of solving non-linear filtering problem. The proposal distribution incorporates all the information about the to be estimated current state form both the available state and observation processes. This makes it more effective than the state transition density which is more commonly used but ignores the recent observation. Because of its Gaussian nature it is also very easy to implement. We show further that the introduced proposal performs better than other similar importance functions which also incorporate both state and observations.

Research paper thumbnail of On the Monte Carlo marginal MAP estimator for general state space models

IEEE Transactions on Magnetics, 2008

Research paper thumbnail of Non-parametric bayesian measurement noise density estimation in non-linear filtering

In this study, we investigate online Bayesian estimation of the measurement noise density of a gi... more In this study, we investigate online Bayesian estimation of the measurement noise density of a given state space model using particle filters and Dirichlet process mixtures. Dirichlet processes are widely used in statistics for nonparametric density estimation. In the proposed method, the unknown noise is modeled as a Gaussian mixture with unknown number of components. The joint estimation of the

Research paper thumbnail of Parameter estimation in a general state space model from short observation data: A SMC based approach

IEEE Transactions on Aerospace and Electronic Systems, 2009

In this article, we propose a SMC based method for estimating the static parameter of a general s... more In this article, we propose a SMC based method for estimating the static parameter of a general state space model. The proposed method is based on maximizing the joint likelihood of the observation and unknown state sequence with respect to both the unknown parameters and the unknown state sequence. This in turn, casts the problem into simultaneous estimations of state and parameter. We show the efficacy of this method by numerical simulation results.

Research paper thumbnail of Particle filtering with dependent noise

The theory and applications of the particle filter (PF) have developed tremendously during the pa... more The theory and applications of the particle filter (PF) have developed tremendously during the past two decades. However, there appear to be no version of the PF readily applicable to the case of dependent process and measurement noise. This is in contrast to the Kalman filter, where the case of correlated noise is a standard modification. Further, the fact that sampling continuous time models give dependent noise processes is an often neglected fact in literature. We derive the optimal proposal distribution in the PF for general and Gaussian noise processes, respectively. The main result is a modified prediction step. It is demonstrated that the original Bootstrap particle filter gets a particular simple and explicit form for dependent Gaussian noise. Finally, the practical importance of dependent noise is motivated in terms of sampling of continuous time models.

Research paper thumbnail of Particle based MAP state estimation: A comparison

MAP estimation is a good alternative to MMSE for certain applications involving nonlinear non Gau... more MAP estimation is a good alternative to MMSE for certain applications involving nonlinear non Gaussian systems. Recently a new particle filter based MAP estimator has been derived. This new method extracts the MAP directly from the output of a running particle filter. In the recent past, a Viterbi algorithm based MAP sequence estimator has been developed. In this paper, we compare these two methods for estimating the current state and the numerical results show that the former performs better.

Research paper thumbnail of Particle filter based MAP state estimation: a comparison

IEEE Transactions on Aerospace and Electronic Systems, 2009

MAP estimation is a good alternative to MMSE for certain applications involving nonlinear non Gau... more MAP estimation is a good alternative to MMSE for certain applications involving nonlinear non Gaussian systems. Recently a new particle filter based MAP estimator has been derived. This new method extracts the MAP directly from the output of a running particle filter. In the recent past, a Viterbi algorithm based MAP sequence estimator has been developed. In this paper, we compare these two methods for estimating the current state and the numerical results show that the former performs better.

Research paper thumbnail of On parameter estimation of stochastic volatility models from stock data using particle filter - Application to AEX index

International Journal of Innovative Computing Information and Control, 2009

We consider the problem of estimating stochastic volatility from stock data. The estimation of th... more We consider the problem of estimating stochastic volatility from stock data. The estimation of the volatility process of the Heston model is not in the usual framework of the filtering theory. Discretizing the continuous Heston model to the discrete-time one, we can derive the ...