Shovan Bhaumik

Cubature quadrature Kalman filter

In this correspondence, the authors develop a novel method based on spherical radial cubature and Gauss-Laguerre quadrature rule for non-linear state estimation problems. The proposed filter, referred as cubature quadrature Kalman filter (CQKF) would be able to overcome inherent disadvantages associated with the earlier reported cubature Kalman filter (CKF). The theory and formulation of CQKF has been presented. Using two well-known non-linear examples, the superior performance of CQKF has been demonstrated. Owing to computational efficiency (compared to the particle and grid-based filter) and enhanced accuracy compared to the extended Kalman filter and the CKF, the developed algorithm may find place in on-board real life applications.

Central Difference Formulation of Risk-Sensitive Filter

A numerically efficient algorithm for risk-sensitive filters (known to be robust to model uncertainties) of nonlinear plants, using central difference approximation is proposed. The proposed filter, termed central difference risk-sensitive filter (CDRSF), overcomes several disadvantages associated with the extended risk-sensitive filter (ERSF), reported earlier. The theory of formulation and the algorithm of the CDRSF are presented. With an example, it is demonstrated that the proposed new filter would give much better tracking performance compared to the ERSF for certain nonlinear systems. The CDRSF would be nearly as fast as the ERSF, thus making it more preferable for real-time applications compared to the risk-sensitive particle filter

Full- and reduced-order observer design for rectangular descriptor systems with unknown inputs

Abstract In this paper, methods are proposed to design Luenberger type full- and reduced-order observers for rectangular descriptor systems with unknown inputs. These methods are based on the effect of pre- and post-multiplicative operation of a linear transformation, derived here by means of simple matrix theory. Sufficient conditions for the existence of observers are given and proved. Numerical examples are given to illustrate the effectiveness of the proposed method.

Bearing only tracking using Gauss-Hermite filter

In this paper, performance of Gauss-Hermite filter (GHF) in bearing only tracking problem has been compared with that of extended Kalman filter (EKF) and unscented Kalman filter (UKF) in terms of estimation accuracy, probability of track-loss and computational efficiency. The performance improvement of the GHF with increase in quadrature points and enhanced robustness compared to EKF and UKF with respect to large initial uncertainty has been reported. It has been concluded that without introducing substantial computational burden, GHF with three or more quadrature points exhibits better performance compared to UKF and EKF.

Particle-method-based formulation of risk-sensitive filter

A novel particle implementation of risk-sensitive filters (RSF) for nonlinear, non-Gaussian state-space models is presented. Though the formulation of RSFs and its properties like robustness in the presence of parametric uncertainties are known for sometime, closed-form expressions for such filters are available only for a very limited class of models including finite state-space Markov chains and linear Gaussian models. The proposed particle filter-based implementations are based on a probabilistic re-interpretation of the RSF recursions. Accuracy of these filtering algorithms can be enhanced by choosing adequate number of random sample points called particles. These algorithms significantly extend the range of practical applications of risk-sensitive techniques and may also be used to benchmark other approximate filters, whose generic limitations are discussed. Appropriate choice of proposal density is suggested. Simulation results demonstrate the performance of the proposed algorithms.

Adaptive Grid Solution of Risk Sensitive Estimator Problems

An on-going work proposing a novel method for numerical computation of risk sensitive state estimates for non-linear non-Gaussian problems is reported. The algorithm is based on point mass approximation also called the grid method and utilises a modified form of information state based recursive relation, proposed and proved as a theorem. The modified form is claimed to be more efficient for numerical evaluation of risk sensitive estimate, especially for aposteriori risk sensitive state estimation. Though grid based filters are known for low numerical efficiency, heuristics for adaptive choice of grid points has been proposed to alleviate the shortcoming. The performance of this filter is demonstrated with a linear Gaussian case. Salient features of this Adaptive Grid RSF is then contrasted against the recently proposed Risk Sensitive Filters using the particle approach.

Risk Sensitive Estimators for Inaccurately Modelled Systems

Robustness of risk sensitive (RSE) estimators/filters for inaccurately modelled plant are elucidated and exemplified. A theorem which allows alternative pathway for deriving RSE filter relation and derivation of different closed form relations for RS filters in linear Gaussian cases is provided. Consequently, errors in expressions in earlier publications have been detected and rectified. Properties of RS filters are briefly reviewed and the interpretation of robustness of RS filters elaborated. Using Monte Carlo simulation, it is shown that RS filters perform significantly better compared to risk-neutral filters when (i) process noise covariance is in error (ii) the true system (truth model) contains unmodelled bias (iii) the state transition matrix is inaccurately known. Design pragmatics for the choice of the risk sensitive parameter is indicated.

Nonlinear estimation using cubature quadrature points

In this paper, a novel method based on spherical radial cubature and Gauss Laguerre quadrature rule has been proposed for nonlinear state estimation problem. The proposed method is named as cubature quadrature Kalman filter (CQKF). The performance of CQKF is demonstrated with a severely nonlinear single dimensional problem. Preliminary result suggests that the proposed filter has potential to outperform conventional extended Kalman filter (EKF) and more advanced cubature Kalman filter (CKF). Due to computational efficiency and enhanced accuracy compared to standard nonlinear estimators, the projected algorithm may find place in on-board real life applications.

Nonlinear estimation using transformed Gauss-Hermite quadrature points

An ongoing work proposing a new method for nonlinear filtering problem is reported. The intractable integrals have appeared in nonlinear estimation problem been approximately evaluated using Gauss-Hermite quadrature rule. An orthogonal transformation has been applied on Gauss-Hermite points in order to obtain more accurate estimation for higher order problems. The developed method is named transformed Gauss-Hermite filter. The efficacy of proposed filter compared to ordinary Gauss-Hermite filter is demonstrated with the help of an example.

Alternative Formulation of Risk-Sensitive Particle Filter (Posterior)

An algorithm for posterior risk-sensitive particle filter for nonlinear non-Gaussian system has been proposed in this paper. For Gaussian linear measurement case optimal proposal and for nonlinear Gaussian measurement case linearized version of optimal proposal for risk-sensitive particle filter is derived. The applicability of nonlinear risk-sensitive filters such as extended risk-sensitive filter (ERSF), central difference risk-sensitive filter (CDRSF) as a proposal for risk-sensitive particle filter is discussed. The proposed filter is applied to a highly nonlinear Gaussian system. Results are provided to show the comparative performance of extended risk-sensitive filter (ERSF), posterior risk-sensitive particle filter (RSPF) and adaptive grid risk-sensitive filter (AGRSF) for a representative run. Root mean square error (RMSE) of the proposed filter has also been provided and compared with ERSF and AGRSF. The computational cost of the proposed risk-sensitive estimator is studied and compared with other nonlinear risk-sensitive filters