Abhinoy Kumar Singh

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.

A Modified Bayesian Filter for Randomly Delayed Measurements

The traditional Bayesian approximation framework for filtering in discrete time systems assumes that the measurement is available at every time instant. But in practice, the measurements could be randomly delayed. In the literature, the problem has been examined and solution is provided by restricting the maximum number of delay to one or two time steps. This technical note develops an approach to deal with the filtering problems with an arbitrary number of delays in measurement. Pursuing this objective, traditional Bayesian approximation to nonlinear filtering problem is modified by reformulating the expressions of mean and covariances which appear during the measurement update. We use the cubature quadrature rule to evaluate the multivariate integral expressions for the mean vector and the covariance matrix which appear in the developed filtering algorithm. We compare the new algorithm which accounts for delay with the existing CQKF heuristics on two different examples and demonstrate how accounting for a random delay improves the filtering performance.

Unscented Kalman filter for arbitrary step randomly delayed measurements

The conventional Bayesian framework of filtering is based on the assumption that the measurements are available at each time-step without any delay. But in real-life problems, measurements may be randomly delayed in time. In this paper, we modified the unscented Kalman filter (UKF) for arbitrary time delayed measurements. With the help of simulation results, it has been shown that the proposed filter provides more accurate estimation compared to the ordinary UKF in presence of randomly delayed measurements.

Nonlinear estimation with transformed cubature quadrature points

An ongoing work, proposing a modified method to solve the nonlinear filtering problems is presented in this paper. The proposed method, which uses orthogonally transformed cubature quadrature points, is an extension of cubature quadrature Kalman filter (CQKF). The modified filtering method, developed here is regarded as transformed cubature quadrature Kalman filter (TCQKF). The computational load of TCQKF remains similar to the ordinary CQKF, while its accuracy improves for the systems having dimension higher than two. The proposed filter is simulated for a nonlinear filtering problem and the results are compared with the existing cubature based filters.

Quadrature filters for maneuvering target tracking

In this paper, a maneuvering target tracking problem has been solved by using the Guss-Hermite filter (GHF) and sparse-grid Gauss-Hermite filter (SGHF). Univariate Gauss-Hermite quadrature rule is extended for multidimensional systems by using the product rule and the Smolyaks rule in GHF and SGHF respectively. The SGHF, which is an alternative of GHF reduces the computational burden considerably. The performance of the quadrature filters have been compared with the cubature Kalman filter (CKF), and the unscented Kalman filter (UKF) for the maneuvering target tracking problem. The simulation results exhibit the improvement of performance with the quadrature filters compared to the CKF and the UKF.

Quadrature Filters for Underwater Passive Bearings-Only Target Tracking

A typical underwater passive bearings-only target tracking problem is solved using nonlinear filters namely cubature Kalman filter (CKF), Gauss-Hermite filter (GHF) and sparse-grid Gauss-Hermite filter (SGHF). The performance of the filters is compared in terms of estimation accuracy, track-loss count and computational time. Theoretical Cramer-Rao lower bound (CRLB) is used to determine the maximum achievable performance and to compare the error bounds of various filters used.

Adaptive sparse-grid Gauss–Hermite filter

In this paper, a new nonlinear filter based on sparse-grid quadrature method has been proposed. The proposed filter is named as adaptive sparse-grid Gauss-Hermite filter (ASGHF). Ordinary sparse-grid technique treats all the dimensions equally, whereas the ASGHF assigns a fewer number of points along the dimensions with lower nonlinearity. It uses adaptive tensor product to construct multidimensional points until a predefined error tolerance level is reached. The performance of the proposed filter is illustrated with two nonlinear filtering problems. Simulation results demonstrate that the new algorithm achieves a similar accuracy as compared to sparse-grid Gauss-Hermite filter (SGHF) and Gauss-Hermite filter (GHF) with a considerable reduction in computational load. Further, in the conventional GHF and SGHF, any increase in the accuracy level may result in an unacceptably high increase in the computational burden. However, in ASGHF, a little increase in estimation accuracy is possible with a limited increase in computational burden by varying the error tolerance level and the error weighting parameter. This enables the online estimator to operate near full efficiency with a predefined computational budget.

Computationally efficient sparse-grid Gauss-Hermite filtering

A new nonlinear filtering algorithm based on sparse-grid Gauss-Hermite filter (SGHF) incorporated with the technique of algorithm adapting to dimensions based on their nonlinearity, is presented. The motive of this work is to reduce the computatioanl load of SGHF, while maintaining similar filtering accuracy. This is achieved by implementing adaptive tensor product to construct the multidimensional sparse-grid quadrature points. This reduction in computational burden may increase the scope of application of this filtering algorithm for higher dimensional problems in on-board applications. Performance of the proposed algorithm is illustrated by estimating the frequency and amplitude of multiple superimposed sinusoids.

Bearing-Only Tracking Using Sparse-Grid Gauss–Hermite Filter

In this paper, performance of sparse-grid Gauss–Hermite filter (SGHF) in bearings-only tracking (BOT) problem has been studied and compared with the performance of unscented Kalman filter (UKF), cubature Kalman filter (CKF), and Gauss–Hermite filter (GHF). The performance has been compared in terms of estimation accuracy and percentage of track loss, subjected to high initial uncertainty. It has been found that track loss of SGHF is less than all other quadrature filters with comparable estimation accuracy.

Cubature quadrature Kalman filter for maneuvering target tracking

In this paper, the cubature quadrature Kalman filter (CQKF) has been applied to solve a maneuvering target tracking problem. The CQKF, which has been developed in house, uses third order spherical cubature and higher order Gauss quadrature rule to solve the intractable integrals encountered in Bayesian framework of filtering. The CQKF is the generalized form of well established cubature Kalman filter (CKF) and under certain simplification, the CQKF reduces to the CKF. The performance of the CQKF has been compared with the CKF, and the unscented Kalman filter (UKF) for a maneuvering target tracking problem. The simulation results exhibit the improvement of performance with the CQKF compared to the CKF and the UKF.