Rahul Radhakrishnan

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 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.

Ballistic target tracking and its interception using suboptimal filters on reentry

In this work, tracking of a ballistic target on reentry using an interceptor missile is studied where the main motive is to accurately estimate the acceleration of the incoming ballistic target. To achieve this, nonlinear filters like the unscented Kalman filter (UKF), cubature Kalman filter (CKF) and cubature quadrature Kalman filter (CQKF) are used. For a possible interception of the target by an interceptor, proportional navigation guidance (PNG) law has been used. Efficiency of the filtering techniques has been studied by plotting the root mean square error (RMSE) of the target acceleration and by calculating the final miss-distance.

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.