Published Works
Journal Articles
Quaternion Attitude Estimation
This paper presents a systematic approach to a low cost, readily available solution for orientation estimation using commonly available computing and sensing resources. A Quaternion state is employed to facilitate the use of the linear Kalman Filter algorithm for state estimation. Low cost, commercially available accelerometers, gyroscopes, and compass sensors are employed for measurement. The filter model is developed and simulated by use of the popular commercial software, MATLAB/Simulink. The objective of the paper is to develop a mathematical model of the system under estimation, and provide reasonable estimates of its performance, obtained through numerical simulation.
Optimal Parameter Selection in Weeksβ Method for Numerical Laplace Transform Inversion based on Machine Learning
The Weeks method for the numerical inversion of the Laplace transform utilizes a MoΜbius transformation which is parameterized by two real quantities, π and π. Proper selection of these parameters depends highly on the Laplace space function πΉ (π ) and is generally a nontrivial task. In this paper, a convolutional neural network is trained to determine optimal values for these parameters for the specific case of the matrix exponential. The matrix exponential ππ΄ is estimated by numerically inverting the cor- responding resolvent matrix (π πΌ βπ΄)β1 via the Weeks method at (π, π) pairs provided by the network. For illustration, classes of square real matrices of size three to six are studied. For these small matrices, the Cayley-Hamilton theorem and rational approx- imations can be utilized to obtain values to compare with the results from the network derived estimates. The network learned by minimizing the error of the matrix expo- nentials from the Weeks method over a large data set spanning (π, π) pairs. Network training using the Jacobi identity as a metric was found to yield a self-contained approach that does not require a truth matrix exponential for comparison.