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In estimation theory, the extended Kalman filter (EKF) is the nonlinear version of the Kalman filter which linearizes about an estimate of the current mean and covariance.In the case of well defined transition models, the EKF has been considered [1] the de facto standard in the theory of nonlinear state estimation, navigation systems and GPS.
In applied statistics, optimal estimation is a regularized matrix inverse method based on Bayes' theorem. It is used very commonly in the geosciences , particularly for atmospheric sounding . A matrix inverse problem looks like this:
The PDF at the previous timestep is assumed inductively to be the estimated state and covariance. This is justified because, as an optimal estimator, the Kalman filter makes best use of the measurements, therefore the PDF for given the measurements is the Kalman filter estimate.
The PROPT [1] MATLAB Optimal Control Software is a new generation platform for solving applied optimal control (with ODE or DAE formulation) and parameters estimation problems. The platform was developed by MATLAB Programming Contest Winner, Per Rutquist in 2008. The most recent version has support for binary and integer variables as well as an ...
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers.
In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design.
This application is called design optimization. One subset is the engineering optimization, and another recent and growing subset of this field is multidisciplinary design optimization, which, while useful in many problems, has in particular been applied to aerospace engineering problems. This approach may be applied in cosmology and ...
Anne E. Gelb is a mathematician interested in numerical analysis, partial differential equations and Fourier analysis of images. She is John G. Kemeny Parents Professor of Mathematics at Dartmouth College .