OPEKs

OPEKs, or Optimized Polynomial Extended Kalman Filters, are a class of algorithms used for state estimation in dynamic systems. They are an extension of the standard Kalman Filter, designed to handle nonlinear system dynamics and measurement models more efficiently. The core idea behind OPEKs is to approximate the nonlinear functions using polynomial expansions, such as Taylor series or Chebyshev polynomials. This approximation allows for a more accurate propagation of the state's probability distribution through the nonlinearities compared to traditional Extended Kalman Filters, which often linearize the system around the current state estimate.

The optimization aspect of OPEKs refers to the selection and order of the polynomial terms used in the approximation. By carefully choosing these terms, the filter aims to achieve a balance between computational complexity and the accuracy of the state estimation. Higher-order polynomial approximations can capture more complex nonlinearities but come at a greater computational cost. The choice of polynomial basis and its degree is often problem-dependent and can be tuned for specific applications.

OPEKs have found applications in various fields where nonlinear state estimation is crucial, including robotics, autonomous navigation, and control systems. They offer a potential improvement over standard Extended Kalman Filters when dealing with systems exhibiting significant nonlinear behavior, providing more robust and accurate state estimates. However, like all model-based estimators, their performance is contingent on the accuracy of the system model and the chosen polynomial approximation.