Polynomial Filtering Algorithm Applied to Navigation Data Processing under Quadratic Nonlinearities in System and Measurement Equations. Part 1. Description and Comparison with Kalman Type Algorithms
О. А. Степанов, Yu. А. Litvinenko, V. A. Vasiliev, A. B. Toropov, Michael Basin
Abstract
The paper considers the filtering problems solved in navigation data processing under quadratic nonlinearities both in system and measurement equations. A Kalman type recursive algorithm is proposed, where the predicted estimate and gain at each step are calculated based on the assumption on the Gaussian posterior probability density function of the estimated vector at the previous step and minimization of estimation error covariance matrices using a linear procedure with respect to the current measurement. The similarities between this algorithm and other Kalman type algorithms such as extended and second-order Kalman filters are discussed. The procedure for evaluating the performance and comparing the algorithms is presented.