Some New Array Information Formulations of the UD-based Kalman Filter
Julia Vladimirovna Tsyganova, Maria Vyacheslavovna Kulikova, Andrey Vladimirovich Tsyganov · 2019
The paper addresses the UD factorization based Kalman filtering (KF) implementation methods. We propose two new numerically favored and convenient array information formulations of the UD-based KF: the UD-based array Information Filter (algorithm UD-IF) and the extended UD-based array Information Filter (algorithm eUD-IF). To confirm the correctness of our results, we have proved that the newly constructed UD based array computational schemes are algebraically equivalent to the “straight” (conventional) information filter. Although all these information-type algorithms are theoretically equivalent, their computational properties are different. The newly proposed algorithms are numerically robust to machine round-off errors due to the numerically stable orthogonal transformations applied on each iteration. Additionally, algorithm eUD-IF has the extended array form, i. e., it allows updating absolutely all required filter quantities with the use of the numerically stable modified weighted Gram-Schmidt orthogonalization procedure. So, our results extend the existing class of numerically efficient KF implementation methods and can be used in practical applications.