TY - JOUR
T1 - Algorithm 1051
T2 - UltimateKalman, Flexible Kalman Filtering and Smoothing Using Orthogonal Transformations
AU - Toledo, Sivan
N1 - Publisher Copyright: © 2024 Copyright held by the owner/author(s). Publication rights licensed to ACM.
PY - 2024/12/12
Y1 - 2024/12/12
N2 - UltimateKalman is a flexible linear Kalman filter and smoother implemented in three popular programming languages: MATLAB, C, and Java. UltimateKalman is a slight simplification and slight generalization of an elegant Kalman filter and smoother that was proposed in 1977 by Paige and Saunders. Their algorithm appears to be numerically superior and more flexible than other Kalman filters and smoothers, but curiously has never been implemented or used before. UltimateKalman is flexible: it can easily handle time-dependent problems, problems with state vectors whose dimensions vary from step to step, problems with varying numbers of observations in different steps (or no observations at all in some steps), and problems in which the expectation of the initial state is unknown. The programming interface of UltimateKalman is broken into simple building blocks that can be used to construct filters, single or multi-step predictors, multi-step or whole-Track smoothers, and combinations. The article describes the algorithm and its implementation as well as a test suite of examples and tests.
AB - UltimateKalman is a flexible linear Kalman filter and smoother implemented in three popular programming languages: MATLAB, C, and Java. UltimateKalman is a slight simplification and slight generalization of an elegant Kalman filter and smoother that was proposed in 1977 by Paige and Saunders. Their algorithm appears to be numerically superior and more flexible than other Kalman filters and smoothers, but curiously has never been implemented or used before. UltimateKalman is flexible: it can easily handle time-dependent problems, problems with state vectors whose dimensions vary from step to step, problems with varying numbers of observations in different steps (or no observations at all in some steps), and problems in which the expectation of the initial state is unknown. The programming interface of UltimateKalman is broken into simple building blocks that can be used to construct filters, single or multi-step predictors, multi-step or whole-Track smoothers, and combinations. The article describes the algorithm and its implementation as well as a test suite of examples and tests.
KW - Kalman filter
KW - Kalman smoother
KW - QR factorization
UR - http://www.scopus.com/inward/record.url?scp=85212398632&partnerID=8YFLogxK
U2 - https://doi.org/10.1145/3699958
DO - https://doi.org/10.1145/3699958
M3 - مقالة
SN - 0098-3500
VL - 50
JO - ACM Transactions on Mathematical Software
JF - ACM Transactions on Mathematical Software
IS - 4
M1 - 27
ER -