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On wrapping the Kalman filter and estimating with the SO(2) group


Marković, Ivan; Ćesić, Josip; Petrović, Ivan
On wrapping the Kalman filter and estimating with the SO(2) group // 19th International Conference on Information Fusion (FUSION), Special Session on Directional Estimation
Heidelberg, Germany, 2016. str. 2245-2250 (pozvano predavanje, međunarodna recenzija, cjeloviti rad (in extenso), znanstveni)


Naslov
On wrapping the Kalman filter and estimating with the SO(2) group

Autori
Marković, Ivan ; Ćesić, Josip ; Petrović, Ivan

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
19th International Conference on Information Fusion (FUSION), Special Session on Directional Estimation / - Heidelberg, Germany, 2016, 2245-2250

ISBN
978-0-9964527-4-8

Skup
19th International Conference on Information Fusion (FUSION), Special Session on Directional Estimation

Mjesto i datum
Heidelberg, Germany, 05-08.07.2016.

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Lie groups; Special orthogonal group; Kalman filter

Sažetak
This paper analyzes directional tracking in 2D with the extended Kalman filter on Lie groups (LG-EKF). The study stems from the problem of tracking objects moving in 2D Euclidean space, with the observer measuring direction only, thus rendering the measurement space and object position on the circle — a non-Euclidean geometry. The problem is further inconvenienced if we need to include higher-order dynamics in the state space, like angular velocity which is a Euclidean variables. The recently proposed LG-EKF offers a different solution to this issue by modeling the state space as a Lie group or combinations thereof, e.g., SO(2) or its combinationswith R^n . In the present paper, we first derive the LG-EKF on SO(2) and subsequently show that this derivation, based on the mathematically grounded framework of filtering on Lie groups, yields the same result as heuristically wrapping the angular variable within the EKF framework. This result applies only to the SO(2) and SO(2)×R^n LG-EKFs and is not intended to be extended to other Lie groups or combinations thereof. In the end, we showcase the SO(2)×R^2 LG-EKF, as an example of a constant angular acceleration model, on the problem of speaker tracking with a microphone array for which real-world experiments are conducted and accuracy is evaluated with ground truth data obtained by a motion capture system.

Izvorni jezik
Engleski

Znanstvena područja
Elektrotehnika, Računarstvo, Temeljne tehničke znanosti



POVEZANOST RADA


Ustanove
Fakultet elektrotehnike i računarstva, Zagreb