TY - GEN
T1 - On the Move
T2 - 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
AU - Tabaghi, Puoya
AU - Dokmanic, Ivan
AU - Vetterli, Martin
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/5
Y1 - 2019/5
N2 - In this paper, we propose kinetic Euclidean distance matrices (KEDMs) - a new algebraic tool for localization of moving points from spatio-temporal distance measurements. KEDMs are inspired by the well-known Euclidean distance matrices (EDM) which model static points. When objects move, trajectory models may enable better localization from fewer samples by trading off samples in space for samples in time. We develop the theory for polynomial trajectory models used in tracking and simultaneous localization and mapping. Concretely, we derive a semidefinite relaxation for KEDMs inspired by similar algorithms for the usual EDMs, and propose a new spectral factorization algorithm adapted to trajectory reconstruction. Numerical experiments show that KEDMs and the new semidefinite relaxation accurately reconstruct trajectories from incomplete, noisy distance observations, scattered over multiple time instants. In particular, they show that temporal oversampling can considerably reduce the required number of measured distances at any given time.
AB - In this paper, we propose kinetic Euclidean distance matrices (KEDMs) - a new algebraic tool for localization of moving points from spatio-temporal distance measurements. KEDMs are inspired by the well-known Euclidean distance matrices (EDM) which model static points. When objects move, trajectory models may enable better localization from fewer samples by trading off samples in space for samples in time. We develop the theory for polynomial trajectory models used in tracking and simultaneous localization and mapping. Concretely, we derive a semidefinite relaxation for KEDMs inspired by similar algorithms for the usual EDMs, and propose a new spectral factorization algorithm adapted to trajectory reconstruction. Numerical experiments show that KEDMs and the new semidefinite relaxation accurately reconstruct trajectories from incomplete, noisy distance observations, scattered over multiple time instants. In particular, they show that temporal oversampling can considerably reduce the required number of measured distances at any given time.
KW - Euclidean distance matrix
KW - polynomial spectral factorization
KW - semidefinite programming
KW - trajectory localization
UR - http://www.scopus.com/inward/record.url?scp=85068961206&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85068961206&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2019.8682653
DO - 10.1109/ICASSP.2019.8682653
M3 - Conference contribution
AN - SCOPUS:85068961206
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 4893
EP - 4897
BT - 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 12 May 2019 through 17 May 2019
ER -