TY - JOUR
T1 - Properties of the characteristic function generator of the two-state Cauchy estimator
AU - Bai, Yu
AU - Speyer, Jason L.
AU - Idan, Moshe
N1 - Funding Information: ∗Received by the editors June 1, 2018; accepted for publication (in revised form) April 29, 2019; published electronically November 12, 2019. https://doi.org/10.1137/18M1191580 Funding: This work was supported by National Science Foundation (NSF) grant 1607502, and by the joint NSF and United States–Israel Binational Science Foundation (BSF), NSF-BSF ECCS grant 2015702. †Doctoral Student, Department of Mechanical and Aerospace Engineering, UCLA, Los Angeles, CA 90095 ([email protected]). ‡Ronald and Valerie Sugar Distinguished Professor, Department of Mechanical and Aerospace Engineering, UCLA, Los Angeles, CA 90095 ([email protected]). §Associate Professor, Aerospace Engineering, Technion, 32000 Haifa, Israel (moshe.idan@ technion.ac.il).
PY - 2019
Y1 - 2019
N2 - In order to better capture impulsive noises in dynamic systems, a state estimator in the presence of Cauchy distributed process and measurement noises has been studied in recent years. The Cauchy estimator is determined by expressing in closed form the characteristic function (CF) of the unnormalized conditional probability density functions of the states given measurement history. The CF is comprised of a sum of exponentials multiplied by a coefficient, both being nonlinear functions of the measurements and the spectral variable. In this paper, we uncover important properties of the exponential terms in the CF for the two-state Cauchy estimator. These properties can be used to simplify the estimator structure significantly.
AB - In order to better capture impulsive noises in dynamic systems, a state estimator in the presence of Cauchy distributed process and measurement noises has been studied in recent years. The Cauchy estimator is determined by expressing in closed form the characteristic function (CF) of the unnormalized conditional probability density functions of the states given measurement history. The CF is comprised of a sum of exponentials multiplied by a coefficient, both being nonlinear functions of the measurements and the spectral variable. In this paper, we uncover important properties of the exponential terms in the CF for the two-state Cauchy estimator. These properties can be used to simplify the estimator structure significantly.
KW - Cauchy probability density function
KW - Characteristic functions
KW - Nonlinear estimation with heavy tailed noises
UR - http://www.scopus.com/inward/record.url?scp=85077089959&partnerID=8YFLogxK
U2 - 10.1137/18M1191580
DO - 10.1137/18M1191580
M3 - مقالة
SN - 0363-0129
VL - 57
SP - 3639
EP - 3665
JO - SIAM Journal on Control and Optimization
JF - SIAM Journal on Control and Optimization
IS - 6
ER -