TY  - GEN
A1  - Nüsken, Nikolas
A1  - Reich, Sebastian
A1  - Rozdeba, Paul J.
T1  - State and parameter estimation from observed signal increments
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean–Vlasov equations as the starting point to derive ensemble Kalman–Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 916 
KW  - parameter estimation
KW  - continuous-time data assimilation
KW  - ensemble Kalman filter
KW  - correlated noise
KW  - multi-scale diffusion processes
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-442609
SN  - 1866-8372
IS  - 916
ER  - 
TY  - JOUR
A1  - Nüsken, Nikolas
A1  - Reich, Sebastian
A1  - Rozdeba, Paul J.
T1  - State and parameter estimation from observed signal increments
JF  - Entropy : an international and interdisciplinary journal of entropy and information studies
N2  - The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean-Vlasov equations as the starting point to derive ensemble Kalman-Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems.
KW  - parameter estimation
KW  - continuous-time data assimilation
KW  - ensemble Kalman filter
KW  - correlated noise
KW  - multi-scale diffusion processes
Y1  - 2019
U6  - https://doi.org/10.3390/e21050505
SN  - 1099-4300
VL  - 21
IS  - 5
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Mutothya, Nicholas Mwilu
A1  - Xu, Yong
A1  - Li, Yongge
A1  - Metzler, Ralf
A1  - Mutua, Nicholas Muthama
T1  - First passage dynamics of stochastic motion in heterogeneous media driven by correlated white Gaussian and coloured non-Gaussian noises
JF  - Journal of physics. Complexity
N2  - We study the first passage dynamics for a diffusing particle experiencing a spatially varying diffusion coefficient while driven by correlated additive Gaussian white noise and multiplicative coloured non-Gaussian noise. We consider three functional forms for position dependence of the diffusion coefficient: power-law, exponential, and logarithmic. The coloured non-Gaussian noise is distributed according to Tsallis' q-distribution. Tracks of the non-Markovian systems are numerically simulated by using the fourth-order Runge-Kutta algorithm and the first passage times (FPTs) are recorded. The FPT density is determined along with the mean FPT (MFPT). Effects of the noise intensity and self-correlation of the multiplicative noise, the intensity of the additive noise, the cross-correlation strength, and the non-extensivity parameter on the MFPT are discussed.
KW  - first passage
KW  - diffusion
KW  - non-Gaussian
KW  - correlated noise
Y1  - 2021
U6  - https://doi.org/10.1088/2632-072X/ac35b5
SN  - 2632-072X
VL  - 2
PB  - IOP Publishing
CY  - Bristol
ER  -