TY - JOUR
T1 - Fixed lag smoothing of scalar diffusions. Part I. The filtering-smoothing equation
AU - Liptser, R. Sh
AU - Steinberg, Y.
AU - Bobrovsky, B. Z.
AU - Schuss, Z.
N1 - Funding Information:
‘This work is partially supported by the ONR Grant N00014-96-1-0413
PY - 1996/11/29
Y1 - 1996/11/29
N2 - The problem of optimal fixed lag smoothing of a diffusion process, xt is to estimate xt - τ for t > τ, given the output of a nonlinear noisy sensor up to time t. The nonlinear filtering-smoothing problem is to estimate both xt and xt - τ. The optimal estimators are the conditional expectations of the processes, given the measurements. We derive evolution equations for both the normalized and unnormalized versions of the joint probability density function of xt and xt - τ) given the noisy measurements. The former is an equation of Kushner's type and the latter is of Zakai's type.
AB - The problem of optimal fixed lag smoothing of a diffusion process, xt is to estimate xt - τ for t > τ, given the output of a nonlinear noisy sensor up to time t. The nonlinear filtering-smoothing problem is to estimate both xt and xt - τ. The optimal estimators are the conditional expectations of the processes, given the measurements. We derive evolution equations for both the normalized and unnormalized versions of the joint probability density function of xt and xt - τ) given the noisy measurements. The former is an equation of Kushner's type and the latter is of Zakai's type.
KW - Filtering
KW - Kushner and Zakai equations
KW - Smoothing
UR - http://www.scopus.com/inward/record.url?scp=16144366244&partnerID=8YFLogxK
U2 - 10.1016/S0304-4149(96)00086-5
DO - 10.1016/S0304-4149(96)00086-5
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AN - SCOPUS:16144366244
SN - 0304-4149
VL - 64
SP - 237
EP - 255
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 2
ER -