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 -