Approximate MMSE Estimator for Linear Dynamic Systems With Gaussian Mixture Noise
نویسندگان
چکیده
منابع مشابه
Analytic MMSE Bounds in Linear Dynamic Systems with Gaussian Mixture Noise Statistics
Using state-space representation, mobile object positioning problems can be described as dynamic systems, with the state representing the unknown location and the observations being the information gathered from the location sensors. For linear dynamic systems with Gaussian noise, the Kalman filter provides the Minimum Mean-Square Error (MMSE) state estimation by tracking the posterior. Hence, ...
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15 صفحه اولJointly Gaussian random variables, MMSE and linear MMSE estimation
• Proof: X is j G implies that V = uX is G with mean uμ and variance uΣu. Thus its characteristic function, CV (t) = e ituμe−t 2uTΣu/2. But CV (t) = E[e itV ] = E[e TX ]. If we set t = 1, then this is E[e TX ] which is equal to CX(u). Thus, CX(u) = CV (1) = e iuμe−u TΣu/2. • Proof (other side): we are given that the charac function ofX, CX(u) = E[eiuTX ] = e μe−u TΣu/2. Consider V = uX. Thus, C...
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ژورنال
عنوان ژورنال: IEEE Transactions on Automatic Control
سال: 2017
ISSN: 0018-9286,1558-2523
DOI: 10.1109/tac.2016.2594378