Filtering Problem (Stochastic Processes)

The filtering problem is to obtain the best linear estimate $\hat{z}_t$ of $z_t$ based on the past observations ( $y_s | s\leq t)$ . Abstractly, the solution to the problem of filtering corresponds to explicitly computing $\hat{z}_t = P_t^y(z_t)$ where $P_t^y$ is the projection operator onto the Hilbert space $H_t^y$ .

Parameters

$n$ : number of dimensions in state space

Filters

Computational Model

Randomization

Approximation

Algorithms Table

Displaying 4 of 4 algorithms


Particle filter Del Moral	1996	$O(n^3)$	$O(nN)$
Maybeck; Peter S Extended Kalman Filter	1979	$O(n^2 \log^2 n)$	$O(n^2)$
Kushner non-linear filter	1967	$O(n^3)$	$O(n^2)$
Kalman Filter	1960	$O(n^3)$	$O(n^2)$

Reductions Table

Insuffient Data to display table

Other relevant algorithms

Displaying 6 of 6 other relevant algorithms


Ocone	1999
Damiano Brigo; Bernard Hanzon and François LeGland	1998
Del Moral; Pierre	1998
Zakai	1969
Stratonovich	1960
Stratonovich	1959