Gaussian Filter

Gaussian Filters is a tractable implementation of the Bayes filter (Bayes Filter) for continuous spaces.

Key Idea

Beliefs are represented by a multi-variate normal distribution.

$p (x) = det (2 π Σ)^{- \frac{1}{2}} exp (- \frac{1}{2} (x - μ)^{T} Σ^{- 1} (x - μ))$

The density of variable $x$ is characterized by mean $μ$ and covariance $Σ$ .

Ramifications

Since beliefs are represented by a multi-variate normal distribution, this means that beliefs are uni-modal. This is suitable for many tracking problems. However, this is a poor match for many global estimation problems with multiple hypotheses that should give rise to their own modes in the posterior.

Representations

moments representation: The Gaussian is represented by its mean and covariance (first and second moments)

canonical representation :

These representations have a bijective mapping, and are functionally equivalent, but give rise to different algorithms.

Using the moments representation gives rise to the Kalman Filter.

Jethro's Braindump

Gaussian Filter

Key Idea

Ramifications

Representations

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