Unscent Kalman Filter

Extended Kalman Filter extends Kalman Filters by linearizing the non-linear models with first-order Taylor expansion.

Unscent Kalman Filter instead extends Kalman Filters with Unscent transformation.

Unscent transformation

• Compute a set of (so-called) sigma points
• Transform each sigma point through the non-linear function
• Compute Gaussian from the transformed and weighted sigma points
• Compute a Gaussian from weighted points

Sigma Points Q: How to choose the sigma points & How to set the weights? A: Choose the sigma points $X$ and the corresponding weights $W$ so that the chosen points and weights fit exactly the orignial Gaussian distribution:

$$\sum_{i} w_i x_i = 1$$ $$\mu = \sum_{i} w_i x_i$$ $$\Sigma = \sum_{i} w_i (x_i - \mu_i) (x_i - \mu_i)^T$$

(No unique solution for $X$, $W$)

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