# Difference between revisions of "CDS 110b: Sensor Fusion"

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In this lecture we show how the Kalman filter can be used for sensor fusion and explore some variations on the basic Kalman filter, including the extended Kalman filter.

## Lecture Outline

1. Sensor fusion using Kalman filters
2. The extended Kalman filter
3. Parameter estimation using EKF

## Lecture Materials

Correlated noise can be put into the Kalman filtering framework by using a (linear) filter to give a correlated noise source with a given correlation function (or spectral density). Suppose that $H(s)$ is a transfer function that filters Gaussian white noise and provides the desired correlation. Let $(A_{f},B_{f},C_{f})$ be a state space representation for the filter. Then the entire system can be written as $\left[{\begin{matrix}x\\z\end{matrix}}\right]=\left[{\begin{matrix}A&FC_{f}\\0&A_{f}\end{matrix}}\right]\left[{\begin{matrix}x\\z\end{matrix}}\right]+\left[{\begin{matrix}B\\0\end{matrix}}\right]u+\left[{\begin{matrix}0\\B_{f}\end{matrix}}\right]v$ $y=\left[{\begin{matrix}C&0\end{matrix}}\right]\left[{\begin{matrix}x\\z\end{matrix}}\right]+w$
This system takes a Guassian white noise input $v$, filters it to give the desired spectrum, and uses it to drive the system.