When to Choose the KF

1. The system has to be Linear.
2. We know that the pdf of $f_x(x(t)|Y^t)$ is a Gaussian distribution.

NOTE: $f_x(x(t)|Y^t)$ means: pdf (probability distribution function) of $x(t)$ knowing the measurements ($Y^t$) up to time $t$.

---

• The KF will always provide the LSME (Lest Mean Square Error)* solution.
• If $w(t)$, $v(t)$ and $x(0)$ have Gaussian distributions the prediction will also be the MSE (Mean Square Error) solution.
• We can also write the pdf $f_x$ as:

$$f_x(x(t)|Y^t)=N\left(\hat{x}(t|t),P(t|t)\right)$$

Where $N$ means a Gaussian distribution with $\hat{x}(t|t)$ mean, and $P(t|t)$ variance.