SI&DA - Lecture 22 'Derivation of the Kalman Filter - Part I'

Summary

NOTE: $P(t|t):=\mathrm{Var}\left[(x(t)-\hat{x}(t|t)\right]$ Defined as “covariance matrix of the prediction error”.

• PREDICTION STEP: we compute the one step ahead prediction of $\hat{x}(t+1|t)$, and for the covariance of the prediction error $P(t+1|t)$, using the model $\mathcal{M}(A,B,C,G,Q,R)$.
• We then receive the measurement from the sensor at time $t+1$: $y(t+1)$.
• CORRECTION STEP: with $y(t+1)$, the calculated predictions $\hat{x}(t+1|t)$ and $P(t+1|t)$, still using the same model $\mathcal{M}$ we compute $\hat{x}(t+1|t+1)$ and $P(t+1|t+1)$.

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#TODO Is e(t+1) an error???

What’s $\mathcal{L}$ ?

It means that $\hat{x}(t+1|t)$ is a linear combination of $Y^t$