RLS 'Recursive Least Squares' Algorithm

---

Relationship between the RLS and the KF

Simple problem: KF algorithm: Correction step of the KF transformed to be really similar to the RLS algorithm: Let’s make a little transformation: With this little transformation we will obtain the RLS algorithm from the correction step of the KF algorithm.

==We can see the RLS as the KF algorithm applied to a specific problem==, where the state doesn’t change, in fact the parametric vector to identify the system (the original problem from which we obtained the RLS) must me constant.

---

Extension to other estimation problem:

1. Slowly time-varying parameters:

2. RLS with exponential data weighting The idea is that older information is less useful, sometimes ever wrong old information might be outdated.

Typical values of $\lambda$:

NOTE: $\lambda >1$ would mean that older information is more useful than new information. A smaller $\lambda$ will increase the reactivity of the system to new information but it will also increase uncertainty, this is way we choose an exponential $\lambda$ with value a little less than $1$.