Dual Estimation

A special case of machine learning arises when the input ${\bf x}_k$ is unobserved, and requires coupling both state-estimation and parameter estimation. For these dual estimation problems, we again consider a discrete-time nonlinear dynamic system,

$${\bf x}_{k+1} = F({\bf x}_k,{\bf v}_k,{\bf w})$$ (6)

$${\bf y}_{k} = H({\bf x}_k,{\bf n}_k,{\bf w}).$$ (7)

where both the system states ${\bf x}_k$ and the set of model parameters ${\bf w}$ for the dynamic system must be simultaneously estimated from only the observed noisy signal ${\bf y}_k$.

Approaches to dual-estimation are discussed in Section 4.2.

In the next section we explain the basic assumptions and flaws with the using the EKF. In Section 3, we introduce the Unscented Kalman Filter (UKF) as a method to amend the flaws in the EKF. Finally, in Section 4, we present results of using the UKF for the different areas of nonlinear estimation.