Altitude hold: state and parameter estimation with KF

Main Changes

New altitude dynamics model

$$\begin{aligned} z_{t+1} {}={}& z_t + T_s v_t + \tfrac{1}{2}T_s^2 a_t + w^zt, \\ v{t+1} {}={}& v_t + T_s a_t + w^v_t, \\ a_t {}={}& \alpha_t \tau_t + \betat, \\ \alpha{t+1} {}={}& \alpha_t + w^\alphat, \\ \beta{t+1} {}={}& \beta_t + w_t^\beta. \end{aligned}$$

The output is

$$y_t = z_t + \epsilon_t.$$

Link to Overleaf document: ...

Comments

You are currently using a corrected version of $\tau$, which is defined as $\tilde{\tau} = \tau\; \cos\phi \; \cos\theta $. This should be reported in the Overleaf document
Since we are using a quaternion-based model, it would be better (for the sake of consistency, but not only) to avoid having to compute the Euler angles. We can apply a rotation using the quaternion.
In the future, it would be interesting to see whether there is any benefit from using the acceleration measurements from the IMU; then, the output would be $y_t = (z_t, a_t) + \epsilon_t$. We cannot measure the acceleration too accurately, so the variance of the corresponding noise would have to be large. We can explore the possible benefits in simulation first.

QUB-ASL / bzzz

Altitude hold: state and parameter estimation with KF #83

Main Changes

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