Suppose I have some process which is governed by:

$$ \vec{x_{k+1}} = A\vec{x_k} + B\vec{u_k} + w_k$$

where $u_k$ is the input, and $w_k$ is process disturbance.

This process is continuous time in nature, but I am modelling it in discrete time, and don't have access to $A$.

Suppose I have some estimate of the model, $\hat{A}$ which I would like to estimate the current state, $\vec{x_k}$.

The problem is that I have some non-negligible sampling error. I have a nominal sampling interval of $\bar{\Delta t}$, but for each individual interval between $x_k$ and $x_{k-1}$, I have an interval of $\Delta t_k$.

Question 1: Supposing that $\Delta t_k$ is distributed normally, does this just come out naturally as disturbance? i.e. could I account for this with my Kalman gain

Question 2: Suppose that $\Delta t_k$ is not distributed normally, and instead has an asymmetric distribution, possibly even pareto. Is there any way to account for this?

Thank you.

Suppose I have some process which is governed by:

$$ \vec{x_{k+1}} = A\vec{x_k} + B\vec{u_k} + w_k$$

where $u_k$ is the input, and $w_k$ is process disturbance.

This process is continuous time in nature, but I am modelling it in discrete time, and don't have access to $A$.

Suppose I have some estimate of the model, $\hat{A}$, which I want to use in order to estimate the current state, $\vec{x_k}$.

The problem is that I have some non-negligible sampling error. I have a nominal sampling interval of $\bar{\Delta t}$, but for each individual interval between $x_k$ and $x_{k-1}$, I have an interval of $\Delta t_k$.

Question 1: Supposing that $\Delta t_k$ is distributed normally, does this just come out naturally as disturbance? i.e. could I account for this with my Kalman gain

Question 2: Suppose that $\Delta t_k$ is not distributed normally, and instead has an asymmetric distribution, possibly even pareto. Is there any way to account for this?

Thank you.