Atomic clock simulation
Project description
stochasticclock
A module calculating the stochastic deviations in timepoints for atomic clocks.
The code is an application of the theory presented in Galleani et al. (2003), doi:10.1088/0026-1394/40/3/305.
The module's current functionality calculates stochastic deviations using the exact iterative solution to the stochastic differential equation in Galleani_exact()
$$\begin{equation} \mathbf{X}(t_{n+1}) = \begin{pmatrix} 1 & \delta t \\ 0 & 1 \end{pmatrix} \mathbf{X}(t_n) + \begin{pmatrix} \delta t \mu_1 + \frac{1}{2} \delta t^2 \mu_2 \\ \delta t \mu_2 \end{pmatrix} + \mathbf{J}(t_n) \end{equation}$$
$$\begin{equation} \mathbf{J}(t_n) \sim \mathcal{N} \bigg( \mathbf{0}, \begin{bmatrix} \sigma_1^2 \delta t + \frac{1}{3} \sigma_2^2 \delta t^3 & \frac{1}{2}\sigma_2^2 \delta t^2 \\ \frac{1}{2}\sigma_2^2 \delta t^2 & \sigma_2^2 \delta t \end{bmatrix} \bigg) \end{equation}$$
Stochastic deviations can be visualised using clock_error()
, and their distributions simulated with deviation_distribution()
.
Please consult the Jupyter notebook for examples.
Project details
Release history Release notifications | RSS feed
Download files
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.
Source Distribution
Built Distribution
Hashes for stochasticclock-0.0.2-py3-none-any.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 766eab349c079218fa56aff38da3b275ede693a806851fa729f4f5efe36bcbe8 |
|
MD5 | abd6ff1f895afbee8f6d4897554b8a04 |
|
BLAKE2b-256 | 8d43e9f9fdae547e56b4397a7e2b58b2bec0f3ea1a39a1dc1b49a5976e7fcb4d |