Parallel Iterated Extended and Sigma-Point Kalman Smoothers

Companion code in JAX for the paper Parallel Iterated Extended and Sigma-Point Kalman Smoothers [2].

What is it?

This is an implementation of parallelized Extended and Sigma-Points Bayesian Filters and Smoothers with CPU/GPU/TPU support coded using JAX primitives, in particular associative scan.

Supported features

• Extended Kalman Filtering and Smoothing
• Cubature Kalman Filtering and Smoothing
• Iterated versions of the above

Installation

• With GPU CUDA 11.0 support
  • Using pip
    Run pip install https://github.com/EEA-sensors/parallel-non-linear-gaussian-smoothers.git -f https://storage.googleapis.com/jax-releases/jax_releases.html
  • By cloning
    Clone https://github.com/EEA-sensors/parallel-non-linear-gaussian-smoothers.git
    Run pip install -r requirements.txt -f https://storage.googleapis.com/jax-releases/jax_releases.html
    Run python setup.py [install|develop] depending on the level of installation you want
• Without GPU support
  • By cloning
    Clone https://github.com/EEA-sensors/parallel-non-linear-gaussian-smoothers.git
    Run python setup.py [install|develop] --no-deps depending on the level of installation you want
    Manually install the dependencies jax and jaxlib, and for examples only matplotlib, numba, tqdm

Example

from parsmooth.parallel import ieks
from parsmooth.utils import MVNormalParameters

initial_guess = MVNormalParameters(...)
data = ...
Q = ...  # transition noise covariance matrix
R = ...  # observation error covariance matrix

def transition_function(x):
  ...
  return next_x
  
def observation_function(x):
  ...
  return obs
  
iterated_smoothed_trajectories = ieks(initial_guess, 
                                      data, 
                                      transition_function, 
                                      Q, 
                                      observation_function, 
                                      R, 
                                      n_iter=100)  # runs the parallel IEKS 100 times.

For more examples, see the notebooks.

Acknowlegments

This JAX-based code was created by Adrien Corenflos to implement the original idea by Fatemeh Yaghoobi [2] who provided the initial code for the parallelized extended Kalman filter in pure Python. The sequential cubature filtering code was adapted from some original code by Zheng Zhao.

References

[1] S. Särkkä and A. F. García-Fernández. Temporal Parallelization of Bayesian Smoothers. In: IEEE Transactions on Automatic Control 2020.

[2] F. Yaghoobi and A. Corenflos and S. Hassan and S. Särkkä. Parallel Iterated Extended and Sigma-Points Kalman Smoothers. To appear in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). (arXiv)