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parallel-non-linear-gaussian-smoothers

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

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# 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](https://github.com/google/jax) primitives, in particular [associative scan](https://en.wikipedia.org/wiki/Prefix_sum?wprov=sfla1).

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
-------

```python
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](https://github.com/EEA-sensors/parallel-non-linear-gaussian-smoothers/tree/master/notebooks).

Acknowlegments
--------------
This JAX-based code was created by [Adrien Corenflos](https://adriencorenflos.github.io/) to implement the original idea by [Fatemeh Yaghoobi](https://fatameh-yaghoobi.github.io/) [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](https://users.aalto.fi/~zhaoz1/).

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](http://arxiv.org/abs/2102.00514))

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