LowLevelParticleFilters.jl is a library for state estimation, that is, given measurements y(t) from a dynamical system with inputs u(t), estimate the state vector x(t). Throughout, we assume discretetime dynamics on the form
where p are some form of parameters, t is the time and w,e are disturbances (noise).
The documentation describes how to handle continuoustime ODEs on the form
as well.
The library has existed for a while, but has never really been announced before. I just pushed it over to version 3.0, breaking the previous interface by moving to an interface similar to the SciML ecosystem where many functions accept a parameter vector p
. The Documentation has also seen some improvements in the process.
We provide a number of filter types

KalmanFilter
. A standard Kalman filter. Is restricted to linear dynamics (possibly time varying) and Gaussian noise. 
ExtendedKalmanFilter
: For nonlinear systems, the EKF runs a regular Kalman filter on linearized dynamics. Uses ForwardDiff.jl for linearization. The noise model must be Gaussian. 
UnscentedKalmanFilter
: The Unscented Kalman filter often performs slightly better than the Extended Kalman filter but may be slightly more computationally expensive. The UKF handles nonlinear dynamics and measurement model, but still requires an additive Gaussian noise model and assumes all posterior distributions are Gaussian, i.e., can not handle multimodal posteriors. 
ParticleFilter
: The particle filter is a nonlinear estimator. This filter is simple to use and assumes that both dynamics noise and measurement noise are additive. Particle filters handle multimodal posteriors. 
AuxiliaryParticleFilter
: This filter is identical toParticleFilter
, but uses a slightly different proposal mechanism for new particles. 
AdvancedParticleFilter
: This filter gives you more flexibility, at the expense of having to define a few more functions. This filter does not require the noise to be additive and is thus the most flexible filter type. 
DAEUnscentedKalmanFilter
: An Unscented Kalman filter for differentialalgebraic systems (DAE). Still somewhat experimental.
The code has been written to be reasonably fast and it supports StaticArrays everywhere. For simple systems, we can push about 7k particles per millisecond. We also support particle and Kalman smoothing as well as automatic differentiation through the filters using ForwardDiff.jl, making parameter estimation with the PredictionError Method (PEM) relatively easy. We also have a new example of estimating timevarying parameters in ODEs.
Happy filtering
Fredrik