$$ % Define your custom commands here \newcommand{\bmat}[1]{\begin{bmatrix}#1\end{bmatrix}} \newcommand{\E}{\mathbb{E}} \newcommand{\P}{\mathbb{P}} \newcommand{\S}{\mathbb{S}} \newcommand{\R}{\mathbb{R}} \newcommand{\S}{\mathbb{S}} \newcommand{\norm}[2]{\|{#1}\|_{{}_{#2}}} \newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\pdd}[2]{\frac{\partial^2 #1}{\partial #2^2}} \newcommand{\vectornorm}[1]{\left|\left|#1\right|\right|} \newcommand{\abs}[1]{\left|{#1}\right|} \newcommand{\mbf}[1]{\mathbf{#1}} \newcommand{\mc}[1]{\mathcal{#1}} \newcommand{\bm}[1]{\boldsymbol{#1}} \newcommand{\nicefrac}[2]{{}^{#1}\!/_{\!#2}} \newcommand{\argmin}{\operatorname*{arg\,min}} \newcommand{\argmax}{\operatorname*{arg\,max}} \newcommand{\dd}{\operatorname{d}\!} $$

filters.ekf

filters.ekf

Extended Kalman filter using JAX automatic differentiation.

Included for comparison rather than as the default. The extended filter linearises the transition about the current mean,

\[ F_k = \left. \frac{\partial f}{\partial z} \right|_{z = \hat z_k}, \]

and propagates covariance through that linear map. Historically this meant deriving and maintaining Jacobians by hand – error-prone, and the single most common source of silent bugs in filtering code. With jax.jacfwd the Jacobian is exact to machine precision and free to obtain, which removes that objection entirely and leaves only the approximation-quality one.

That remaining objection is real. Linearisation is first-order accurate; the unscented transform is third-order for Gaussian inputs. Where the two disagree on this model, the unscented answer is the one to believe. Running both is a genuinely informative diagnostic: large divergence means the posterior is spread over a region where the dynamics are meaningfully curved, which is itself worth knowing.

Functions

Name	Description
extended_filter	Forward extended-filtering pass with a linear observation.

extended_filter

filters.ekf.extended_filter(
    transition,
    process_cov,
    h,
    obs_var,
    m0,
    p0,
    inputs,
    y,
    observed,
    *,
    gate_sigma=4.0,
    dof=None,
)

Forward extended-filtering pass with a linear observation.

Signature matches wdm.filters.ukf.unscented_filter so the two can be swapped without touching call sites.