Repairing a Nonlinear Strict Filter Without Reference Targets

Thu, 30 Apr 2026 13:16:00 +0530

After the scalar benchmark, the work moved to a nonlinear sine-observation model:

\[ z_t = z_{t-1} + w_t,\quad w_t \sim \mathcal{N}(0,Q) \]\[ y_t = x_t \sin(z_t) + v_t,\quad v_t \sim \mathcal{N}(0,R) \]

The strict filtering contract stayed the same:

\[ q^F_t = \operatorname{update}(q^F_{t-1}, x_t, y_t) \]

No hidden sequence state was allowed in the headline rows. The filter had to export an explicit online filtering marginal at each time step.

Elbo on mlbot.blog