Recurrent state estimation gets a convergence guarantee: one gain drives the error exponentially into any small neighborhood
Recurrent models for state estimation previously had empirical success but no formal convergence or robustness guarantees. This work treats a recurrent network as a discretization of continuous latent dynamics and requires the latent flow to contract, proving that a smooth injective map embeds the true physical state into latent space; raising a single scalar gain κ drives the estimation error exponentially fast into an arbitrarily small neighborhood of zero, at the cost of decoder capacity growing polynomially in κ. On a real mobile-robot pose-estimation task, the provably contracting model outperforms a vanilla GRU and trains more stably.