A Novel Neural Filter to Improve Accuracy of Neural Network Models of Dynamic Systems

The paper introduces an EKF-style “neural filter” and empirically claims that its covariance remains bounded while the open-loop neural network diverges, but it provides no formal conditions or proofs for invertibility of the innovation covariance, monotonic covariance reduction, or boundedness; it only presents the recursion and experiments (see Eqs. (6)–(11) and the accompanying remarks, and the concluding claims) . The candidate solution supplies the missing hypotheses and standard linear-Gaussian proofs: S = CPC^T + R ≻ 0 when R ≻ 0, P+ = P − P C^T S^{-1} C P ⪯ P, and boundedness/convergence under detectability/stabilizability with divergence of open-loop when ρ(A) ≥ 1 and Q ≻ 0, which are textbook results.