Reviewers agree that this is a clear contribution to the HMM and SMC set of methods that allows for robustness in the face of likelihood misspecification. Additionally, the method is both theoretically and empirically justified. While the main reviewer concern is novelty, there is agreement that the work is correct, thorough, and effective. An additional concern is the lack of clear attribution of theoretical results (e.g. proofs in the supplement) --- it would be useful for these statements to point to either the relevant work in the literature.