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State-space models are used in a wide range of time series analysisformulations. Kalman filtering and smoothing are work-horse algorithms in thesesettings. While classic algorithms assume Gaussian errors to simplifyestimation, recent advances use a broader range of optimization formulations toallow outlier-robust estimation, as well as constraints to capture priorinformation.  Here we develop methods on state-space models where either innovations orerror covariances may be singular. These models frequently arise in navigation(e.g. for `colored noise' models or deterministic integrals) and are ubiquitousin auto-correlated time series models such as ARMA. We reformulate allstate-space models (singular as well as nonsinguar) as constrained convexoptimization problems, and develop an efficient algorithm for thisreformulation. The convergence rate is {\it locally linear}, with constantsthat do not depend on the conditioning of the problem.  Numerical comparisons show that the new approach outperforms competingapproaches for {\it nonsingular} models, including state of the art interiorpoint (IP) methods. IP methods converge at superlinear rates; we expect them todominate. However, the steep rate of the proposed approach (independent ofproblem conditioning) combined with cheap iterations wins against IP in arun-time comparison. We therefore suggest that the proposed approach be the{\it default choice} for estimating state space models outside of the Gaussiancontext, regardless of whether the error covariances are singular or not.

Fast Robust Methods for Singular State-Space Models