Conditions for suboptimal filter stability in SLAM

In this article, we show marginal stability in SLAM, guaranteeing convergence to a non-zero mean state error estimate bounded by a constant value. Moreover, marginal stability guarantees also convergence of the Riccati equation of the one-step ahead state error covariance to at least one psd steady state solution. In the search for real-time implementations of SLAM, covariance inflation methods produce a suboptimal filter that eventually may lead to the computation of an unbounded state error covariance. We provide tight constraints in the amount of decorrelation possible, to guarantee convergence of the state error covariance, and at the same time, a linear-time implementation of SLAM.