Simultaneous Localization and Mapping (SLAM) algorithms are frequently deployed to support a wide range of robotics applications, such as autonomous navigation in unknown environments, and scene mapping in virtual reality. Many of these applications require autonomous agents to perform SLAM in highly dynamic scenes. To this end, this tutorial extends a recently introduced, unifying optimization-based SLAM backend framework to environments with moving objects and features. Using this framework, we consider a rapprochement of recent advances in dynamic SLAM. Moreover, we present dynamic EKF SLAM: a novel, filtering-based dynamic SLAM algorithm generated from our framework, and prove that it is mathematically equivalent to a direct extension of the classical EKF SLAM algorithm to the dynamic environment setting. Empirical results with simulated data indicate that dynamic EKF SLAM can achieve high localization and mobile object pose estimation accuracy, as well as high map precision, with high efficiency.

We investigate the convergence and stability properties of the decoupled extended Kalman filter learning algorithm (DEKF) within the long-short term memory network (LSTM) based online learning framework. For this purpose, we model DEKF as a perturbed extended Kalman filter and derive sufficient conditions for its stability during LSTM training. We show that if the perturbations -- introduced due to decoupling -- stay bounded, DEKF learns LSTM parameters with similar convergence and stability properties of the global extended Kalman filter learning algorithm. We verify our results with several numerical simulations and compare DEKF with other LSTM training methods. In our simulations, we also observe that the well-known hyper-parameter selection approaches used for DEKF in the literature satisfy our conditions.

We specialize the decoupled extended Kalman filter (DEKF) for online parameter learning in factorization models, including factorization machines, matrix and tensor factorization, and illustrate the effectiveness of the approach through simulations. Learning model parameters through the DEKF makes factorization models more broadly useful by allowing for more flexible observations through the entire exponential family, modeling parameter drift, and producing parameter uncertainty estimates that can enable explore/exploit and other applications. We use a more general dynamics of the parameters than the standard DEKF, allowing parameter drift while encouraging reasonable values. We also present an alternate derivation of the regular extended Kalman filter and DEKF that connects these methods to natural gradient methods, and suggests a similarly decoupled version of the iterated extended Kalman filter.