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Abstract-Efficiently solving nonlinear least squares (NLS) problems is crucial for many applications in robotics. In online applications, solving the associated nolinear systems every step may become very expensive. This paper introduces online, incremental solutions, which take full advantage of the sparseblock structure of the problems in robotics. In general, the solution of the nonlinear system is approximated by incrementally solving a series of linearized problems. The most computationally demanding part is to assemble and solve the linearized system at each iteration. In our solution, this is mitigated by incrementally updating the factorized form of the linear system and changing the linearization point only if needed. The incremental updates are done using a resumed factorization only on the parts affected by the new information added to the system at every step. The sparsity of the factorized form directly affects the efficiency. In order to obtain an incremental factorization with persistent reduced fill-in, a new incremental ordering scheme is proposed. Furthermore, the implementation exploits the block structure of the problems and offers efficient solutions to manipulate block matrices, including a highly efficient Cholesky factorization on sparse block matrices. In this work, we focus our efforts on testing the method on SLAM applications, but the applicability of the technique remains general. The experimental results show that our implementation outperforms the state of the art SLAM implementations on all the tested datasets.

Many estimation problems in robotics rely on efficiently solving nonlinear least squares (NLS). For example, it is well known that the simultaneous localisation and mapping (SLAM) problem can be formulated as a maximum likelihood estimation (MLE) and solved using NLS, yielding a mean state vector. However, for many applications recovering only the mean vector is not enough. Data association, active decisions, next best view, are only few of the applications that require fast state covariance recovery. The problem is not simple since, in general, the covariance is obtained by inverting the system matrix and the result is dense.The main contribution of this paper is a novel algorithm for fast incremental covariance update, complemented by a highly efficient implementation of the covariance recovery. This combination yields to two orders of magnitude reduction in computation time, compared to the other state of the art solutions. The proposed algorithm is applicable to any NLS solver implementation, and does not depend on incremental strategies described in our previous papers, which are not a subject of this paper.

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This paper describes a systems for emotion recognition and its application on the dataset from the AV+EC 2016 Emotion Recognition Challenge. The realized system was produced and submitted to the AV+EC 2016 evaluation, making use of all three modalities (audio, video, and physiological data). Our work primarily focused on features derived from audio. The original audio features were complement with bottleneck features and also text-based emotion recognition which is based on transcribing audio by an automatic speech recognition system and applying resources such as word embedding models and sentiment lexicons. Our multimodal fusion reached CCC=0.855 on dev set for arousal and 0.713 for valence. CCC on test set is 0.719 and 0.596 for arousal and valence respectively.