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In this article, we consider the problem of planar graph-based simultaneous localization and mapping (SLAM) that involves both poses of the autonomous agent and positions of observed landmarks. We present complex (CPL)-SLAM, an efficient and certifiably correct algorithm to solve planar graph-based SLAM using the complex number representation. We formulate and simplify planar graph-based SLAM as the maximum likelihood estimation on the product of unit complex numbers, and relax this nonconvex quadratic complex optimization problem to convex complex semidefinite programming (SDP). Furthermore, we simplify the corresponding complex SDP to Riemannian staircase optimization (RSO) on the complex oblique manifold that can be solved with the Riemannian trust region method. In addition, we prove that the SDP relaxation and RSO simplification are tight as long as the noise magnitude is below a certain threshold. The efficacy of this work is validated through applications of CPL-SLAM and comparisons with existing state-of-the-art methods on planar graph-based SLAM, which indicates that our proposed algorithm is capable of solving planar graph-based SLAM certifiably, and is more efficient in numerical computation and more robust to measurement noise than existing state-of-the-art methods. The C++ code for CPL-SLAM is available at https://github.com/MurpheyLab/CPL-SLAM. [ABSTRACT FROM AUTHOR]

3-D registration has always been performed invoking singular value decomposition (SVD) or eigenvalue decomposition (EIG) in real engineering practices. However, these numerical algorithms suffer from uncertainty of convergence in many cases. A novel fast symbolic solution is proposed in this article by following our recent publication in this journal. The equivalence analysis shows that our previous solver can be converted to deal with the 3-D registration problem. Rather, the computation procedure is studied for further simplification of computing without complex-number support. Experimental results show that the proposed solver does not loose accuracy and robustness but improves the execution speed to a large extent by almost 50%–80%, on both a personal computer (PC) and an embedded processor. Note to Practitioners—3-D registration usually has a large computational burden in engineering tasks. The proposed symbolic solution can directly solve the eigenvalue and its associated eigenvector. A lot of computation resources can then be saved for better overall system performance. The deterministic behavior of the proposed solver also ensures long-endurance stability and can help an engineer better design thread timing logic. [ABSTRACT FROM AUTHOR]

In this paper, simple methodologies of deep learning application to conventional multiple-input multiple-output (MIMO) communication systems are presented. The deep learning technologies with deep neural network (DNN) structure, emerging technologies in various engineering areas, have been actively investigated in the field of communication engineering as well. In the physical layer of conventional communication systems, there are practical challenges of application of DNN: calculating complex number in DNN and designing proper DNN structure for a specific communication system model. This paper proposes and verifies simple solutions for the difficulty. First, we apply a basic DNN structure for signal detection of one-tap MIMO channel. Second, convolutional neural network (CNN) and recurrent neural network (RNN) structures are presented for MIMO system with multipath fading channel. Our DNN structure for one-tap MIMO channel can achieve the optimal maximum likelihood detection performance, and furthermore, our CNN and RNN structures for multipath fading channel can detect the transmitted signal properly. [ABSTRACT FROM AUTHOR]