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In this paper we study the problem of automatically generating polynomial solvers for minimal problems. The main contribution is a new method for finding small elimination templates by making use of the syzygies (i.e. the polynomial relations) that exist between the original equations. Using these syzygies we can essentially parameterize the set of possible elimination templates. We evaluate our method on a wide variety of problems from geometric computer vision and show improvement compared to both handcrafted and automatically generated solvers. Furthermore we apply our method on two previously unsolved relative orientation problems.

strategy for selecting a basis which improves the conditioning of a crucial elimination step, (ii) use this technique to devise a Gröbner basis with improved precision and (iii) show how solving for the eigenvalues instead of eigenvectors can be used to improve precision further while retaining the same speed.We study these methods on some of the latest reported uses of Gröbner basis methods and demonstrate dramatically improved numerical precision using these new techniques making it possible to solve a larger class of problems than previously.

Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this paper we show how we can make polynomial solvers based on the action matrix method faster, by careful selection of the monomial bases. These monomial bases have traditionally been based on a Gröbner basis for the polynomial ideal. Here we describe how we can enumerate all such bases in an efficient way. We also show that going beyond Gröbner bases leads to more efficient solvers in many cases. We present a novel basis sampling scheme that we evaluate on a number of problems.

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In this paper, we present a robust multipath-based localization and mapping framework that exploits the phases of specular multipath components (MPCs) using a massive multipleinput multiple-output (MIMO) array at the base station. Utilizing the phase information related to the propagation distances of the MPCs enables the possibility of localization with extraordinary accuracy even with limited bandwidth. The specular MPC parameters along with the parameters of the noise and the dense multipath component (DMC) are tracked using an extended Kalman filter (EKF), which enables to preserve the distancerelated phase changes of the MPC complex amplitudes. The DMC comprises all non-resolvable MPCs, which occur due to finite measurement aperture. The estimation of the DMC parameters enhances the estimation quality of the specular MPCs and therefore also the quality of localization and mapping. The estimated MPC propagation distances are subsequently used as input to a distance-based localization and mapping algorithm. This algorithm does not need prior knowledge about the surrounding environment and base station position. The performance is demonstrated with real radio-channel measurements using an antenna array with 128 ports at the base station side and a standard cellular signal bandwidth of 40 MHz. The results show that high accuracy localization is possible even with such a low bandwidth.Index Terms-Parametric channel estimation, extended Kalman filter, massive MIMO radio channel, localization and mapping.