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In this paper we focus on the relative position and orientation estimation between rigid bodies in an anchorless scenario. Several sensor units are installed on the rigid platforms, and the sensor placement on the rigid bodies is known beforehand (i.e., relative locations of the sensors on the rigid body are known). However, the absolute position of the rigid bodies is not known. We show that the relative localization of rigid bodies amounts to the estimation of a rotation matrix and the relative distance between the centroids of the rigid bodies.

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Linear canonical transform (LCT) is an attractive and useful tool in optics and signal processing. In previous work, a generalization of the LCT with two extra parameters, called offset LCT (OLCT), has been developed. In this paper, a different definition of OLCT is proposed, which has a more concise form of inverse transform. We find a linear operator that commutes with the proposed OLCT. We prove that the commuting operator and the proposed OLCT have the same set of eigenfunctions with different eigenvalues.

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The paper quantifies and compares the exact asymptotic performance of multiple measurement vector (MMV) and distributed sensing (DS) models. Both models assume multiple measurement instances y_k = A_kx_k + w_k; k = 1,2,...,K. The difference is that MMV involves identical measurement matrices whereas DS allows different matrices for different measurement instances. It has been recognized that DS works better than MMV empirically. However, the quantification of the performance difference is not available in the literature.

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This paper considers unconstrained convex optimiza- tion problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction steps, while sampling the problem data at a constant rate of 1{h, where h is the length of the sampling interval. The prediction step is derived by analyzing the iso-residual dynamics of the optimality conditions.

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