Adaptive Sparse Cyclic Coordinate Descent for Sparse Frequency Estimation

The frequency estimation of multiple complex sinusoids in the presence of noise is important for many signal processing applications. As already discussed in the literature, this problem can be reformulated as a sparse representation problem. In this letter, such a formulation is derived and an algorithm based on sparse cyclic coordinate descent (SCCD) for estimating the frequency parameters is proposed. The algorithm adaptively reduces the size of the used frequency grid, which eases the computational burden. Simulation results revealed that the proposed algorithm achieves similar performance to the original formulation and the Root-multiple signal classification (MUSIC) algorithm in terms of the mean square error (MSE), with significantly less complexity.

A General Approach Based on Newton’s Method and Cyclic Coordinate Descent Method for Solving the Inverse Kinematics

The inverse kinematics of robot manipulators is a crucial problem with respect to automatically controlling robots. In this work, a Newton-improved cyclic coordinate descent (NICCD) method is proposed, which is suitable for robots with revolute or prismatic joints with degrees of freedom of any arbitrary number. Firstly, the inverse kinematics problem is transformed into the objective function optimization problem, which is based on the least-squares form of the angle error and the position error expressed by the product-of-exponentials formula. Thereafter, the optimization problem is solved by combining Newton’s method with the improved cyclic coordinate descent (ICCD) method. The difference between the proposed ICCD method and the traditional cyclic coordinate descent method is that consecutive prismatic joints and consecutive parallel revolute joints are treated as a whole in the former for the purposes of optimization. The ICCD algorithm has a convenient iterative formula for these two cases. In order to illustrate the performance of the NICCD method, its simulation results are compared with the well-known Newton–Raphson method using six different robot manipulators. The results suggest that, overall, the NICCD method is effective, accurate, robust, and generalizable. Moreover, it has advantages for the inverse kinematics calculations of continuous trajectories.