Orthogonal matching pursuit (OMP) is a commonly used algorithm for recovery sparse signals due to its low complexity and simple implementation. We analyze the convergence property of OMP based on the restricted isometry property (RIP), and show that the OMP algorithm can exactly recover an arbitrary K-sparse signal using K steps provided that the sampling matrix satisfies the RIP with parameter δ K+1 < 1/(1 + 2 √ K). In addition, we also give the convergence analysis of OMP for the case of inaccurate measurements. Moreover, a variant of OMP, referred to as multi-candidate OMP (MOMP) algorithm, is proposed to recover sparse signals, which can further reduce the computational complexity of OMP. The key point of MOMP is that at each step it selects multi-candidates adding to the optimal atom set, whilst OMP only selects one atom. We also present the convergence analysis of MOMP using the RIP. Finally, we testify the performance of the proposed algorithm using several numerical experiments.

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State of charge (SOC) is a key parameter for lithium-ion battery management systems. The square root cubature Kalman filter (SRCKF) algorithm has been developed to estimate the SOC of batteries. SRCKF calculates 2n points that have the same weights according to cubature transform to approximate the mean of state variables. After these points are propagated by nonlinear functions, the mean and the variance of the capture can achieve third-order precision of the real values of the nonlinear functions. SRCKF directly propagates and updates the square root of the state covariance matrix in the form of Cholesky decomposition, guarantees the nonnegative quality of the covariance matrix, and avoids the divergence of the filter. Simulink models and the test bench of extended Kalman filter (EKF), Unscented Kalman filter (UKF), cubature Kalman filter (CKF) and SRCKF are built. Three experiments have been carried out to evaluate the performances of the proposed methods. The results of the comparison of accuracy, robustness, and convergence rate with EKF, UKF, CKF and SRCKF are presented. Compared with the traditional EKF, UKF and CKF algorithms, the SRCKF algorithm is found to yield better SOC estimation accuracy, higher robustness and better convergence rate.