In this paper we study general complex eigenvalue problems in engineering fields. The eigenvalue problems can be transformed into the associated problems for solving large systems of nonlinear ordinary differential equations (dynamic equations) by optimization techniques. The known waveform relaxation method in circuit simulation can then be successfully applied to compute the resulting dynamic equations. The approach reported here, which is implemented on a message passing multi-processor system, can determine all eigenvalues and their eigenvectors for general complex matrices without any restriction on the matrices. The numerical results are provided to confirm the theoretical analysis.

Maneuvering target tracking under mixed line-of-sight/non-line-of-sight (LOS/NLOS) conditions has received considerable interest in the last decades. In this paper, a hierarchical interacting multiple model (HIMM) method is proposed for estimating target position under mixed LOS/NLOS conditions. The proposed HIMM is composed of two layers with Markov switching model. The purpose of the upper layer, which is composed of two interacting multiple model (IMM) filters in parallel, is to handle the switching between the LOS and the NLOS environments. To estimate the target kinetic variables (position, speed and acceleration), the unscented Kalman filter (UKF) with the current statistical (CS) model is used in the lower-layer. Simulation results demonstrate the effectiveness and superiority of the proposed method, which obtains better tracking accuracy than the traditional IMM.