A Real-Valued 2D DOA Estimation Algorithm of Noncircular Signal via Euler Transformation and Rotational Invariance Property

The problem of two-dimensional(2 D)direction of arrival(DOA)estimation for double parallel uniform linear arrays is investigated in this paper.A real-valued DOA estimation algorithm of noncircular(NC)signal is proposed,which combines the Euler transformation and rotational invariance(RI)property between subarrays.In this work,the effective array aperture is doubled by exploiting the noncircularity of signals.The complex arithmetic is converted to real arithmetic via Euler transformation.The main contribution of this work is not only extending the NC-Euler-ESPRIT algorithm from uniform linear array to double parallel uniform linear arrays,but also constructing a new 2 Drotational invariance property between subarrays,which is more complex than that in NCEuler-ESPRIT algorithm.The proposed 2 DNC-Euler-RI algorithm has much lower computational complexity than2 DNC-ESPRIT algorithm.The proposed algorithm has better angle estimation performance than 2 DESPRIT algorithm and 2 D NC-PM algorithm for double parallel uniform linear arrays,and is very close to that of 2 D NC-ESPRIT algorithm.The elevation angles and azimuth angles can be obtained with automatically pairing.The proposed algorithm can estimate up to 2(M-1)sources,which is two times that of 2 D ESPRIT algorithm.Cramer-Rao bound(CRB)of noncircular signal is derived for the proposed algorithm.Computational complexity comparison is also analyzed.Finally,simulation results are presented to illustrate the effectiveness and usefulness of the proposed algorithm.

Implementation of Control Algorithms in Small Embedded Systems

This work describes how a control algorithm can be implemented in a small (8-bit) microcontroller for the main purpose of merging embedded systems and control theory in electrical engineering undergraduate classes. Two different methods for discretizing the control expression are compared: Euler transformation and bilinear transformation. The sampling rate’s impact on the algorithm is discussed and theoretical results are verified by an application to a temperature control system in a heating plant. Four control algorithms are compared: PID and PI algorithms discretized with Euler and bilinear transformation, respectively. It is shown that for the heating plant used in this work, a bilinear PI algorithm implemented in a small 8-bit microcontroller outperforms a commercial controller from Panasonic. It is also demonstrated that all the derived algorithms can be implemented using integer calculations only, obviating the need for expensive and time-consuming floating-point calculations. This work bridges the gap between control theory equations and the implementation of control systems in small embedded systems with no inherent floating-point processing power.

Analysis of Dynamic Characteristics of Crustal Horizontal Deformation in the South Segment of Longmenshan Fault Zone Revealed by GPS Data after the Wenchuan Earthquake

In order to obtain deformation parameters in the south segment of Longmenshan fault zone,Euler datum transformation and the least square collocation for data interpolation and smoothing are used to process GPS displacement time series data in the south segment of Longmenshan fault zone,and the rigid and elastic-plastic block motion model is used to calculate the strain parameters in each subarea. Conjoint analysis of displacement,velocity of each station and strain parameters of each subarea reveals that the influence of the Wenchuan earthquake on the south segment of Longmenshan fault zone increases from southeast to northwest,causing a highest deformation rate 6 times the background value and heightening the influence of the hidden faults on the difference of the earth surface along its two sides,which leads to the seismic risk of the southern segment increasing from north to south. The comparison of seismic risk among subareas based on the tectonic and seismicity background indicates that the most dangerous area is on the southeast of Longmenshan faults,and the background strain accumulation and the promoting effect of the Wenchuan earthquake advanced the occurrence of Lushan earthquake and the sinistral strike-slip on the rupture plane. The Wenchuan earthquake also caused a slight two-year long continuous strain release in the south segment of Xianshuihe fault,but the influence is far less than the effect of the compressive strain caused by the Sichuan-Yunnan block.