Method for array gain and phase uncertainties calibration based on ISM and ESPRIT

A new method for array calibration of array gain and phase uncertainties, which severely degrade the performance of spatial spectrum estimation, is presented. The method is based on the idea of the instrumental sensors method （ISM）, two well-calibrated sensors are added into the original array. By applying the principle of estimation of signal parameters via rotational invariance techniques （ESPRIT）, the direction-of-arrivals （DOAs） and uncertainties can be estimated simultaneously through eigen-decomposition. Compared with the conventional ones, this new method has less computational complexity while has higher estimation precision, what＇s more, it can overcome the problem of ambiguity. Both theoretical analysis and computer simulations show the effectiveness of the proposed method.

Study on fast calibration of a ULA's gain and phase error

Array calibration is important in engineering practice. In this paper, fast calibration methods for a ULA's gain and phase errors both in far and near fields are proposed. In the far field, using a single sound source without exact orientation, this method horizontally rotates the array exactly once, performs eigen value decomposition for the covariance matrix of received data, then computes the gain and phase error according to the formulas. In the near field, using the same single sound source, it is necessary to rotate the array horizontally at most three times, build equations according to geometric relations, then solve them. Using the formula proposed in this paper, spherical waves are modified into plane waves. Then eigen values decomposition is performed. These two calibration methods were shown to be valid by simulation and are fast, accurate and easy to use. Finally, an analysis of factors influencing estimation precision is given.

Array calibration of angularly dependent gain and phase uncertainties with carry-on instrumental sensors

Array calibration with angularly dependent gain and phase uncertainties has long been a difficult problem. Although many array calibration methods have been reported extensively in the literature, they almost all assumed an angularly independent model for array uncertainties. Few calibration methods have been developed for the angularly dependent array uncertainties. A novel and efficient auto-calibration method for angularly dependent gain and phase uncertainties is proposed in this paper, which is called ISM (Instrumental Sensors Method). With the help of a few well-calibrated instrumental sensors, the ISM is able to achieve favorable and unambiguous direction-of-arrivals (DOAs) estimate and the corresponding angularly dependent gain and phase estimate simultaneously, even in the case of multiple non-disjoint sources. Since the mutual coupling and sensor position errors can all be described as angularly dependent gain/phase uncertainties, the ISM proposed still works in the presence of a combination of all these array perturbations. The ISM can be applied to arbitrary array geometries including linear arrays. The ISM is computationally efficient and requires only one-dimensional search, with no high-dimensional nonlinear search and convergence burden involved. Besides, no small error assumption is made, which is always an essential prerequisite for many existing array calibration techniques. The estimation performance of the ISM is analyzed theoretically and simulation results are provided to demonstrate the effectiveness and behavior of the proposed ISM.

Joint calibration algorithm for gain-phase and mutual coupling errors in uniform linear array

The effect of gain-phase perturbations and mutual coupling significantly degrades the performance of digital array radar (DAR). This paper investigates array calibration problems in the scenario where the true locations of auxiliary sources deviate from nominal values but the angle intervals are known. A practical algorithm is proposed to jointly calibrate gain-phase errors and mutual coupling errors. Firstly, a simplified model of the distortion matrix is developed based on its special structure in uniform linear array (ULA). Then the model is employed to derive the precise locations of the auxiliary sources by one-dimension search. Finally, the least-squares estimation of the distortion matrix is obtained. The algorithm has the potential of achieving considerable improvement in calibration accuracy due to the reduction of unknown parameters. In addition, the algorithm is feasible for practical applications, since it requires only one auxiliary source with the help of rotation platforms. Simulation results demonstrate the validity, robustness and high performance of the proposed algorithm. Experiments were carried out using an S-band DAR test-bed. The results of measured data show that the proposed algorithm is practical and effective in application. (C) 2016 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics.

Robustness assessment for flight control system of an oceanographic unmanned aerial vehicle

A post-design robustness assessment for the longitudinal flight control system of an oceanographic unmanned aerial vehicle （UAV） is presented in this paper. Two novel systematic approaches of generating the linear fractional transformation （LFT） model directly from nonlinear equations are proposed for this particular robustness analysis problem. The closed-loop system combined with each controller is used to determine combinations of aerodynamic parameters that result in worst-case performance. Classical simultaneous gain and phase margin stability metrics currently used in the aerospace industry are introduced for the certification of robustness of this uncertain multivariable system. The results show that the control system remains stable and achieves desired performance for all possible parameter variations over a specified range in both frequency domain and time domain.

Analysis and Design of Scaling Optimal GPM-PID Control with Application to Liquid Level Control

In this paper, a new analysis and design method for proportional-integrative-derivative （PID） tuning is proposed based on controller scaling analysis. Integral of time absolute error （ITAE） index is minimized for specified gain and phase margins （GPM） constraints, so that the transient performance and robustness are both satisfied. The requirements on gain and phase margins are ingeniously formulated by real part constraints （RPC） and imaginary part constraints （IPC）. This set of new constraints is simply related with three parameters and decoupling of the remaining four unknowns, including three controller parameters and the gain margin, in the nonlinear and coupled characteristic equation simultaneously. The formulas of the optimal GPM-PID are derived based on controller scaling analysis. Finally, this method is applied to liquid level control of coke fractionation tower, which demonstrate that the proposed method provides better disturbance rejection and robust tracking performance than some commonly used PID tuning methods.