key: cord-0060950-o6jhkaq4 authors: Ji, Yv; Yao, Xu; Wang, Xiaodong; Shen, Mingwei title: Wind Turbine Clutter Suppression for Weather Radar Using Improved Ridge Regression Approach date: 2020-06-13 journal: Multimedia Technology and Enhanced Learning DOI: 10.1007/978-3-030-51103-6_40 sha: 7e558465e004461190aef83edba9e95451e66aa5 doc_id: 60950 cord_uid: o6jhkaq4 The problem of clutter suppression is gaining importance because of many disadvantages. However, conventional clutter suppression methods cannot eliminate the great disturbances to radar system caused by wind turbines. An improved ridge regression algorithm is investigated to accurately estimate the spectral moment of the weather signal contaminated by wind turbine clutter (WTC) in this paper. Firstly, a weighted regression model is introduced to solve the problem that the strong collinearity of the data in the regression model leads to unstable parameter estimation. Then the optimal regression parameter in the model is obtained by generalized cross validation (GCV) to improve the estimation accuracy of weather signal. Theoretical analysis and simulation results show that the spectral moment recovered by the proposed algorithm has better accuracy and stability in lower SNR. In recent years, the clutter suppression technology of wind turbine by weather radar has be widely concerned by more and more countries. By using simulation and measured data, scientists from various countries have analyzed the distribution characteristics of clutter and weather echo of wind turbine under different working modes of weather radar both in the time-domain and frequency-domain in detail. Accordingly, different suppression algorithms are proposed as followings: the adaptive spectrum processing algorithm proposed by Kong [1] ; the range-doppler regression (RDR) algorithm proposed by Nail [2] , the turbine clutter suppression method based on the adaptive filter (such as wiener filter, etc.) proposed by Yan [3] , and the signal separation method proposed by Frank [4] . Regression algorithm is widely used in clutter suppression for the simple model and high operational efficiency. However, due to the limitations of wind farm scale, fan speed, weather radar working mode and other practical conditions, the above algorithm cannot take into account clutter suppression of wind turbines and lossless recovery of weather information. In view of the above problems, in this paper, based on the RDR algorithm, an improved ridge regression algorithm is studied. By introducing the weighted regression model, and selecting generalized cross validation (GCV) in solving the optimal regression parameter achieve the effect of optimizing the solving process. Moreover, the calculated ridge regression coefficient for the collinearity and stronger robustness is ensured, and the high precision of the recover of contaminated weather echo signal information is realized. Assuming that the wind turbine clutter(WTC) signal is received by the i th range bin of the weather radar, and the received signal under the k th pulse is [5] : where K is the pulse number, s i (k) is the weather signal, w i (k) is the wind turbine clutter, n i (k) denotes the noise. Adjacent range bins do not contain WTC signals, and the received signal under the k th pulse is: The dynamic clutter caused by the high-speed rotation of the blades of wind turbines has a wide doppler spectrum, so WTC and weather targets will produce serious overlap in time and frequency domains, that is, the weather signal will be submerged in the clutter of wind turbines, and the spectral moment information of the weather signal of the polluted range bin will be seriously disturbed. Ridge regression is an improved method of least square estimation. Regularization is carried out on the original regression model and the solution process was optimized by adding penalty term. The general regression model is defined as follows: where Y is the real values of spectral moment parameters, b is the regression coefficient to be found, and X is a fitting matrix defined as: where r i is the slant distance size of scattered points of the i th range bin, the dimension of X LÂM is L  M. L is the amount of selected units which is defined as L = 20, that is to take 10 range bins on both sides of the i th range bin with WTC contamination, and M is the degree of polynomial which is defined as M = 3. A fitting estimation matrix including distance units contaminated by WTC is denoted as X à : Ridge regression cost function is given by: where k ridge is ridge regression parameter. Ridge regression coefficient is solved as follows: The estimated value of the corresponding parameter Y is given by: The algorithm uses the weather information of unpolluted range bins, introduces an improved ridge regression algorithm, and then estimates the average doppler velocity, velocity spectrum width, power and other effective information of weather signals in the polluted range bin through efficient fitting. The average doppler velocity of the echo signal is estimated as follows [6] : The average spectral width is estimated as: The average power is estimated as: where R 0l Represents zero delay auto-correlation parameter of echo signal sequence of the l th unit to be processed, and R 1l represents the first order auto-correlation parameter of the echo signal sequence of the l th range bin. Ultimately the estimated spectral moment parameters of the weather signal in the unit polluted by WTC can be obtained as V est , r est and p est . An improved ridge regression uses the weighted regression model, and solves the optimal regression parameter by introducing GCV. Suppose the singular value decomposition of the X in the regression model is: where U is a positive definite matrix of order L, and V is that of M. The dimension of D is L  M, the diagonal element of which is the square root of the eigenvalue where W is the fitting weight corresponding to each range bin. The fitting weight of the j th range bin nearby is: where L prox is the distance threshold, and L prox ¼ 10. The validation function of generalized cross validation is as follows: which can be simplified as: where U T Y ¼ ðy 1 ; y 2 ; . . .; y L Þ, and c n is defined by: The obtained optimal ridge regression parameter k à ridge is substituted into the improved ridge regression model, and the estimated values of spectral moment parameters of the weather signal in the range bin polluted by WTC are input to obtain the fitting values of spectral moment parameters of meteorological signals in the range bin polluted by WTC, which contains v ridge , r ridge and p ridge . The validity of the proposed algorithm is verified by computer simulation. The main simulation parameters of the radar system are listed in Table 1. RDR algorithm [2] proposed by Nail is selected for performance comparison in this paper. Firstly, the solution of optimal ridge regression parameters is verified. GCV is introduced into ridge regression algorithm to solve the optimal ridge regression parameter. Due to the fitting matrix of every scatter points is in contact with the weather signal model of oblique distance only, the optimal value of the ridge regression parameter given by GCV is a constant. The polynomial fitting method is adopted to estimate spectral moment of weather signals in the polluted range bin. As shown in Fig. 1, 2 and 3 , when the SNR is lower than 5 dB, the fitting error of this algorithm is better than that of RDR. That is, this algorithm can still estimate spectral moment with higher accuracy under the condition of low SNR, and the recovered weather signal returns have higher accuracy, which effectively suppressing the influence of WTC on weather information. This paper proposes the weighted ridge regression model for suppression of WTC for weather radars. GCV is introduced to solve the optimal regression parameter, and the spectral moment parameters of weather signals in the range bin polluted by WTC are fitted with high accuracy. Compared with RDR algorithm, the fitting error of the algorithm in this paper is smaller under the condition of low SNR, and the recovered spectral moment information is more accurate. Characterization of micro-Doppler radar signature of commercial wind turbines On the mitigation of wind turbine clutter for weather radars using range-Doppler spectral processing 3 Wind turbine clutter mittigation for weather radar: a feasibility study by means of scaled measurement Mitigation of wind turbine clutter for weather radar by signal separation Signal processing for wind turbine interference mitigation in Doppler weather radars: Data synthesis, clutter detector performance, and spectral interpolation in range-azimuth-Doppler Automatic detection of wind turbine clutter for weather radars Acknowledgement. This work was supported in part by National Natural Science Foundation of China (No. 41830110, No. 61771182).