Chaotic systems are complex dynamical systems that play a very important role in the study of the atmosphere, aerospace engineering, finance, etc. To improve the accuracy of chaotic time series prediction, this study proposes a hybrid model CEEMDAN-LSTM which combines Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and long short-term memory (LSTM). In the model, the original time series is decomposed into several intrinsic mode functions (IMFs) and a residual component. To reduce the difficulty of predicting chaotic time series and provide a high level of predictive accuracy, the LSTM prediction model is built for all each characteristic series from CEEMDAN deposition. Finally, the final prediction results are obtained by combining all the prediction sequences. To test the effectiveness of this model we proposed, we examined the CEEMDAN-LSTM model using the Lorenz-63 system. Further compared to Autoregressive Integrated Moving Average (ARIMA ), Support Vector Regression (SVR), multilayer perceptron (MLP), and the single LSTM model, the results of the experiment show that the proposed model performs better in the prediction of chaotic time series. Besides, the hybrid model proposed in this paper has better results than the LSTM model alone. Therefore, hybrid models based on deep learning methods and signal decomposition methods have great potential in the field of chaotic time series prediction.
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As an emerging orbital system with flexibility and brand application prospects, the highly elliptical orbit synthetic aperture radar (HEO SAR) can achieve both a low orbit detailed survey and continuous earth surface observation in high orbit, which could be applied to marine reconnaissance and surveillance. However, due to its large eccentricity, two challenges have been faced in the signal processing of HEO SAR at present. The first challenge is that the traditional equivalent squint range model (ESRM) fails to accurately describe the entire range for the whole orbit period including the perigee, the apogee, and the squint subduction section. The second one is to exploit an efficient HEO SAR imaging algorithm in the squinted case which solves the problem that traditional imaging algorithm fails to achieve the focused imaging processing of HEO SAR during the entire orbit period. In this paper, a novel imaging algorithm for HEO SAR is presented. Firstly, the signal model based on the geometric configuration of the large elliptical orbit is established and the Doppler parameter characteristics of SAR are analyzed. Secondly, due to the particularity of Doppler parameters variation in the whole period of HEO, the equivalent velocity and equivalent squint angle used in MESRM can no longer be applied, a refined fourth-order equivalent squint range model(R4-ESRM) that is suitable for HEO SAR is developed by introducing fourth-order Doppler parameter into Modified ESRM (MESRM), which accurately reconstructs the range history of HEO SAR. Finally, a novel imaging algorithm combining azimuth resampling and time-frequency domain hybrid correlation based on R4-ESRM is derived. Simulation is performed to demonstrate the feasibility and validity of the presented algorithm and range model, showing that it achieves the precise phase compensation and well focusing.
A novel space-borne SAR technique, azimuthal multi-angle observation (AMAO), has recently been proposed. It has highly flexible working modes and powerful capability of target information acquisition, but has challenges in achieving radiometric measurement accuracy. The larger the squint angle, the higher the resolution and the more variations involved. Radiometric calibration is a necessary approach to consistent and accurate SAR measurements, but has so far not been carefully considered for AMAO space-borne SAR. This paper addressed the new issues in radiometric calibration arising from the AMAO space-borne SAR system. The AMAO imaging modes are firstly been illustrated, based on which the influences of the AMAO on radiometric calibration are analyzed. To guarantee the accuracy of the radiometric calibration, an appropriate form of the SAR radar equation is derived for AMAO space-borne SAR. On these bases, the calibration models can be obtained by reformulating the novel AMAO SAR equation, and the corresponding normalization method is then proposed. The good experimental performance indicators verify the correctness of proposed models and the effectiveness of the correction method.
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