弱GNSS信号下基于EMD和LSTM的车辆位置预测方法研究

针对弱GNSS环境下组合导航（INS/GNSS）系统存在的定位偏差问题，提出一种基于经验模态分解和长短期记忆网络的车辆位置预测算法。首先，针对训练数据中噪声较大的惯导数据，提出一种融合经验模态分解与离散小波变换的降噪算法。该算法基于噪声能量估计和各阶本征模态函数的功率谱密度函数，提出一种确定混合模态函数阶数上下界的方法，并采用离散小波变换硬阈值法对混合模态函数进行滤波处理，最终利用经过处理的各阶模态函数重构原始数据以达到降噪目的。训练数据经过预处理后，采用改进的堆叠式长短期记忆网络离线训练位置预测模型，利用该训练模型可在线实时进行位置预测。针对车辆定位序贯数据预测，提出一种局部数据降噪方法，该方法利用一定长度时间窗口的历史数据，通过线性最小二乘给出当下时刻数据的预估值，并与实际量测值进行滑动平均滤波，优化位置预测的结果。在封闭场地模拟隧道环境下，对长短期记忆网络输入端进行局部数据降噪与不进行降噪处理比较，经度和纬度的归一化均方误差分别下降了13.34%和9.38%，经度和纬度的归一化平均绝对误差分别下降了8.64%和5.41%；在复杂城市交通环境下，检验提出的方法，经度和纬度的归一化均方误差分别下降了6.51%和5.66%，经度和纬度的归一化平均绝对误差分别下降了5.70%和8.23%。试验结果表明，在弱GNSS信号环境下，提出的车辆位置预测方法有效提高了车辆定位精度和稳定性。

Position Prediction Based on Empirical Mode Decomposition and Long Short-term Memory Under Global Navigation Satellite System Outages

To solve the problem of performance deterioration for the inertial navigation system (INS) and global navigation satellite system (GNSS) integrated navigation system during GNSS outages, a position prediction algorithm based on empirical mode decomposition (EMD) and a long short-term memory (LSTM) network is presented. First, we propose a filtering algorithm combining EMD and the discrete wavelet transform to denoise the INS data. This algorithm is used to determine the upper and lower bounds of the order for the mixed intrinsic mode functions (IMFs) based on noise energy estimation and features of the power spectral density function for each IMF. Meanwhile, hard wavelet thresholding is adopted to filter the mixed IMFs, and the processed IMFs are then used to reconstruct the original data. After data preprocessing, a stacked LSTM network is applied to train the position predictor, and the trained model is then used to predict the longitude and latitude online. By considering the sequential arrival characteristics of the practical data, a local denoising approach is proposed. This approach uses partial historical data to predict the value at the present moment, and then moving average filtering is applied to promote the prediction accuracy. The performance of the long short-term memory network combined with the data noise reduction method is compared with that of the method in which no data noise reduction is implemented. In a tunnel of the closed field testbed, the normalized mean square error of longitude and latitude are, respectively, reduced by 13.34% and 9.38%, and the normalized mean absolute error are, respectively, reduced by 8.64% and 5.41%. In a complex urban traffic environment, the normalized mean square error of longitude and latitude are, respectively, reduced by 6.51% and 5.66%, and the normalized mean absolute error are, respectively, reduced by 5.70% and 8.23%. The experimental results demonstrate that the proposed model improves the accuracy and robustness of poisoning under GNSS outages.