This study presents a radial basis function (RBF) aided extended Kalman filter (EKF) (namely, novel RBFEKF: NRBFEKF) to improve attitude estimation solutions in GPS-Denied environments. The NRBFEKF has been developed and applied for attitude estimation using only the outputs of strap-down IMU (gyroscopes and accelerometers) and strap-down magnetometer. In general, neural networks have the capability to map input-output relationships of a system without a-priori knowledge about them. A properly designed RBF neural network is able to learn and extract complex relationships given enough training. Furthermore, if there is a platform with inputs, outputs and many sensors, the RBF is able to adapt all the changes of sensors output. The RBFEKF, which is based on EKF aided by RBF network is validated in Matlab environment using simulated trip data and real data acquired during an UAV's trip. The RBFEKF has increased the accuracy of attitude estimation compared to typical EKF. In addition, the RBF is trained to map the vehicle manoeuvre for tuning measurement noise covariance matrix. Simulation results show that estimated measurement noise covariance matrix is closed to the nominal values in cruise flight (stationary phase), while in non-stationary phase the trained RBF neglects measurements from accelerometers, where accelerometer measurement model is not valid during this phase.

中文翻译：

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径向基函数卡尔曼滤波器在GPS拒绝环境下的姿态估计

这项研究提出了一种径向基函数（RBF）辅助扩展卡尔曼滤波器（EKF）（即新颖的RBFEKF：NRBFEKF），以改善GPS拒绝环境中的姿态估计解决方案。NRBFEKF已开发，仅用于捷联IMU（陀螺仪和加速度计）和捷联磁力计的输出，用于姿态估计。通常，神经网络具有映射系统的输入-输出关系的能力，而无需先验知识。经过适当设计的RBF神经网络能够通过足够的训练来学习和提取复杂的关系。此外，如果有一个带有输入，输出和许多传感器的平台，则RBF能够适应传感器输出的所有变化。RBFEKF，在RBF网络的帮助下，基于EKF的飞机在Matlab环境中使用模拟行程数据和无人机飞行期间获取的实际数据进行了验证。与典型的EKF相比，RBFEKF提高了姿态估计的准确性。另外，RBF被训练以映射车辆操纵以调整测量噪声协方差矩阵。仿真结果表明，估计的测量噪声协方差矩阵在巡航飞行中（平稳阶段）接近标称值，而在非平稳阶段，训练的RBF忽略了来自加速度计的测量，其中加速度计测量模型在此阶段无效。RBF经过训练，可以绘制车辆操纵图以调整测量噪声协方差矩阵。仿真结果表明，估计的测量噪声协方差矩阵在巡航飞行中（平稳阶段）接近标称值，而在非平稳阶段，训练有素的RBF忽略了来自加速度计的测量，其中加速度计测量模型在此阶段无效。RBF经过训练可以绘制车辆操纵图，以调整测量噪声协方差矩阵。仿真结果表明，估计的测量噪声协方差矩阵在巡航飞行中（平稳阶段）接近标称值，而在非平稳阶段，训练的RBF忽略了来自加速度计的测量，其中加速度计测量模型在此阶段无效。