We present a pure data-driven method to estimate vehicle dynamics from the measurements of sideslip and yaw rate in the use of GPS and inertial navigation system. The GPS and INS configuration provides vehicle position, velocity vector, vehicle orientation, and yaw rate observations. A new dynamic mode decomposition with control (DMDc) method denoises the state observations by adopting the total least-squares algorithm. The total least-squares DMD with control (tlsDMDc) helps discover the underlying dynamics with the time-dependent observations of states and external control. The experiments of a simulated linear dynamic model with synthetic Gaussian noise illustrate that the solutions of tlsDMDc are more accurate than the standard DMDc to characterize underlying dynamics with imperfect measurements. We additionally investigate how the algorithm performs on vehicle motion deduction and sensor bias correction. It has been shown that the tlsDMDc-based state estimator with the couple of GPS and inertial sensor measurements provides accurate and robust observation in the presence of model error and measurement noise.

我们提出了一种纯粹的数据驱动方法，可通过使用GPS和惯性导航系统从侧滑和偏航率的测量值估算车辆动力学。GPS和INS配置可提供车辆位置，速度矢量，车辆方向和偏航率观测结果。一种新的带有控制的动态模式分解（DMDc）方法通过采用总最小二乘算法对状态观测值进行降噪。带控制权的总最小二乘DMD（tlsDMDc）通过状态和外部控制的时间依赖性观察来帮助发现潜在的动态。具有合成高斯噪声的模拟线性动力学模型的实验表明，tlsDMDc的解决方案比标准DMDc更加准确，可以用不完美的测量来表征潜在的动力学。我们还研究了该算法如何在车辆运动推导和传感器偏差校正上执行。研究表明，在存在模型误差和测量噪声的情况下，基于tlsDMDc的状态估计器具有GPS和惯性传感器测量功能，可以提供准确而可靠的观察结果。