Real-time states estimation of a farm tractor using dynamic mode decomposition

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.