Precise instantaneous velocimetry and accelerometry with a stand-alone GNSS receiver based on sparse kernel learning

A new method is proposed to determine instantaneous velocities and accelerations with a stand-alone GNSS receiver. It is based on sparse kernel learning theory. Kernel trick is employed to represent the kinematics, and L1 norm regularization is used to get sparse solution. Analytical models rather than data series are provided, with which velocity and acceleration at any instant could be calculated. Between-epoch displacements, provided by GNSS time difference carrier phase technique, are used as training data. Efficient numerical algorithms, such as the tri-diagonal matrix algorithm and the fast iterative shrinkage thresholding algorithm, are employed to deal with the between-epoch correlations in the data and the L1 norm regularization, respectively. The hyperparameters are optimized using general cross validation or Akaike information criterion, both tailored for the L1 norm regularization problem. Both simulation and real-data results show the superior performance of the proposed method compared to the conventional finite difference method. Especially for dynamic cases, the proposed method can better represent the real dynamics and provide high-accuracy velocimetry and accelerometry results. (C) 2020 Elsevier Ltd. All rights reserved.