Robust Generalized Loss-Based Nonlinear Filtering with Generalized Conversion

To address the nonlinear state estimation problem, the generalized conversion filter (GCF) is proposed using a general conversion of the measurement under minimum mean square error (MMSE) criterion. However, the performance of the GCF significantly deteriorates in the presence of complex non-Gaussian noise as the symmetry of the MMSE is compromised, leading to performance degradation. To address this issue, this paper proposes a new GCF, named generalized loss-based GCF (GLGCF) by utilizing the generalized loss (GL) as the loss function instead of the MMSE criterion. In contrast to other robust loss functions, the GL adjusts the shape of the function through the shape parameter, allowing it to adapt to various complex noise environments. Meanwhile, a linear regression model is developed to obtain residual vectors, and the negative log-likelihood of GL is introduced to avoid the problem of manually selecting the shape parameter. The proposed GLGCF not only retains the advantage of GCF in handling strong measurement nonlinearity, but also exhibits robust performance against non-Gaussian noises. Finally, simulations on the target-tracking problem validate the strong robustness and high filtering accuracy of the proposed nonlinear state estimation algorithm in the presence of non-Gaussian noise.