Maximum Correntropy Polynomial Chaos Kalman Filter for Underwater Navigation

This paper develops an underwater navigation solution that utilizes a strapdown inertial navigation system (SINS) and fuses a set of auxiliary sensors such as an acoustic positioning system, Doppler velocity log, depth meter, attitude meter, and magnetometer to accurately estimate an underwater vessel's position and orientation. The conventional integrated navigation system assumes Gaussian measurement noise, while in reality, the noises are non-Gaussian, particularly contaminated by heavy-tailed impulsive noises. To address this issue, and to fuse the system model with the acquired sensor measurements efficiently, we develop a square root polynomial chaos Kalman filter based on maximum correntropy criteria. The filter is initialized using acoustic beaconing to accurately locate the initial position of the vehicle. The computational complexity of the proposed filter is calculated in terms of flops count. The proposed method is compared with the existing maximum correntropy sigma point filters in terms of estimation accuracy and computational complexity. The simulation results demonstrate an improved accuracy compared to the conventional deterministic sample point filters.

Robust Maximum Correntropy Kalman Filter

The Kalman filter provides an optimal estimation for a linear system with Gaussian noise. However when the noises are non-Gaussian in nature, its performance deteriorates rapidly. For non-Gaussian noises, maximum correntropy Kalman filter (MCKF) is developed which provides an improved result. But when the system model differs from nominal consideration, the performance of the MCKF degrades. For such cases, we have proposed a new robust filtering technique which maximize a cost function defined by exponential of weighted past and present errors along with the Gaussian kernel function. By solving this cost criteria we have developed prior and posterior mean and covariance matrix propagation equations. By maximizing the correntropy function of error matrix, we have selected the kernel bandwidth value at each time step. Further the conditions for convergence of the proposed algorithm is also derived. Two numerical examples are presented to show the usefulness of the new filtering technique.