Multi-Scaled Unscented Kalman Filter

The unscented Kalman filter (UKF) is a commonly used algorithm capable of estimating the states of nonlinear dynamic systems. It carefully chooses a set of sample points, called sigma points that capture the nonlinear system states posterior mean and covariance. The filter is based on the scaled unscented transform, where the scaling parameters impact the spreading of the sigma points, determining the estimated model capturing. In its current form, the UKF employs a single set of scaling parameters shared by all sigma points. Because states in multi-dimensional models often exhibit substantially different behaviors, this imposes a critical limitation: the standard UKF parameters cannot be tuned to extend the spread for one dimension while reducing it for another. To bridge this gap, we propose the multi-scaled UKF to enable spreading differently per state, while maintaining the key properties of the sigma points and UKF. A rigorous mathematical foundation is provided, introducing a novel theoretical approach to multi-scaling. The benefits of this approach are demonstrated through two distinct nonlinear dynamic systems. Consequently, our multi-scaled UKF captures the nonlinear behavior of multi-dimensional states more effectively, leading to improved estimation accuracy.

Adaptive Neural Unscented Kalman Filter

The unscented Kalman filter is an algorithm capable of handling nonlinear scenarios. Uncertainty in process noise covariance may decrease the filter estimation performance or even lead to its divergence. Therefore, it is important to adjust the process noise covariance matrix in real time. In this paper, we developed an adaptive neural unscented Kalman filter to cope with time-varying uncertainties during platform operation. To this end, we devised ProcessNet, a simple yet efficient end-to-end regression network to adaptively estimate the process noise covariance matrix. We focused on the nonlinear inertial sensor and Doppler velocity log fusion problem in the case of autonomous underwater vehicle navigation. Using a real-world recorded dataset from an autonomous underwater vehicle, we demonstrated our filter performance and showed its advantages over other adaptive and non-adaptive nonlinear filters.