Gaussian Integral based Bayesian Smoother

This work introduces the Gaussian integration to address a smoothing problem of a nonlinear stochastic state space model. The probability densities of states at each time instant are assumed to be Gaussian, and their means and covariances are evaluated by utilizing the odd-even properties of Gaussian integral, which are further utilized to realize Rauch-Tung-Striebel (RTS) smoothing expressions. Given that the Gaussian integration provides an exact solution for the integral of a polynomial function over a Gaussian probability density function, it is anticipated to provide more accurate results than other existing Gaussian approximation-based smoothers such as extended Kalman, cubature Kalman, and unscented Kalman smoothers, especially when polynomial types of nonlinearity are present in the state space models. The developed smoothing algorithm is applied to the Van der Pol oscillator, where the nonlinearity associated with their dynamics is represented using polynomial functions. Simulation results are provided to demonstrate the superiority of the proposed algorithm.

Dynamics of a Towed Cable with Sensor-Array for Underwater Target Motion Analysis

During a war situation, many times an underwater target motion analysis (TMA) is performed using bearing-only measurements, obtained from a sensor array, which is towed by an own-ship with the help of a connected cable. It is well known that the own-ship is required to perform a manoeuvre in order to make the system observable and localise the target successfully. During the maneuver, it is important to know the location of the sensor array with respect to the own-ship. This paper develops a dynamic model of a cable-sensor array system to localise the sensor array, which is towed behind a sea-surface vessel. We adopt a lumped-mass approach to represent the towed cable. The discretized cable elements are modelled as an interconnected rigid body, kinematically related to one another. The governing equations are derived by balancing the moments acting on each node. The derived dynamics are solved simultaneously for all the nodes to determine the orientation of the cable and sensor array. The position of the sensor array obtained from this proposed model will further be used by TMA algorithms to enhance the accuracy of the tracking system.

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.