Modification of unscented Kalman filter using a set of scaling parameters

Abstract

This work, based on the standard unscented Kalman filter (UKF), proposes a modified UKF for highly non-linear stochastic systems, assuming that the associated probability distributions are normal. In the standard UKF with 2n + 1 sample points, the estimated mean and covariance match the true mean and covariance up to the third order, besides, there exists a scaling parameter that plays a crucial role in minimising the fourth-order errors. The proposed method consists of a computationally efficient formulation of the unscented transform that incorporates N − 1, N ≥ 2, constant parameters to scale 2n(N − 1) + 1 sample points such that the 2Nth order errors are minimised. The scaling parameters are obtained by solving a set of algebraic equations. Through rigorous analytical processes and numerical simulations, it is demonstrated that the new filter provides consistent estimates and the estimation error of the modified UKF is smaller than that of the standard UKF. With the help of a well-studied case, univariate non-stationary growth model, the authors evaluate the estimation performance of the new technique using 4n + 1 sample points over 100 independent runs.

An Adaptive Turn Rate Estimation for Tracking a Maneuvering Target

“…If v is assumed to be constant, then angular speed, i.e., the turn rate is also constant. The speed v of the target can be calculated at each time step from the estimated velocity components in the output state estimate vector given by v = ξ 2 +η 2 (25) whereξ andη are the velocity components in the x and y directions. Therefore, our aim is to estimate the radius R of the turn at a given instant.…”

“…Furthermore, the speed of the target is calculated from the output state estimate of the algorithm. This output state vector contains the estimated components for both the position and velocity of the target, where the target speed is calculated using (25). The output of the last two mentioned blocks, R k and v k , are then used to calculate the turn rate ω k , which in turn is used in the next time step of the algorithm.…”

“…is more expressive in terms of displaying the results [25]. When the value of LANEES is equal or less than zero, the estimator is said to be consistent at this time step.…”

“…One of these types uses a known turn rate, whereas the other adaptively estimates it using the speed and acceleration. These algorithms are evaluated in various maneuvers in terms of the normalized position error [18] and estimator consistency [25].…”

Tracking Algorithms Aided by the Pose of Target

“…Particle filter algorithm (PF) is not adopted because of its large amount of calculation and low engineering application value. In this paper, the proposed algorithms are compared with the traditional extended Kalman filter algorithm (EKF) [21]- [23] and the traditional UKF [24]- [26] in the following aspects: the root mean square error of the target position, the mean square error of the velocity, the convergence speed and the computation time. The proposed algorithms can greatly improve the target tracking accuracy (position precision and velocity precision) and the convergence speed, and the Pose-EKF is better than Pose-UKF in terms of computation time.…”