• ETRI Journal
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• v.35 no.5
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• pp.943-946
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• 2013

Instead of the extended Kalman filter, the unscented Kalman filter (UKF) has been used in nonlinear systems without initial accurate state estimates over the last decade because the UKF is robust against large initial estimation errors. However, in a multirate integrated system, such as an inertial navigation system (INS)/Global Positioning System (GPS) integrated navigation system, it is difficult to implement a UKF-based navigation algorithm in a low-grade or mid-grade microcontroller, owing to a large computational burden. To overcome this problem, this letter proposes a modified UKF that has a reduced computational burden based on the basic idea that the change of probability distribution for the state variables between measurement updates is small in a multirate INS/GPS integrated navigation filter. The performance of the modified UKF is verified through numerical simulations.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.2
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• pp.87-94
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• 2013

UKF (Unscented Kalman Filter) has been used in the nonlinear systems without initial accurate state estimates instead of EKF (Extended Kalman Filter) of the last decade because the UKF has robustness to the large initial estimation error. In the multirate integrated system such as INS (Inertial Navigation System)/GPS (Global Positioning System) integrated navigation system, however, it is difficult to implement the UKF based navigation algorithm in the mid-grade micro-processor due to the large computational burden. To overcome this problem, this paper proposes a MUKF (Modified UKF) that has a reduced computation burden using the basic idea that the change of the provability distribution for the state variables between measurement updates is small in the multi-rate INS/GPS integrated navigation filter. The performance of the proposed MUKF is verified by numerical simulations.

• Smart Structures and Systems
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• v.14 no.6
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• pp.1105-1129
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• 2014

The unscented Kalman filter (UKF) has been developed for nonlinear model parametric identification, and it assumes that the model parameters are symmetrically distributed about their mean values without any constrains. However, the parameters in many applications are confined within certain ranges to make sense physically. In this paper, a constrained unscented Kalman filter (CUKF) algorithm is proposed to improve accuracy of numerical substructure modeling in hybrid testing. During hybrid testing, the numerical models of numerical substructures which are assumed identical to the physical substructures are updated online with the CUKF approach based on the measurement data from physical substructures. The CUKF method adopts sigma points (i.e., sample points) projecting strategy, with which the positions and weights of sigma points violating constraints are modified. The effectiveness of the proposed hybrid testing method is verified by pure numerical simulation and real-time as well as slower hybrid tests with nonlinear specimens. The results show that the new method has better accuracy compared to conventional hybrid testing with fixed numerical model and hybrid testing based on model updating with UKF.

• Journal of Astronomy and Space Sciences
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• v.26 no.1
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• pp.59-74
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• 2009

Relative navigation system is presented using GPS measurements from a single-channel global positioning system (GPS) simulator. The objective of this study is to provide the real-time inter-satellite relative positions as well as absolute positions for two formation flying satellites in low earth orbit. To improve the navigation performance, the absolute states are estimated using ion-free GRAPHIC (group and phase ionospheric correction) pseudo-ranges and the relative states are determined using double differential carrier-phase data and singled-differential C/A code data based on the extended Kalman filter and the unscented Kalman filter. Furthermore, pseudo-relative dynamic model and modified relative measurement model are developed. This modified EKF method prevents non-linearity of the measurement model from degrading precision by applying linearization about absolute navigation solutions not about the priori estimates. The LAMBDA method also has been used to improve the relative navigation performance by fixing ambiguities to integers for precise relative navigation. The software-based simulation has been performed and the steady state accuracies of 1 m and 6 mm ($1{\sigma}$ of 3-dimensional difference errors) are achieved for the absolute and relative navigation using EKF for a short baseline leader/follower formation. In addition, the navigation performances are compared for the EKF and the UKF for 10 hours simulation, and relative position errors are mm-level for the two filters showing the similar trends.