Set Of Sigma Points Research Articles

Sigma-Point Kalman Filtering for Tightly Coupled GPS/INS Integration

Sigma-point Kalman filtering (SPKF) uses a set of sigma points to completely capture the first and second order moments of the a priori random variable. Using the SPKF, a tightly-coupled GPS/INS integration can be designed in either the navigation state space or the error state space. This paper uses the error state space. This approach blends the INS error model with the nonlinear range and range-rate equations, and can avoid the time-consuming unscented transformation on the strapdown computation which is needed when the implementation occurs through the navigation state space. The SPKF demonstrated its ability to track INS errors in the field test. The comparison between SPKF and EKF was conducted in terms of accuracy and time consumption. The results show that for the pseudorange-based tightly-coupled GPS/INS integration, the SPKF design provides little performance benefit compared to the EKF.

Survey of Nonlinear Attitude Estimation Methods

This paper provides a survey of modern nonlinear filtering methods for attitude estimation. Early applications relied mostly on the extended Kalman filter for attitude estimation. Since these applications, several new approaches have been developed that have proven to be superior to the extended Kalman filter. Several of these approaches maintain the basic structure of the extended Kalman filter, but employ various modifications in order to provide better convergence or improve other performance characteristics. Examples of such approaches include: filter QUEST, extended QUEST and the backwards-smoothing extended Kalman filter. Filters that propagate and update a discrete set of sigma points rather than using linearized equations for the mean and covariance are also reviewed. A twostep approach is discussed with a first-step state that linearizes the measurement model and an iterative second step to recover the desired attitude states. These approaches are all based on the Gaussian assumption that the probability density function is adequately specified by its mean and covariance. Other approaches that do not require this assumption are reviewed, Associate Professor, Department of Mechanical & Aerospace Engineering. Email: johnc@eng.buffalo.edu. Associate Fellow AIAA. Aerospace Engineer, Guidance, Navigation and Control Systems Engineering Branch. Email: Landis.Markley@nasa.gov. Fellow AIAA. Postdoctoral Research Fellow, Department of Mechanical & Aerospace Engineering. Email: cheng3@eng.buffalo.edu. Member AIAA.

Unscented Kalman filtering for additive noise case: augmented versus nonaugmented

This paper concerns the unscented Kalman filtering (UKF) for the nonlinear dynamic systems with additive process and measurement noises. It is widely accepted for such a case that the system state needs not to be augmented with noise vectors and the resultant nonaugmented UKF yields similar, if not the same, results to the augmented UKF. In this letter, we find that under the condition of n+/spl kappa/=const, the basic difference between them is that the augmented UKF draws a sigma set only once within a filtering recursion, while the nonaugmented UKF has to redraw a new set of sigma points to incorporate the effect of additive process noise. This difference generally favors the augmented UKF in that the odd-order moment information is partly captured by the nonlinearly transformed sigma points and propagated throughout the recursion. The simulation results agree well with the analyses.