Search

This article considers a nonlinear filtering method for handling outliers. The presence of outliers that are gross observation errors can greatly reduce the accuracy of filtering methods that assume Gaussian distributed errors. There are some existing methods that assume a Gaussian observation error, and estimate the error covariance matrix at each time step to avoid overfitting to the outliers. However, the estimates of the covariance matrix under such methods can become unstable. This results in underfitting or overfitting to observations when filtering. This paper presents a new method for handling outliers in nonlinear filtering problems by extending the unscented Kalman filter. In this method, two Gaussian observation error models with distinct covariance matrices are used: one for observations with regular errors, and another with a larger variance specified by a scale parameter for outliers. In addition to the system state, this method estimates an indicator variable that switches between the two models and the scale parameter for outliers. With the inclusion of the indicator variable and scale parameter, the estimated error covariance matrix can handle both regular observations and outliers appropriately at each time step. Furthermore, by estimating the scale parameter, the proposed method can be applied to a dataset without additional tuning to account for outlier characteristics. Through numerical experiments, we find that our method can estimate the system state better than existing methods for both datasets with and without outliers. [ABSTRACT FROM AUTHOR]

Recent space plasma observations have provided us with three‐dimensional velocity distributions having multiple peaks. We propose a method for analyzing such velocity distributions via a multivariate Maxwellian mixture model where each component of the model represents each of the multiple peaks. The parameters of the model are determined through an iterative nonlinear optimization technique, specifically the expectation‐maximization (EM) algorithm. For the automatic judgment of the preferable number of components in the mixture model, we introduce a method of examining the number of extrema of a resulting mixture model. We show applications of our method to ion observations in the plasma sheet boundary layer (PSBL) and in the central plasma sheet (CPS) of the Earth's magnetotail. From an analysis of the PSBL and CPS, low‐energy ions that have properties similar to those of lobe ions were detected also in the PSBL and CPS. In the PSBL, middle‐energy ion component which is flowing dawnward and directed the neutral sheet was extracted. We suggested that magnetic field fluctuations in the PSBL can be explained only when the two ion components were properly treated.