Invariant extended Kalman filter

About: Invariant extended Kalman filter is a research topic. Over the lifetime, 7079 publications have been published within this topic receiving 187702 citations.

Suboptimal FIR Filtering of Nonlinear Models in Additive White Gaussian Noise

Abstract: The first- and second-order extended finite impulse response (EFIR1 and EFIR2, respectively) filters are addressed for suboptimal estimation of nonlinear discrete-time state-space models with additive white Gaussian noise. It is shown that, unlike the extended Kalman filter (EKF) and EFIR2 filter, the EFIR1 one does not require noise statistics and initial errors. Only within a narrow region around actual noise covariances, EFIR filters fall a bit short of EKF and they demonstrate better performance otherwise. It is shown that the optimal averaging interval for EFIR filters can be determined via measurement without a reference model in a learning cycle. We also notice that the second-order approximation can improve the local performance, but it can also deteriorate it. We thus have no recommendations about its use, at least for tracking considered as an example of applications.

On the Kalman filtering method in neural network training and pruning

Abstract: In the use of the extended Kalman filter approach in training and pruning a feedforward neural network, one usually encounters the problems of how to set the initial condition and how to use the result obtained to prune a neural network. In this paper, some cues on the setting of the initial condition are presented with a simple example illustrated. Then based on three assumptions: 1) the size of training set is large enough; 2) the training is able to converge; and 3) the trained network model is close to the actual one, an elegant equation linking the error sensitivity measure (the saliency) and the result obtained via an extended Kalman filter is devised. The validity of the devised equation is then testified by a simulated example.

Maneuvering Target Tracking in the Presence of Glint using the Nonlinear Gaussian Mixture Kalman Filter

Abstract: The problem of maneuvering target tracking in the presence of glint noise is addressed in this work. The main challenge in this problem stems from its nonlinearity and non-Gaussianity. A new estimator, named as nonlinear Gaussian mixture Kalman filter (NL-GMKF) is derived based on the minimum-mean-square error (MMSE) criterion and applied to the problem of maneuvering target tracking in the presence of glint. The tracking performance of the NL-GMKF is evaluated and compared with the interacting multiple modeling (IMM) implemented with extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filter (PF) and the Gaussian sum PF (GSPF). It is shown that the NL-GMKF outperforms these algorithms in several examples with maneuvering target and/or glint noise measurements.

Polynomial extended Kalman filter

Abstract: This work presents a polynomial version of the well-known extended Kalman filter (EKF) for the state estimation of nonlinear discrete-time stochastic systems. The proposed filter, denoted polynomial EKF (PEKF), consists in the application of the optimal polynomial filter of a chosen degree /spl mu/ to the Carleman approximation of a nonlinear system. When /spl mu/=1 the PEKF algorithm coincides with the standard EKF. For the filter implementation the moments of the state and output noises up to order 2/spl mu/ are required. Numerical simulations compare the performances of the PEKF with those of some other existing filters, showing significant improvements.

A receding horizon Kalman FIR filter for linear continuous-time systems

Abstract: A receding horizon Kalman finite-impulse response (FIR) filter is suggested for continuous-time systems, combining the Kalman filter with the receding horizon strategy. In the suggested filter, the horizon initial state is assumed to be unknown. It can always be obtained irrespective of unknown information on the horizon initial state. The filter may be the first stochastic FIR form for continuous-time systems that may have many good inherent properties. The suggested filter can be represented in an iterative form and also in a standard FIR form. The suggested filter turns out to be a remarkable deadbeat observer. The validity of the suggested filter is illustrated by numerical examples.