Non-linear filtering based on observations from Gaussian processes

2011-03-12
Gustafsson, Fredrik
Saha, Saikat
Orguner, Umut
We consider a class of non-linear filtering problems, where the observation model is given by a Gaussian process rather than the common non-linear function of the state and measurement noise. The new observation model can be considered as a generalization of the standard one with correlated measurement noise in both time and space. We propose a particle filter based approach with a measurement update step that requires a memory of past observations which can be truncated using a moving window to obtain a finite-dimensional filter with arbitrarily good accuracy. The validity of the conceptual solution is proved via simulations on a one dimensional tracking problem and implementation issues are discussed.

Suggestions

Continuous-time nonlinear estimation filters using UKF-aided gaussian sum representations
Gökçe, Murat; Kuzuoğlu, Mustafa; Department of Electrical and Electronics Engineering (2014)
A nonlinear filtering method is developed for continuous-time nonlinear systems with observations/measurements carried out in discrete-time by means of UKFaided Gaussian sum representations. The time evolution of the probability density function (pdf) of the state variables (or the a priori pdf) is approximated by solving the Fokker-Planck equation numerically using Euler’s method. At every Euler step, the values of the a priori pdf are evaluated at deterministic sample points. These values are used with Ga...
Exact kalman filtering of respiratory motion
Çetinkaya, Mehmet; Erkmen, Aydan Müşerref (2018-10-01)
In this paper we propose a novel Exact Kalman Filter for state estimation of quasi-periodic signals such as respiratory motion. Nonlinear functions of interest are approximations as truncated Fourier series. Instead of relying on approximations provided by Extended Kalman Filter or Unscented Kalman Filter, our filter performs exact calculation of the mean and covariances of interest. We then compare, through simulations, the performance of our filter to the two. Our results show that the theoretically deriv...
Real-Time Detection of Interharmonics and Harmonics of AC Electric Arc Furnaces on GPU Framework
Uz-Logoglu, Eda; Salor, Ozgul; Ermiş, Muammer (2019-11-01)
In this paper, a method based on the multiple synchronous reference frame analysis is recommended and implemented to detect time-varying harmonics and interharmonics of rapidly fluctuating asymmetrical industrial loads. The experimental work has been carried out on a typical three-phase alternating current arc furnace installation. In the recommended method, the reference frame is rotated in both directions at speeds corresponding to the positive and negative sequences of all harmonics and all interharmonic...
Real-Time Detection of Interharmonics and Harmonics of AC Electric Arc Furnaces on GPU Framework
Uz-Logoglu, Eda; Salor, Ozgul; Ermiş, Muammer (2017-10-05)
In this paper, a method based on the multiple synchronous reference frame (MSRF) analysis is recommended and implemented to detect time-varying harmonics and interharmonics of rapidly fluctuating asymmetrical industrial loads. The experimental work has been carried out on a typical three-phase alternating current arc furnace (AC EAF) installation. In the recommended method, the reference frame is rotated in both directions at speeds corresponding to the positive and negative sequences of all harmonics and a...
ON PARAMETRIC LOWER BOUNDS FOR DISCRETE-TIME FILTERING
Fritsche, Carsten; Orguner, Umut; Gustafsson, Fredrik (2016-03-25)
Parametric Cramer-Rao lower bounds (CRLBs) are given for discrete-time systems with non-zero process noise. Recursive expressions for the conditional bias and mean-square-error (MSE) (given a specific state sequence) are obtained for Kalman filter estimating the states of a linear Gaussian system. It is discussed that Kalman filter is conditionally biased with a non-zero process noise realization in the given state sequence. Recursive parametric CRLBs are obtained for biased estimators for linear state esti...
Citation Formats
F. Gustafsson, S. Saha, and U. Orguner, “Non-linear filtering based on observations from Gaussian processes,” 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47993.