The most widely used nonlinear Kalman filtering
algorithms are extended Kalman filter (EKF) [6,7] and unscented Kalman filter (UKF) [8,9], respectively.
Haykin, Kalman filtering
and neural networks, John Wiley & Sons, Inc, NewYork, USA, 2001.
has been proved to be an effective algorithm for state estimation of dynamic processes [2, 3].
In the Kalman filtering
, motion blocks have quite weak filtering strength to keep their motion characteristic, while still blocks have strong filtering strength to reduce the noise.
Basically, the Kalman filtering
estimation algorithm comprises two steps, namely prediction and update with external measurements.
Some applications examined include electricity load demand and price forecasting using HONNs trained by Kalman filtering
, a novel recurrent polynomial neural network for financial time series prediction, and foreign exchange rate forecasting using a higher order flexible neural tree.
The algorithmic technique of Kalman filtering
has been applied in a wide range of applications, including spacecraft navigation, the prediction of short-term stock market fluctuations, and hand-held global positioning systems.
The core issue in nonlinear Kalman filtering
is to calculate the intractable multidimensional vector integral such as the "nonlinear function x Gaussian probability density function (pdf)," for which it is difficult to achieve the analytical solution [3, 4].
In this study, we introduce Kalman filtering
to neural network model , inspired by Kalman iteration and Bucy and Sunahara's nonlinear extended Kalman filtering
Steer, "Distributed data fusion using Kalman filtering
: a robotics application," in Data, Fusion in Robotics and Machine Intelligence, M.
The original material--covering Markov chain Monte Carlo methods, derivative pricing using jump diffusion with closed-form formulas, value at risk calculation using extreme value theory base on a nonhomogeneous two-dimensional Poisson process, and multivariate volatility models with time-varying correlations--has been expanded to include discussion consistent covariance estimation under heteroscedasticity and serial correlation, alterative approaches to volatility modeling, financial factor models, stat-space models, Kalman filtering
, and estimation of stochastic diffusion models.
The problem of robust Kalman filtering
and optimal filtering in the presence of unknown inputs and unknown faults has received considerable attention in the last two decades due to its significations role in many applications, for example, geophysical and environmental applications, fault detection and isolation (FDI) problems, and fault tolerant control (FTC) problems.