Extended Kalman Filter Training of Neural Networks on a SIMD Parallel Machine

Li, Shuhui; Wunsch, Donald C.; O’Hair, E.; Giesselmann, M.

doi:10.1006/jpdc.2001.1807

Cited by 16 publications

(8 citation statements)

References 12 publications

(14 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This learning rule is acceptable to estimation type problems where the number of inputs is not too large (Grewal and Andrews, 2001). A Kalman filter attempts to estimate the state of a system that can be modeled as a linear system driven by additive white Gaussian noise and where the measurements available are linear combinations of the system states corrupted by additive white Gaussian noise (Li et al, 2002). For neural network training the weights of the networks are the states process of state equation the Kalman filter attempts to estimate and the desired output of the network is the measurement (measurement equation) used by the Kalman filter as shown in the equations below (Rivals and Personnaz, 1998):…”

Section: Cascade Correlation Artificial Neural Network (Ccann)mentioning

confidence: 99%

See 1 more Smart Citation

Estimating tree bole volume using artificial neural network models for four species in Turkey

Özçelık

Diamantopoulou

Brooks

et al. 2010

Journal of Environmental Management

103

View full text Add to dashboard Cite

Section: Cascade Correlation Artificial Neural Network (Ccann)mentioning

confidence: 99%

“…For a nonlinear network, the usual Kalman Filtering algorithm can be used if the model of the system is linearized, resulting in the Extended Kalman Filter (EKF). The EKF training algorithm tries to minimize the cost function (Li et al, 2002):…”

Section: Cascade Correlation Artificial Neural Network (Ccann)mentioning

confidence: 99%

Estimating tree bole volume using artificial neural network models for four species in Turkey

Özçelık

Diamantopoulou

Brooks

et al. 2010

Journal of Environmental Management

103

View full text Add to dashboard Cite

“…First, for completeness, we give the Kalman filter algorithm for parameter estimation [2], [5], [8], [10], [20].…”

Section: The Proposed Training Schemementioning

confidence: 99%

Memory-Efficient Fully Coupled Filtering Approach for Observational Model Building

Mussa

Glen

2010

IEEE Trans. Neural Netw.

View full text Add to dashboard Cite

Generally, training neural networks with the global extended Kalman filter (GEKF) technique exhibits excellent performance at the expense of a large increase in computational costs which can become prohibitive even for networks of moderate size. This drawback was previously addressed by heuristically decoupling some of the weights of the networks. Inevitably, ad hoc decoupling leads to a degradation in the quality (accuracy) of the resultant neural networks. In this paper, we present an algorithm that emulates the accuracy of GEKF, but avoids the construction of the state covariance matrix-the source of the computational bottleneck in GEKF. In the proposed algorithm, all the synaptic weights remain connected while the amount of computer memory required is similar to (or cheaper than) the memory requirements in the decoupling schemes. We also point out that the new method can be extended to derivative-free nonlinear Kalman filters, such as the unscented Kalman filter and ensemble Kalman filters.

show abstract

“…This learning rule is acceptable for forecasting the type of problems where the number of inputs is not too large (Grewal and Andrews, 2001). A Kalman filter (Brown and Hwang, 1992;Rivals and Personnaz, 1998;Demuth and Beale, 2001;Grewal and Andrews, 2001;Li et al, 2002) attempts to estimate the state of a system that can be modeled as a linear system driven by additive white Gaussian noise and where the available measurements are linear combinations of the system states that are corrupted by additive white Gaussian noise (Li et al, 2002). A detailed description of the Cascade Correlation architecture where Kalman's learning rule is embedded can be found in Diamantopoulou (2010).…”

Section: Study Area and Meteorological Data Setsmentioning

confidence: 99%

Performance evaluation of artificial neural networks in estimating reference evapotranspiration with minimal meteorological data

Diamantopoulou¹,

Georgiou²,

Papamichail³

2013

Issue 1

View full text Add to dashboard Cite

Detailed meteorological data required for the equation of FAO-56 Penman-Monteith (P-M) method that was adopted by Food and Agriculture Organization (FAO) as a standard method in estimating reference evapotranspiration (ET o ) are not often available, especially in developing countries. The Hargreaves equation (HG) has been successfully used in some locations to estimate ET o where sufficient data were not available to use the P-M method. This paper investigates the potential of two Artificial Neural Network (ANN) architectures, the multilayer perceptron architecture, in which a backpropagation algorithm (BPANN) is used, and the cascade correlation architecture (CCANN), in which Kalman's learning rule is embedded in modeling the daily ET o with minimal meteorological data. An overview of the features of ANNs and traditional methods such as P-M and HG is presented, and the advantages and limitations of each method are discussed. Daily meteorological data from three automatic weather stations located in Greece were used to optimize and test the different models. The exponent value of the HG equation was locally optimized, and an adjusted HGadj equation was used. The comparisons were based on error statistical techniques using P-M daily ET o values as reference. According to the results obtained, it was found that taking into account only the mean, maximum and minimum air temperatures, the selected ANN models markedly improved the daily ET o estimates and provided unbiased predictions and systematically better accuracy compared with the HGadj equation. The results also show that the CCANN model performed better than the BPANN model at all stations. KEYWORDS: neural network techniques, evapotranspiration, calibration, validation. INTRODUCTIONKnowledge of evapotranspiration, which involves the evaporation of water from land surfaces and transpiration by vegetation, is essential for estimating irrigation water requirements (Allen et al., 1998). Methods for estimating evapotranspiration are based on micrometeorological techniques (aerodynamic method, eddy covariance, etc.) or on the use of lysimeters. The methods for estimating evapotranspiration require complex and very costly instruments and are generally recommended only for specific research purposes (Allen et al., 1998). The evapotranspiration rate from a reference crop is called reference evapotranspiration (ET o ) and expresses the evaporating power of the atmosphere at a specific location and time of the year (Allen et al., 1998). The FAO-56 Penman-Monteith (P-M) equation (Allen et al., 1998) was adopted by FAO as a standard method for estimating daily ET o , as it provides more consistent ET o estimates and has been shown to perform better than other ET o methods. However, the detailed meteorological data required by the P-M equation are not often available, especially in developing countries. Under such conditions, simplified or empirical equations, which require less meteorological data, should be used. Allen et al. (1998) have proposed that when s...

show abstract

Extended Kalman Filter Training of Neural Networks on a SIMD Parallel Machine

Cited by 16 publications

References 12 publications

Estimating tree bole volume using artificial neural network models for four species in Turkey

Estimating tree bole volume using artificial neural network models for four species in Turkey

Memory-Efficient Fully Coupled Filtering Approach for Observational Model Building

Performance evaluation of artificial neural networks in estimating reference evapotranspiration with minimal meteorological data

Contact Info

Product

Resources

About