Kalman filtering as an alternative to Ordinary Least Squares — Some theoretical considerations and empirical results

Watson, Patrick Kent

doi:10.1007/bf01973191

Cited by 22 publications

(13 citation statements)

References 9 publications

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“…In order to use the Kalman measurement equation for updating the motion state with a new gradient constraint instance, the gradient constraint of Equation (3) is recast into the linear regression form of Equation (13) (see [27] or [28] for the theory on Kalman filtering for linear regression problems with time series data). Then, the temporal derivative Z i,T (k) is considered a linear function of the motion components and the partial derivatives in space.…”

Section: Temporal Coherence: Kalman Filter For Motion Estimationmentioning

confidence: 99%

Field Motion Estimation with a Geosensor Network

Fitzner

Sester

2016

IJGI

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Physical environmental processes, such as the evolution of precipitation or the diffusion of chemical clouds in the atmosphere, can be approximated by numerical models based on the underlying physics, e.g., for the purpose of prediction. As the modeling process is often very complex and resource demanding, such models are sometimes replaced by those that use historic and current data for calibration. For atmospheric (e.g., precipitation) or oceanographic (e.g., sea surface temperature) fields, the data-driven methods often concern the horizontal displacement driven by transport processes (called advection). These methods rely on flow fields estimated from images of the phenomenon by computer vision techniques, such as optical flow (OF). In this work, an algorithm is proposed for estimating the motion of spatio-temporal fields with the nodes of a geosensor network (GSN) deployed in situ when images are not available. The approach adapts a well-known raster-based OF algorithm to the specifics of GSNs, especially to the spatial irregularity of data. In this paper, the previously introduced approach has been further developed by introducing an error model that derives probabilistic error measures based on spatial node configuration. Further, a more generic motion model is provided, as well as comprehensive simulations that illustrate the performance of the algorithm in different conditions (fields, motion behaviors, node densities and deployments) for the two error measures of motion direction and motion speed. Finally, the algorithm is applied to data sampled from weather radar images, and the algorithm performance is compared to that of a state-of-the-art OF algorithm applied to the weather radar images directly, as often done in nowcasting.

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Section: Temporal Coherence: Kalman Filter For Motion Estimationmentioning

confidence: 99%

Field Motion Estimation with a Geosensor Network

Fitzner

Sester

2016

IJGI

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“…(13). The Kalman filter can be defined as an optimal method to provide minimum variance unbiased estimators of the unknown coefficients (Watson, 1983). In regression analysis, when two or more of the predictors in a regression model are highly correlated, a statistical phenomenon known as multicollinearity can be referred to.…”

Section: Weight Updatementioning

confidence: 99%

“…Both the Kalman filter and RLS suffer from the presence of multicollinearity, but the first method is capable of detecting the presence and severity of multicollinearity as well as adjusting the estimates in a fashion similar to ridge regression since the filter is less data sensitive, and the estimates are more reliable. A detailed discussion over the superiority of Kalman filter to handle the multicollinearity effects can be found in Watson (1983).…”

Section: Weight Updatementioning

confidence: 99%

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Kalman filter-based method for Online Sequential Extreme Learning Machine for regression problems

Nóbrega

Oliveira

2015

Engineering Applications of Artificial Intelligence

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“…Thus, the Kalman filter can always provide optimal estimates whenever OLS does and is also capable of doing so even when OLS does not. For instance, Watson (1983) …”

Section: The Kalman Filter Approachmentioning

confidence: 99%