Bias-correction of Kalman filter estimators associated to a linear state space model with estimated parameters

Costa, Marco; Monteiro, Magda

doi:10.1016/j.jspi.2016.04.002

Cited by 9 publications

(10 citation statements)

References 26 publications

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“…The G/R calibration factor of the two rainfall events was used for the correction of the radar-based rainfall estimates in the evaluation zone. The corrected radar-based rainfall estimate was used for the comparison of the data from the precipitation stations inside the evaluation area (Costa et al, 2016).…”

Section: Error Analysismentioning

confidence: 99%

Quantitative Rainfall Estimation Using Weather Radar Based on the Improved Kalman Filter Method

Rui¹,

Qu²,

Yu³

et al. 2019

Appl. Ecol. Env. Res.

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To reduce the error of radar rainfall evaluations, an improved Kalman filter (KF) method is used to calibrate the radar quantitative rainfall estimation (QRE). First, the rain gauge rain rate/radar rain rate (G/R) calibration factor model is created in this approach. The prediction and measurement system of the G/R are then established based on the KF. The calibration process of the system parameters and the adaptive estimation process of the system error are introduced to dynamically adjust the KF parameters. Subsequently, the G/R calibration ratio is used to correct the quantitative radar rainfall estimation. The radar and rain gauge hourly rain data of two rain cases in Changchun, China on August 19-20, 2015, and August 6-7, 2016, are used to test the efficiency of the proposed method. The results show that the QRE result based on the KF calibration is better than that without calibration. The average relative errors of the two rain cases decreased from 0.6047 to 0.3557 and 0.2645 and from 0.8052 to 0.3096 and 0.1715 due to the ordinary and improved KFs, respectively. The improved KF is even better than the ordinary KF.

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Section: Error Analysismentioning

confidence: 99%

Quantitative Rainfall Estimation Using Weather Radar Based on the Improved Kalman Filter Method

Rui¹,

Qu²,

Yu³

et al. 2019

Appl. Ecol. Env. Res.

View full text Add to dashboard Cite

show abstract

“…The state-space model has in its structure a latent process, the state, which is not observable and must be predicted. The most common procedure to make this prediction is the Kalman filter algorithm [34,35]. This procedure computes, at each moment t, the optimal estimator of the state vector based on the information available up to that time t. The Kalman filter's success lies in the fact that it is an online estimation procedure.…”

Section: Calibration Model (Miii)mentioning

confidence: 99%

“…However, optimum properties can only be guaranteed when all parameters of model are known [36]. When parameters of the state-space model have to be estimated, the uncertainty associated with Kalman's filter estimators is underestimated, and some procedures can be implemented [35]. Hence, the parameters of the model can be estimated using the maximum likelihood (ML) method, incorporating the Kalman filter algorithm, and numerical procedures, such as Newton-Raphson, in order to achieve the optimal value of the likelihood.…”

Section: Calibration Model (Miii)mentioning

confidence: 99%

A Time Series Model Comparison for Monitoring and Forecasting Water Quality Variables

Monteiro

Costa

2018

Hydrology

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Abstract:The monitoring and prediction of water quality parameters are important tasks in the management of water resources. In this work, the performances of time series statistical models were evaluated to predict and forecast the dissolved oxygen (DO) concentration in several monitoring sites located along the main river Vouga, in Portugal, during the period from January 2002 to May 2015. The models being compared are a regression model with correlated errors and a state-space model, which can be seen as a calibration model. Both models allow the incorporation of water quality variables, such as time correlation or seasonality. Results show that, for the DO variable, the calibration model outperforms the regression model for sample modeling, that is, for a short-term forecast, while the regression model with correlated errors has a better performance for the forecasting h-steps ahead framework. So, the calibration model is more useful for water monitoring using an online or real-time procedure, while the regression model with correlated errors can be applied in order to forecast over a longer period of time.

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“…However, if the normality is dropped, then the Kalman filter predictors are the best linear unbiased estimators. When parameters of the state‐space model are estimated, the uncertainty associated with the Kalman filter estimators are underestimated and some procedures can be implemented (Costa & Monteiro, ; Rodríguez & Ruiz, ).…”

Section: The Periodic Mixed Linear State‐space Modelmentioning

confidence: 99%

A periodic mixed linear state‐space model to monthly long‐term temperature data

Costa

Monteiro

2018

Environmetrics

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In recent decades, the world has been confronted with the consequences of global warming; however, this phenomenon is not reflected equally in every part of the globe. Thus, the warming phenomenon must be monitored in a more regional or local scale. This paper analyzes monthly long‐term time series of air temperatures in three Portuguese cities: Lisbon, Oporto, and Coimbra. We propose a periodic state‐space framework, associated with a suitable version of the Kalman filter; which allows for the estimation of monthly warming rates taking into account the seasonal behavior and serial correlation. Results about the monthly mean of the daily midrange temperature time series show that there are different monthly warming rates. The greatest annual mean rise was found in Oporto with 2.17°C, whereas in Lisbon and Coimbra, it was respectively 0.62°C and 0.55°C per century.

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Bias-correction of Kalman filter estimators associated to a linear state space model with estimated parameters

Cited by 9 publications

References 26 publications

Quantitative Rainfall Estimation Using Weather Radar Based on the Improved Kalman Filter Method

Quantitative Rainfall Estimation Using Weather Radar Based on the Improved Kalman Filter Method

A Time Series Model Comparison for Monitoring and Forecasting Water Quality Variables

A periodic mixed linear state‐space model to monthly long‐term temperature data

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