Terrance Wilms - Academia.edu (original) (raw)

Papers by Terrance Wilms

Research paper thumbnail of Comparison of Unscented Kalman Filter Design for Agricultural Anaerobic Digestion Model

arXiv (Cornell University), Oct 23, 2023

Dynamic operation of biological processes, such as anaerobic digestion (AD), requires reliable pr... more Dynamic operation of biological processes, such as anaerobic digestion (AD), requires reliable process monitoring to guarantee stable operating conditions at all times. Unscented Kalman filters (UKF) are an established tool for nonlinear state estimation, and there exist numerous variants of UKF implementations, treating state constraints, improvements of numerical performance and different noise cases. So far, however, a unified comparison of proposed methods emphasizing the algorithmic details is lacking. The present study thus examines multiple unconstrained and constrained UKF variants, addresses aspects crucial for direct implementation and applies them to a simplified AD model. The constrained UKF considering additive noise delivered the most accurate state estimations. The long run time of the underlying optimization could be vastly reduced through pre-calculated gradients and Hessian of the associated cost function, as well as by reformulation of the cost function as a quadratic program. However, unconstrained UKF variants showed lower run times at competitive estimation accuracy. This study provides useful advice to practitioners working with nonlinear Kalman filters by paying close attention to algorithmic details and modifications crucial for successful implementation.

Research paper thumbnail of Adaptive optimal operation of a parallel robotic liquid handling station

IFAC-PapersOnLine, 2018

Results are presented from the optimal operation of a fully automated robotic liquid handling sta... more Results are presented from the optimal operation of a fully automated robotic liquid handling station where parallel experiments are performed for calibrating a kinetic fermentation model. To increase the robustness against uncertainties and/or wrong assumptions about the parameter values, an iterative calibration and experiment design approach is adopted. Its implementation yields a stepwise reduction of parameter uncertainties together with an adaptive redesign of reactor feeding strategies whenever new measurement information is available. The case study considers the adaptive optimal design of 4 parallel fed-batch strategies implemented in 8 mini-bioreactors. Details are given on the size and complexity of the problem and the challenges related to calibration of over-parameterized models and scarce and non-informative measurement data. It is shown how methods for parameter identifiability analysis and numerical regularization can be used for monitoring the progress of the experimental campaigns in terms of generated information regarding parameters and selection of the best fitting parameter subset.

Research paper thumbnail of Online bioprocess data generation, analysis, and optimization for parallel fed-batch fermentations in milliliter scale

Engineering in Life Sciences, Nov 14, 2016

Bioprocess development, optimization, and control in mini-bioreactor systems require information ... more Bioprocess development, optimization, and control in mini-bioreactor systems require information about essential process parameters, high data densities, and the ability to dynamically change process conditions. We present an integration approach combining a parallel mini-bioreactor system integrated into a liquid handling station (LHS) with a second LHS for offline analytics. Non-invasive sensors measure pH and DO online. Offline samples are collected every 20 min and acetate, glucose, and OD 620 subsequently analyzed offline. All data are automatically collected, analyzed, formalized, and used for process control and optimization. Fed-batch conditions are realized via a slow enzymatic glucose release system. The integration approach was successfully used to apply an online experimental redesign method to eight Escherichia coli fed-batch cultivations. The method utilizes generated data to select the following experimental actions online in order to reach the optimization goal of estimating E. coli fed-batch model parameters with as high accuracy as possible. Optimal experimental designs were recalculated online based on the experimental data and implemented by introducing pulses via the LHS to the running fermentations. The LHS control allows for various implementations of advanced control and optimization strategies in milliliter scale.

Research paper thumbnail of Nonlinear state estimation as tool for online monitoring and adaptive feed in high-throughput cultivations

Authorea (Authorea), Aug 9, 2022

Increasing the comparability to large scale fermentations is a constant aim during scale-down, in... more Increasing the comparability to large scale fermentations is a constant aim during scale-down, including growth-limiting feeding of the carbon source. Minibioreactor facilities greatly increase the throughput and offer many advantages. However, online measurements in this small scale often do not include critical process variables, necessary to control the feed rate. State estimators utilize mathematical models to estimate non-measurable states applying existing information about the inputs, outputs, and measurement uncertainties. Though, existing applications focus on bench-top or production-scale applications, where advanced process analytical technologies such as spectroscopic methods are available. Here, we present a concept for model-based nonlinear state estimation in a high-throughput platform with 24 parallel experiments in the mL-scale. An extended and a sigma-point Kalman filter are implemented based on online measurements only. The dissolved oxygen concentration and a relation of biomass growth and nitrogen consumption are used as measurement input. The current state of the cultivation is estimated iteratively throughout Escherichia coli cultivations and used to maintain predefined growth setpoints by adapting the feed rate. With this, we bring a further level of monitoring and process understanding to minibioreactor systems, and therefore enable automatization and optimization of miniaturized bioprocesses under controlled cultivation conditions.

Research paper thumbnail of Dynamic Optimization of the PyNP/PNP Phosphorolytic Enzymatic Process Using MOSAICmodeling

Chemie Ingenieur Technik, Oct 11, 2017

Pyrimidine and purine nucleoside phosphorylases catalyze the reversible phosphorolytic cleavage a... more Pyrimidine and purine nucleoside phosphorylases catalyze the reversible phosphorolytic cleavage and formation of the glycosidic bond of purine and pyrimidine nucleosides, respectively, and are thus, key catalysts for the synthesis of new compounds. The selection of the best combination of enzyme and reaction conditions is not trivial, as each of the two enzymes can perform the reaction in two directions and thus, also competes with the other one for the reaction intermediates. A generic approach to the solution of this problem based on the formulation of a mixed integer dynamic optimization program using MOSAICmodeling is presented.

Research paper thumbnail of Nonlinear state estimation as tool for online monitoring and adaptive feed in high-throughput cultivations

Increasing the comparability to large scale fermentations is a constant aim during scale-down, in... more Increasing the comparability to large scale fermentations is a constant aim during scale-down, including growth-limiting feeding of the carbon source. Minibioreactor facilities greatly increase the throughput and offer many advantages. However, online measurements in this small scale often do not include critical process variables, necessary to control the feed rate. State estimators utilize mathematical models to estimate non-measurable states applying existing information about the inputs, outputs, and measurement uncertainties. Though, existing applications focus on bench-top or production-scale applications, where advanced process analytical technologies such as spectroscopic methods are available. Here, we present a concept for model-based nonlinear state estimation in a high-throughput platform with 24 parallel experiments in the mL-scale. An extended and a sigma-point Kalman filter are implemented based on online measurements only. The dissolved oxygen concentration and a rel...

Research paper thumbnail of Model-Based Process Optimization for the Production of Macrolactin D by Paenibacillus polymyxa

Processes, Jun 28, 2020

In this study, we show the successful application of different model-based approaches for the max... more In this study, we show the successful application of different model-based approaches for the maximizing of macrolactin D production by Paenibacillus polymyxa. After four initial cultivations, a family of nonlinear dynamic biological models was determined automatically and ranked by their respective Akaike Information Criterion (AIC). The best models were then used in a multi-model setup for robust product maximization. The experimental validation shows the highest product yield attained compared with the identification runs so far. In subsequent fermentations, the online measurements of CO 2 concentration, base consumption, and near-infrared spectroscopy (NIR) were used for model improvement. After model extension using expert knowledge, a single superior model could be identified. Model-based state estimation with a sigma-point Kalman filter (SPKF) was based on online measurement data, and this improved model enabled nonlinear real-time product maximization. The optimization increased the macrolactin D production even further by 28% compared with the initial robust multi-model offline optimization.

Research paper thumbnail of Model reduction of aerobic bioprocess models for efficient simulation

Chemical Engineering Science, 2020

Abstract Owing to the increasing demand for large scale and high efficiency in manufacturing proc... more Abstract Owing to the increasing demand for large scale and high efficiency in manufacturing processes, computer aided tools for process operation and control are rapidly gaining popularity. An important state variable in aerobic processes is the dissolved oxygen, which can be easily measured online and is an important indicator of the metabolic activity. However, due to the fast kinetics of the oxygen transfer, dynamical models describing aerobic bioprocesses tend to be highly stiff. This can lead to significant numerical problems hampering its use for fixed step discretization methods and computationally costly applications such as computer fluid dynamics. In this work we use the slow-motion invariant manifold and the quasi steady state assumption methods to eliminate the differential equation describing the dissolved oxygen (the fast mode). By doing this, the tractability of the model is significantly increased with a neglectable loss in description power. The reduced model is also useful for simplifying the observer design problems, which is demonstrated by a state and parameter estimation example at the end of the work.

Research paper thumbnail of Dynamic Optimization of the PyNP/PNP Phosphorolytic Enzymatic Process Using MOSAICmodeling

Chemie Ingenieur Technik, 2017

Pyrimidine and purine nucleoside phosphorylases catalyze the reversible phosphorolytic cleavage a... more Pyrimidine and purine nucleoside phosphorylases catalyze the reversible phosphorolytic cleavage and formation of the glycosidic bond of purine and pyrimidine nucleosides, respectively, and are thus, key catalysts for the synthesis of new compounds. The selection of the best combination of enzyme and reaction conditions is not trivial, as each of the two enzymes can perform the reaction in two directions and thus, also competes with the other one for the reaction intermediates. A generic approach to the solution of this problem based on the formulation of a mixed integer dynamic optimization program using MOSAICmodeling is presented.

Research paper thumbnail of Adaptive optimal operation of a parallel robotic liquid handling station ⁎ ⁎T.B. and A.S. acknowledge partial funding of this project by the Austrian Research Funding Association (FFG) within the programme Bridge in the project modELTES (project No. 851262). M.N.C.B. acknowledge financial support...

IFAC-PapersOnLine, 2018

Results are presented from the optimal operation of a fully automated robotic liquid handling sta... more Results are presented from the optimal operation of a fully automated robotic liquid handling station where parallel experiments are performed for calibrating a kinetic fermentation model. To increase the robustness against uncertainties and/or wrong assumptions about the parameter values, an iterative calibration and experiment design approach is adopted. Its implementation yields a stepwise reduction of parameter uncertainties together with an adaptive redesign of reactor feeding strategies whenever new measurement information is available. The case study considers the adaptive optimal design of 4 parallel fed-batch strategies implemented in 8 mini-bioreactors. Details are given on the size and complexity of the problem and the challenges related to calibration of over-parameterized models and scarce and non-informative measurement data. It is shown how methods for parameter identifiability analysis and numerical regularization can be used for monitoring the progress of the experimental campaigns in terms of generated information regarding parameters and selection of the best fitting parameter subset.

Research paper thumbnail of Online bioprocess data generation, analysis and optimization for parallel fed-batch fermentations at mL scale

Engineering in Life Sciences, 2016

Bioprocess development, optimization, and control in mini-bioreactor systems require information ... more Bioprocess development, optimization, and control in mini-bioreactor systems require information about essential process parameters, high data densities, and the ability to dynamically change process conditions. We present an integration approach combining a parallel mini-bioreactor system integrated into a liquid handling station (LHS) with a second LHS for offline analytics. Non-invasive sensors measure pH and DO online. Offline samples are collected every 20 min and acetate, glucose, and OD 620 subsequently analyzed offline. All data are automatically collected, analyzed, formalized, and used for process control and optimization. Fed-batch conditions are realized via a slow enzymatic glucose release system. The integration approach was successfully used to apply an online experimental redesign method to eight Escherichia coli fed-batch cultivations. The method utilizes generated data to select the following experimental actions online in order to reach the optimization goal of estimating E. coli fed-batch model parameters with as high accuracy as possible. Optimal experimental designs were recalculated online based on the experimental data and implemented by introducing pulses via the LHS to the running fermentations. The LHS control allows for various implementations of advanced control and optimization strategies in milliliter scale.

Research paper thumbnail of Model-Based Process Optimization for the Production of Macrolactin D by Paenibacillus polymyxa

Processes, 2020

In this study, we show the successful application of different model-based approaches for the max... more In this study, we show the successful application of different model-based approaches for the maximizing of macrolactin D production by Paenibacillus polymyxa. After four initial cultivations, a family of nonlinear dynamic biological models was determined automatically and ranked by their respective Akaike Information Criterion (AIC). The best models were then used in a multi-model setup for robust product maximization. The experimental validation shows the highest product yield attained compared with the identification runs so far. In subsequent fermentations, the online measurements of CO2 concentration, base consumption, and near-infrared spectroscopy (NIR) were used for model improvement. After model extension using expert knowledge, a single superior model could be identified. Model-based state estimation with a sigma-point Kalman filter (SPKF) was based on online measurement data, and this improved model enabled nonlinear real-time product maximization. The optimization increa...

Research paper thumbnail of Comparison of Unscented Kalman Filter Design for Agricultural Anaerobic Digestion Model

arXiv (Cornell University), Oct 23, 2023

Dynamic operation of biological processes, such as anaerobic digestion (AD), requires reliable pr... more Dynamic operation of biological processes, such as anaerobic digestion (AD), requires reliable process monitoring to guarantee stable operating conditions at all times. Unscented Kalman filters (UKF) are an established tool for nonlinear state estimation, and there exist numerous variants of UKF implementations, treating state constraints, improvements of numerical performance and different noise cases. So far, however, a unified comparison of proposed methods emphasizing the algorithmic details is lacking. The present study thus examines multiple unconstrained and constrained UKF variants, addresses aspects crucial for direct implementation and applies them to a simplified AD model. The constrained UKF considering additive noise delivered the most accurate state estimations. The long run time of the underlying optimization could be vastly reduced through pre-calculated gradients and Hessian of the associated cost function, as well as by reformulation of the cost function as a quadratic program. However, unconstrained UKF variants showed lower run times at competitive estimation accuracy. This study provides useful advice to practitioners working with nonlinear Kalman filters by paying close attention to algorithmic details and modifications crucial for successful implementation.

Research paper thumbnail of Adaptive optimal operation of a parallel robotic liquid handling station

IFAC-PapersOnLine, 2018

Results are presented from the optimal operation of a fully automated robotic liquid handling sta... more Results are presented from the optimal operation of a fully automated robotic liquid handling station where parallel experiments are performed for calibrating a kinetic fermentation model. To increase the robustness against uncertainties and/or wrong assumptions about the parameter values, an iterative calibration and experiment design approach is adopted. Its implementation yields a stepwise reduction of parameter uncertainties together with an adaptive redesign of reactor feeding strategies whenever new measurement information is available. The case study considers the adaptive optimal design of 4 parallel fed-batch strategies implemented in 8 mini-bioreactors. Details are given on the size and complexity of the problem and the challenges related to calibration of over-parameterized models and scarce and non-informative measurement data. It is shown how methods for parameter identifiability analysis and numerical regularization can be used for monitoring the progress of the experimental campaigns in terms of generated information regarding parameters and selection of the best fitting parameter subset.

Research paper thumbnail of Online bioprocess data generation, analysis, and optimization for parallel fed-batch fermentations in milliliter scale

Engineering in Life Sciences, Nov 14, 2016

Bioprocess development, optimization, and control in mini-bioreactor systems require information ... more Bioprocess development, optimization, and control in mini-bioreactor systems require information about essential process parameters, high data densities, and the ability to dynamically change process conditions. We present an integration approach combining a parallel mini-bioreactor system integrated into a liquid handling station (LHS) with a second LHS for offline analytics. Non-invasive sensors measure pH and DO online. Offline samples are collected every 20 min and acetate, glucose, and OD 620 subsequently analyzed offline. All data are automatically collected, analyzed, formalized, and used for process control and optimization. Fed-batch conditions are realized via a slow enzymatic glucose release system. The integration approach was successfully used to apply an online experimental redesign method to eight Escherichia coli fed-batch cultivations. The method utilizes generated data to select the following experimental actions online in order to reach the optimization goal of estimating E. coli fed-batch model parameters with as high accuracy as possible. Optimal experimental designs were recalculated online based on the experimental data and implemented by introducing pulses via the LHS to the running fermentations. The LHS control allows for various implementations of advanced control and optimization strategies in milliliter scale.

Research paper thumbnail of Nonlinear state estimation as tool for online monitoring and adaptive feed in high-throughput cultivations

Authorea (Authorea), Aug 9, 2022

Increasing the comparability to large scale fermentations is a constant aim during scale-down, in... more Increasing the comparability to large scale fermentations is a constant aim during scale-down, including growth-limiting feeding of the carbon source. Minibioreactor facilities greatly increase the throughput and offer many advantages. However, online measurements in this small scale often do not include critical process variables, necessary to control the feed rate. State estimators utilize mathematical models to estimate non-measurable states applying existing information about the inputs, outputs, and measurement uncertainties. Though, existing applications focus on bench-top or production-scale applications, where advanced process analytical technologies such as spectroscopic methods are available. Here, we present a concept for model-based nonlinear state estimation in a high-throughput platform with 24 parallel experiments in the mL-scale. An extended and a sigma-point Kalman filter are implemented based on online measurements only. The dissolved oxygen concentration and a relation of biomass growth and nitrogen consumption are used as measurement input. The current state of the cultivation is estimated iteratively throughout Escherichia coli cultivations and used to maintain predefined growth setpoints by adapting the feed rate. With this, we bring a further level of monitoring and process understanding to minibioreactor systems, and therefore enable automatization and optimization of miniaturized bioprocesses under controlled cultivation conditions.

Research paper thumbnail of Dynamic Optimization of the PyNP/PNP Phosphorolytic Enzymatic Process Using MOSAICmodeling

Chemie Ingenieur Technik, Oct 11, 2017

Pyrimidine and purine nucleoside phosphorylases catalyze the reversible phosphorolytic cleavage a... more Pyrimidine and purine nucleoside phosphorylases catalyze the reversible phosphorolytic cleavage and formation of the glycosidic bond of purine and pyrimidine nucleosides, respectively, and are thus, key catalysts for the synthesis of new compounds. The selection of the best combination of enzyme and reaction conditions is not trivial, as each of the two enzymes can perform the reaction in two directions and thus, also competes with the other one for the reaction intermediates. A generic approach to the solution of this problem based on the formulation of a mixed integer dynamic optimization program using MOSAICmodeling is presented.

Research paper thumbnail of Nonlinear state estimation as tool for online monitoring and adaptive feed in high-throughput cultivations

Increasing the comparability to large scale fermentations is a constant aim during scale-down, in... more Increasing the comparability to large scale fermentations is a constant aim during scale-down, including growth-limiting feeding of the carbon source. Minibioreactor facilities greatly increase the throughput and offer many advantages. However, online measurements in this small scale often do not include critical process variables, necessary to control the feed rate. State estimators utilize mathematical models to estimate non-measurable states applying existing information about the inputs, outputs, and measurement uncertainties. Though, existing applications focus on bench-top or production-scale applications, where advanced process analytical technologies such as spectroscopic methods are available. Here, we present a concept for model-based nonlinear state estimation in a high-throughput platform with 24 parallel experiments in the mL-scale. An extended and a sigma-point Kalman filter are implemented based on online measurements only. The dissolved oxygen concentration and a rel...

Research paper thumbnail of Model-Based Process Optimization for the Production of Macrolactin D by Paenibacillus polymyxa

Processes, Jun 28, 2020

In this study, we show the successful application of different model-based approaches for the max... more In this study, we show the successful application of different model-based approaches for the maximizing of macrolactin D production by Paenibacillus polymyxa. After four initial cultivations, a family of nonlinear dynamic biological models was determined automatically and ranked by their respective Akaike Information Criterion (AIC). The best models were then used in a multi-model setup for robust product maximization. The experimental validation shows the highest product yield attained compared with the identification runs so far. In subsequent fermentations, the online measurements of CO 2 concentration, base consumption, and near-infrared spectroscopy (NIR) were used for model improvement. After model extension using expert knowledge, a single superior model could be identified. Model-based state estimation with a sigma-point Kalman filter (SPKF) was based on online measurement data, and this improved model enabled nonlinear real-time product maximization. The optimization increased the macrolactin D production even further by 28% compared with the initial robust multi-model offline optimization.

Research paper thumbnail of Model reduction of aerobic bioprocess models for efficient simulation

Chemical Engineering Science, 2020

Abstract Owing to the increasing demand for large scale and high efficiency in manufacturing proc... more Abstract Owing to the increasing demand for large scale and high efficiency in manufacturing processes, computer aided tools for process operation and control are rapidly gaining popularity. An important state variable in aerobic processes is the dissolved oxygen, which can be easily measured online and is an important indicator of the metabolic activity. However, due to the fast kinetics of the oxygen transfer, dynamical models describing aerobic bioprocesses tend to be highly stiff. This can lead to significant numerical problems hampering its use for fixed step discretization methods and computationally costly applications such as computer fluid dynamics. In this work we use the slow-motion invariant manifold and the quasi steady state assumption methods to eliminate the differential equation describing the dissolved oxygen (the fast mode). By doing this, the tractability of the model is significantly increased with a neglectable loss in description power. The reduced model is also useful for simplifying the observer design problems, which is demonstrated by a state and parameter estimation example at the end of the work.

Research paper thumbnail of Dynamic Optimization of the PyNP/PNP Phosphorolytic Enzymatic Process Using MOSAICmodeling

Chemie Ingenieur Technik, 2017

Pyrimidine and purine nucleoside phosphorylases catalyze the reversible phosphorolytic cleavage a... more Pyrimidine and purine nucleoside phosphorylases catalyze the reversible phosphorolytic cleavage and formation of the glycosidic bond of purine and pyrimidine nucleosides, respectively, and are thus, key catalysts for the synthesis of new compounds. The selection of the best combination of enzyme and reaction conditions is not trivial, as each of the two enzymes can perform the reaction in two directions and thus, also competes with the other one for the reaction intermediates. A generic approach to the solution of this problem based on the formulation of a mixed integer dynamic optimization program using MOSAICmodeling is presented.

Research paper thumbnail of Adaptive optimal operation of a parallel robotic liquid handling station ⁎ ⁎T.B. and A.S. acknowledge partial funding of this project by the Austrian Research Funding Association (FFG) within the programme Bridge in the project modELTES (project No. 851262). M.N.C.B. acknowledge financial support...

IFAC-PapersOnLine, 2018

Results are presented from the optimal operation of a fully automated robotic liquid handling sta... more Results are presented from the optimal operation of a fully automated robotic liquid handling station where parallel experiments are performed for calibrating a kinetic fermentation model. To increase the robustness against uncertainties and/or wrong assumptions about the parameter values, an iterative calibration and experiment design approach is adopted. Its implementation yields a stepwise reduction of parameter uncertainties together with an adaptive redesign of reactor feeding strategies whenever new measurement information is available. The case study considers the adaptive optimal design of 4 parallel fed-batch strategies implemented in 8 mini-bioreactors. Details are given on the size and complexity of the problem and the challenges related to calibration of over-parameterized models and scarce and non-informative measurement data. It is shown how methods for parameter identifiability analysis and numerical regularization can be used for monitoring the progress of the experimental campaigns in terms of generated information regarding parameters and selection of the best fitting parameter subset.

Research paper thumbnail of Online bioprocess data generation, analysis and optimization for parallel fed-batch fermentations at mL scale

Engineering in Life Sciences, 2016

Bioprocess development, optimization, and control in mini-bioreactor systems require information ... more Bioprocess development, optimization, and control in mini-bioreactor systems require information about essential process parameters, high data densities, and the ability to dynamically change process conditions. We present an integration approach combining a parallel mini-bioreactor system integrated into a liquid handling station (LHS) with a second LHS for offline analytics. Non-invasive sensors measure pH and DO online. Offline samples are collected every 20 min and acetate, glucose, and OD 620 subsequently analyzed offline. All data are automatically collected, analyzed, formalized, and used for process control and optimization. Fed-batch conditions are realized via a slow enzymatic glucose release system. The integration approach was successfully used to apply an online experimental redesign method to eight Escherichia coli fed-batch cultivations. The method utilizes generated data to select the following experimental actions online in order to reach the optimization goal of estimating E. coli fed-batch model parameters with as high accuracy as possible. Optimal experimental designs were recalculated online based on the experimental data and implemented by introducing pulses via the LHS to the running fermentations. The LHS control allows for various implementations of advanced control and optimization strategies in milliliter scale.

Research paper thumbnail of Model-Based Process Optimization for the Production of Macrolactin D by Paenibacillus polymyxa

Processes, 2020

In this study, we show the successful application of different model-based approaches for the max... more In this study, we show the successful application of different model-based approaches for the maximizing of macrolactin D production by Paenibacillus polymyxa. After four initial cultivations, a family of nonlinear dynamic biological models was determined automatically and ranked by their respective Akaike Information Criterion (AIC). The best models were then used in a multi-model setup for robust product maximization. The experimental validation shows the highest product yield attained compared with the identification runs so far. In subsequent fermentations, the online measurements of CO2 concentration, base consumption, and near-infrared spectroscopy (NIR) were used for model improvement. After model extension using expert knowledge, a single superior model could be identified. Model-based state estimation with a sigma-point Kalman filter (SPKF) was based on online measurement data, and this improved model enabled nonlinear real-time product maximization. The optimization increa...