@article{hamilton_berry_sauer_2019, title={Correcting observation model error in data assimilation}, volume={29}, ISSN={["1089-7682"]}, DOI={10.1063/1.5087151}, abstractNote={Standard methods of data assimilation assume prior knowledge of a model that describes the system dynamics and an observation function that maps the model state to a predicted output. An accurate mapping from model state to observation space is crucial in filtering schemes when adjusting the estimate of the system state during the filter's analysis step. However, in many applications, the true observation function may be unknown and the available observation model may have significant errors, resulting in a suboptimal state estimate. We propose a method for observation model error correction within the filtering framework. The procedure involves an alternating minimization algorithm used to iteratively update a given observation function to increase consistency with the model and prior observations using ideas from attractor reconstruction. The method is demonstrated on the Lorenz 1963 and Lorenz 1996 models and on a single-column radiative transfer model with multicloud parameterization.}, number={5}, journal={CHAOS}, author={Hamilton, Franz and Berry, Tyrus and Sauer, Timothy}, year={2019}, month={May} }
 @article{arthur_attarian_hamilton_tran_2018, title={Nonlinear Kalman filtering for censored observations}, volume={316}, ISSN={0096-3003}, url={http://dx.doi.org/10.1016/j.amc.2017.08.002}, DOI={10.1016/j.amc.2017.08.002}, abstractNote={The use of Kalman filtering, as well as its nonlinear extensions, for the estimation of system variables and parameters has played a pivotal role in many fields of scientific inquiry where observations of the system are restricted to a subset of variables. However in the case of censored observations, where measurements of the system beyond a certain detection point are impossible, the estimation problem is complicated. Without appropriate consideration, censored observations can lead to inaccurate estimates. Motivated by previous work on censored filtering in linear systems, we develop a modified version of the extended Kalman filter to handle the case of censored observations in nonlinear systems. We validate this methodology in a simple oscillator system first, showing its ability to accurately reconstruct state variables and track system parameters when observations are censored. Finally, we utilize the nonlinear censored filter to analyze censored datasets from patients with hepatitis C and human immunodeficiency virus.}, journal={Applied Mathematics and Computation}, publisher={Elsevier BV}, author={Arthur, Joseph and Attarian, Adam and Hamilton, Franz and Tran, Hien}, year={2018}, month={Jan}, pages={155–166} }
 @article{hamilton_setzer_chavez_tran_lloyd_2017, title={Adaptive filtering for hidden node detection and tracking in networks}, volume={27}, number={7}, journal={Chaos (Woodbury, N.Y.)}, author={Hamilton, F. and Setzer, B. and Chavez, S. and Tran, H. and Lloyd, A. L.}, year={2017} }
 @article{hamilton_lloyd_flores_2017, title={Hybrid modeling and prediction of dynamical systems}, volume={13}, number={7}, journal={PLoS Computational Biology}, author={Hamilton, F. and Lloyd, A. L. and Flores, K. B.}, year={2017} }
 @article{hamilton_berry_sauer_2017, title={Kalman-Takens filtering in the presence of dynamical noise}, volume={226}, ISSN={["1951-6401"]}, DOI={10.1140/epjst/e2016-60363-2}, abstractNote={The use of data assimilation for the merging of observed data with dynamical models is becoming standard in modern physics. If a parametric model is known, methods such as Kalman filtering have been developed for this purpose. If no model is known, a hybrid Kalman-Takens method has been recently introduced, in order to exploit the advantages of optimal filtering in a nonparametric setting. This procedure replaces the parametric model with dynamics reconstructed from delay coordinates, while using the Kalman update formulation to assimilate new observations. We find that this hybrid approach results in comparable efficiency to parametric methods in identifying underlying dynamics, even in the presence of dynamical noise. By combining the Kalman-Takens method with an adaptive filtering procedure we are able to estimate the statistics of the observational and dynamical noise. This solves a long standing problem of separating dynamical and observational noise in time series data, which is especially challenging when no dynamical model is specified.}, number={15}, journal={EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS}, author={Hamilton, Franz and Berry, Tyrus and Sauer, Timothy}, year={2017}, month={Dec}, pages={3239–3250} }
 @article{hamilton_berry_sauer_2016, title={Ensemble Kalman Filtering without a Model}, volume={6}, ISSN={["2160-3308"]}, DOI={10.1103/physrevx.6.011021}, abstractNote={Drawing inferences from data is at the heart of many fields of science. A new kind of data analysis, free of assumptions from underlying models, is proposed and its use demonstrated on weather data.}, number={1}, journal={PHYSICAL REVIEW X}, author={Hamilton, Franz and Berry, Tyrus and Sauer, Timothy}, year={2016}, month={Mar} }