Data Assimilation by Conditioning on Future Observations

Conventional recursive filtering approaches, designed for quantifying the state of an evolving uncertain dynamical system with intermittent observations, use a sequence of (i) an uncertainty propagation step followed by (ii) a step where the associated data is assimilated using Bayes' rule. In this paper we switch the order of the steps to: (i) one step ahead data assimilation followed by (ii) uncertainty propagation. This route leads to a class of filtering algorithms named \emph{smoothing filters}. For a system driven by random noise, our proposed methods require the probability distribution of the driving noise after the assimilation to be biased by a nonzero mean. The system noise, conditioned on future observations, in turn pushes forward the filtering solution in time closer to the true state and indeed helps to find a more accurate approximate solution for the state estimation problem

USING TRAJECTORIES FROM A BIVARIATEGROWTH CURVE OF COVARIATES IN A COXMODEL ANALYSIS

In many maintenance treatment trials, patients are first enrolled into an open treatmentbefore they are randomized into treatment groups. During this period, patients are followedover time with their responses measured longitudinally. This design is very common intoday's public health studies of the prevention of many diseases. Using mixed model theory, onecan characterize these data using a wide array of across subject models. A state-spacerepresentation of the mixed model and use of the Kalman filter allow more fexibility inchoosing the within error correlation structure even in the presence of missing and unequallyspaced observations. Furthermore, using the state-space approach, one can avoid invertinglarge matrices resulting in eficient computations. Estimated trajectories from these models can be used as predictors in a survival analysis in judging the efacacy of the maintenance treatments. The statistical problem lies in accounting for the estimation error in these predictors. We considered a bivariate growth curve where the longitudinal responses were unequally spaced and assumed that the within subject errors followed a continuous firstorder autoregressive (CAR (1)) structure. A simulation study was conducted to validatethe model. We developed a method where estimated random effects for each subject froma bivariate growth curve were used as predictors in the Cox proportional hazards model,using the full likelihood based on the conditional expectation of covariates to adjust for the estimation errors in the predictor variables. Simulation studies indicated that error corrected estimators for model parameters are mostly less biased when compared with thenave regression without accounting for estimation errors. These results hold true in Coxmodels with one or two predictors. An illustrative example is provided with data from a maintenance treatment trial for major depression in an elderly population. A Visual Fortran 90 and a SAS IML program are developed

Estimation of Autoregressive Fading Channels Based on Two Cross-Coupled H∞ Filters

This paper deals with the on-line estimation of time-varying frequency-flat Rayleigh fading channels based on training sequences and using H∞ filtering. When the fading channel is approximated by an autoregressive (AR) process, the AR model parameters must be estimated. As their direct estimations from the available noisy observations at the receiver may yield biased values, the joint estimation of both the channel and its AR parameters must be addressed. Among the existing solutions to this joint estimation issue, Expectation Maximization (EM) algorithm or crosscoupled filter based approaches can be considered. They usually require Kalman filtering which is optimal in the H2 sense provided that the initial state, the driving process and measurement noise are independent, white and Gaussian. However, in real cases, these assumptions may not be satisfied. In addition, the state-space matrices and the noise variances are not necessarily accurately estimated. To take into account the above problem,we propose to use two crosscoupled H∞ filters. This method makes it possible to provide robust estimation of the fading channel and its AR parameters

Diffusion Adaptation over Networks under Imperfect Information Exchange and Non-stationary Data

Adaptive networks rely on in-network and collaborative processing among distributed agents to deliver enhanced performance in estimation and inference tasks. Information is exchanged among the nodes, usually over noisy links. The combination weights that are used by the nodes to fuse information from their neighbors play a critical role in influencing the adaptation and tracking abilities of the network. This paper first investigates the mean-square performance of general adaptive diffusion algorithms in the presence of various sources of imperfect information exchanges, quantization errors, and model non-stationarities. Among other results, the analysis reveals that link noise over the regression data modifies the dynamics of the network evolution in a distinct way, and leads to biased estimates in steady-state. The analysis also reveals how the network mean-square performance is dependent on the combination weights. We use these observations to show how the combination weights can be optimized and adapted. Simulation results illustrate the theoretical findings and match well with theory.Comment: 36 pages, 7 figures, to appear in IEEE Transactions on Signal Processing, June 201

Minimax Quantum Tomography: Estimators and Relative Entropy Bounds

© 2016 American Physical Society. A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of nonadaptive tomography scales as O(1/N) - in contrast to that of classical probability estimation, which is O(1/N) - where N is the number of copies of the quantum state used. We trace this deficiency to sampling mismatch: future observations that determine risk may come from a different sample space than the past data that determine the estimate. This makes minimax estimators very biased, and we propose a computationally tractable alternative with similar behavior in the worst case, but superior accuracy on most states

Coping with unobservable and mis-classified states in capture-recapture studies

Multistate mark-recapture methods provide an excellent conceptual framework for considering estimation in studies of marked animals. Traditional methods include the assumptions that (1) each state an animal occupies is observable, and (2) state is assigned correctly at each point in time. Failure of either of these assumptions can lead to biased estimates of demographic parameters. I review design and analysis options for minimizing or eliminating these biases. Unobservable states can be adjusted for by including them in the state space of the statistical model, with zero capture probability, and incorporating the robust design, or observing animals in the unobservable state through telemetry, tag recoveries, or incidental observations. Mis¿classification can be adjusted for by auxiliary data or incorporating the robust design, in order to estimate the probability of detecting the state an animal occupies. For both unobservable and mis-classified states, the key feature of the robust design is the assumption that the state of the animal is static for at least two sampling occasion

Air-sea heat flux climatologies in the Mediterranean Sea : surface energy balance and its consistency with ocean heat storage Authors

Author Posting. © American Geophysical Union, 2017. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 122 (2017): 4068–4087, doi:10.1002/2016JC012254.This study provides an analysis of the Mediterranean Sea surface energy budget using nine surface heat flux climatologies. The ensemble mean estimation shows that the net downward shortwave radiation (192 ± 19 W m−2) is balanced by latent heat flux (−98 ± 10 W m−2), followed by net longwave radiation (−78 ± 13 W m−2) and sensible heat flux (−13 ± 4 W m−2). The resulting net heat budget (Qnet) is 2 ± 12 W m−2 into the ocean, which appears to be warm biased. The annual-mean Qnet should be −5.6 ± 1.6 W m−2 when estimated from the observed net transport through the Strait of Gibraltar. To diagnose the uncertainty in nine Qnet climatologies, we constructed Qnet from the heat budget equation by using historic hydrological observations to determine the heat content changes and advective heat flux. We also used the Qnet from a data-assimilated global ocean state estimation as an additional reference. By comparing with the two reference Qnet estimates, we found that seven products (NCEP 1, NCEP 2, CFSR, ERA-Interim, MERRA, NOCSv2.0, and OAFlux+ISCCP) overestimate Qnet, with magnitude ranging from 6 to 27 W m−2, while two products underestimate Qnet by −6 W m−2 (JRA55) and −14 W m−2 (CORE.2). Together with the previous warm pool work of Song and Yu (2013), we show that CFSR, MERRA, NOCSv2.0, and OAFlux+ISCCP are warm-biased not only in the western Pacific warm pool but also in the Mediterranean Sea, while CORE.2 is cold-biased in both regions. The NCEP 1, 2, and ERA-Interim are cold-biased over the warm pool but warm-biased in the Mediterranean Sea.National Natural Science Foundation of China (NSFC) Grant Number: 41306003 and 41430963; Fundamental Research Funds for the Central Universities Grant Number: 0905-841313038, 1100-841262028, and 0905-201462003; China Postdoctoral Science Foundation Grant Number: 2013M531647; Natural Science Foundation of Shandong Grant Number: BS2013HZ015; Qingdao National Laboratory for Marine Science and Technology2017-11-1

(Near) Real-Time Snow Water Equivalent Observation Using GNSS Refractometry and RTKLIB

Global navigation satellite system (GNSS) refractometry enables automated and continuous in situ snow water equivalent (SWE) observations. Such accurate and reliable in situ data are needed for calibration and validation of remote sensing data and could enhance snow hydrological monitoring and modeling. In contrast to previous studies which relied on post-processing with the highly sophisticated Bernese GNSS processing software, the feasibility of in situ SWE determination in post-processing and (near) real time using the open-source GNSS processing software RTKLIB and GNSS refractometry based on the biased coordinate Up component is investigated here. Available GNSS observations from a fixed, high-end GNSS refractometry snow monitoring setup in the Swiss Alps are reprocessed for the season 2016/17 to investigate the applicability of RTKLIB in post-processing. A fixed, low-cost setup provides continuous SWE estimates in near real time at a low cost for the complete 2021/22 season. Additionally, a mobile, (near) real-time and low-cost setup was designed and evaluated in March 2020. The fixed and mobile multi-frequency GNSS setups demonstrate the feasibility of (near) real-time SWE estimation using GNSS refractometry. Compared to state-of-the-art manual SWE observations, a mean relative bias below 5% is achieved for (near) real-time and post-processed SWE estimation using RTKLIB