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Adaptive Conditional Bias-Penalized Kalman Filter for Improved Estimation of Extremes and its Approximation for Reduced Computation

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A penalty term added to the Kalman filter cuts estimation error on extreme states by 20 to 30 percent.

desk verdict A plausible method for improving Kalman-filter tail estimates, but the headline 20-30% result is in-sample because the adaptive penalty weights are chosen on the same runs used to evaluate them. read the letter →

arxiv 1908.00482 v1 pith:Q3NHGIWC submitted 2019-08-01 eess.SP

Haojing Shen , Haksu Lee , Dong-Jun Seo This is my paper · ORCID
classification eess.SP
keywords KalmanfilterconditionalbiasextremestatesvarianceinflationadaptivefilteringType-IIstateestimationCB-penalized
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the standard Kalman filter, which is optimal in average squared error, is systematically biased toward the middle: with uncertain observations it underestimates high states and overestimates low states. To correct that, the authors extend the conditional-bias-penalized Kalman filter (CBPKF) in two directions: a variance-inflated approximation that keeps computational cost near that of the plain filter, and an adaptive rule that applies the penalty strongly only when the estimated state is extreme. In synthetic one-dimensional linear experiments, adaptive CBPKF is reported to reduce root-mean-square error at the extreme tail ends by 20 to 30 percent relative to the Kalman filter, while matching the Kalman filter's unconditional accuracy. The result matters because flood forecasting, target tracking, and similar tasks care more about extremes than about the median, and the approximation makes the penalty affordable in higher dimensions.

What carries the argument

The central object is the apparent error covariance, $\Sigma_a = (I-WH)\Psi_{XX}(I-WH)^T + WRW^T + \alpha(I-WC)\Psi_{XX}(I-WC)^T$, which adds a $\Sigma_{CB}$ penalty to the usual error covariance. Minimizing it produces the modified structure matrix $\hat H^T = H^T + \alpha C^T$ and modified observation error covariance $\Lambda$, and these define the CBPKF gain. The approximation that carries the computational claim is the substitution $C \approx H$, which turns $\Sigma_a$ into the ordinary filtered covariance with $\Psi_{XX}$ inflated by $(1+\alpha)$; the resulting filter, VIKF, is just the Kalman filter run with forecast covariance $(1+\alpha)\Sigma_{k|k-1}$. The adaptive mechanism $\alpha_k = \gamma\|\hat X_{k|k}^{KF}\|$ is what recovers unconditional performance, because the penalty is then large only when the system is estimated to be far from its median.

What would settle it

Set up the same linear experiment with two state variables and two correlated observations, compute $C$ from equation (8), and compare the VIKF filter (forecast covariance inflated by $1+\alpha$) against the full CBPKF across the paper's $\alpha$ range. If the two filters differ by more than about 1% in RMSE for any $\alpha$ without rescaling the penalty, the approximation claim fails outside the scalar case.

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Extended reading notes

Core claim

The paper claims that conditional bias can be removed from Kalman filtering by penalizing the Type-II conditional bias, defined as $X - E[X^*|X]$, the difference between the truth and the filter's expected estimate given that truth. Minimizing the apparent error covariance $\Sigma_a = \Sigma_{EV} + \alpha\Sigma_{CB}$ yields a modified observation operator $\hat H^T = H^T + \alpha C^T$ and a modified observation noise $\Lambda$. The key simplification is that when the penalty gain $C$ is replaced by $H$, the whole procedure collapses to the ordinary Kalman filter with forecast covariance inflated by $1+\alpha$; this is the variance-inflated KF (VIKF) approximation. The adaptive version sets $\alpha_k = \gamma\|\hat X_{k|k}^{KF}\|$, so the penalty grows when the KF estimate departs from the median. The paper reports that adaptive CBPKF performs comparably to KF unconditionally while improving tail RMSE by 20-30%, and that VIKF uses 1.5-3.5 times the computing time of KF versus 5-28 times for the original CBPKF.

Load-bearing premise

The load-bearing premise is that the conditional-bias gain matrix $C$ can be treated as proportional to the observation operator $H$; the paper derives this only in one dimension, and in higher dimensions the variance-inflated filter is matched to CBPKF by tuning the penalty weight rather than by proof.

Editorial extensions

If this is right

  • In any linear-Gaussian filtering task where extremes are the target, replacing KF with adaptive CBPKF can cut tail RMSE by 20-30% without degrading average performance, provided the penalty weight can be tied to a skillful estimate of the state.
  • VIKF lowers the cost of conditional-bias penalization from 5-28 times the KF runtime to 1.5-3.5 times, making the approach usable when the state or observation dimension is large.
  • Because VIKF is implemented as a single covariance inflation factor, existing Kalman filter code can adopt it by replacing $\Sigma_{k|k-1}$ with $(1+\alpha)\Sigma_{k|k-1}$ and re-tuning $\alpha$.
  • The 1D analytical comparison shows CBPKF and VIKF differ only by a factor of two in the effective penalty, so in scalar problems the approximation is exact after rescaling $\alpha$.
  • If the state is known well enough to prescribe $\alpha$ from the truth, the same experiments show adaptive CBPKF beats KF even in the unconditional sense, so better auxiliary state information should translate directly into better overall filtering.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper does not prove $C \approx H$ beyond the scalar case; in higher dimensions it rescales $\alpha$ by 1.25-1.90 to make VIKF match CBPKF. A fair reading is that VIKF is a practical surrogate whose penalty weight must be re-tuned for each problem, not a derivationally guaranteed equivalence.
  • Tying $\alpha$ to the KF estimate creates a feedback loop, since KF is itself conditionally biased in the tails; the paper's Fig. 4a shows slower tail improvement than with truth-prescribed $\alpha$. A testable extension would use the VIKF estimate or ensemble spread instead.
  • VIKF is mathematically just covariance inflation, the same mechanism used to counteract ensemble underdispersion, so a direct comparison with standard inflation techniques would clarify how much of the tail improvement is specific to the conditional-bias objective.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes two modifications of the conditional-bias-penalized Kalman filter (CBPKF): a variance-inflated Kalman filter (VIKF) approximation intended to reduce computational cost, and an adaptive scheme that sets the CB penalty weight alpha_k proportional to the norm of the KF estimate. The authors provide a self-contained derivation of CB-penalized Fisher-like estimation and CBPKF, present a 1D closed-form comparison among KF, VIKF, and CBPKF (Table I), and report synthetic experiments for a scalar linear state-space model under varied nonstationarity. The central empirical claim is that adaptive CBPKF reduces tail RMSE by about 20-30% relative to KF while matching KF in unconditional RMSE, and that VIKF approximates CBPKF closely while increasing computation time only modestly compared with KF.

Significance. If the claims are sustained, the adaptive CBPKF would be a practically valuable, low-complexity modification of the Kalman filter for applications where extreme-state accuracy matters (e.g., hydrologic extremes), and the VIKF approximation would make CBPKF tractable in higher dimensions. The paper's strengths include the explicit 1D analytical comparison, the careful derivation of the CB-penalized estimator, and the clarity of the proposed adaptive rule as a proof of concept. However, the evidence for the headline 20-30% improvement is currently in-sample, and the theoretical justification of the VIKF approximation is limited to the scalar case. These issues are load-bearing for both advertised contributions, so the significance of the paper will depend on whether the authors can provide out-of-sample validation and a general-dimensional justification or clearly restrict the claims.

major comments (3)
  1. [VI, Eq. (51), Fig. 4] The central adaptive-CBPKF claim is supported only by in-sample results. The gamma values 3.0, 1.0, and 0.5 for Groups 1, 2, and 3 in Section VI are selected on the same 12 synthetic cases used to compute the reported RMSE reductions in Fig. 4a, and no selection criterion, sensitivity analysis, or independent test set is described. The abstract and conclusion state that adaptive CBPKF improves tail RMSE by 20-30% over KF, but this is a fitted outcome of the evaluation rather than a predictive validation. Please provide a training/validation/test split or cross-validation, report how gamma is chosen without using the test cases, and show the sensitivity of the improvement to gamma.
  2. [IV, Eq. (42) and Section V] The equivalence between VIKF and CBPKF rests on the linear approximation C approximately equal to H in Eq. (42). This is verified analytically only for the 1D case in Table I, where the relationship holds up to a factor of 2 in the penalty. For general dimensions, Section V only reports numerical closeness for m=1, n=10 with an ad hoc inflation factor of 1.25-1.90. The computational advantage of VIKF is claimed precisely for higher-dimensional problems in Table III (m=5, 10), but no evidence is given that C approximately H, or that the adjusted-alpha heuristic, works there. Either provide a derivation or numerical verification of the C approximately H approximation for m>1, or restrict the VIKF approximation claim to the scalar-state case and substantiate it with experiments at the dimensions claimed.
  3. [V, Fig. 2] The non-adaptive CBPKF comparison also involves in-sample selection of alpha. The text states that for Cases 1, 5, and 9, alpha values of 0.7, 0.6, and 0.5 produce tail RMSE reductions of 15%, 25%, and 30%, respectively, but these alpha values appear to have been chosen after inspecting the RMSE-versus-alpha curves in Fig. 2. Because the same cases are used to select alpha and to compute the reported improvement, the magnitude of the benefit is optimistic relative to what would be achievable with a fixed or pre-specified alpha. Please report results for a predetermined alpha or over the full alpha range, and identify whether the 20-30% figure refers to the adaptive or non-adaptive variant.
minor comments (5)
  1. [V, Table II cross-reference] The text in Section V refers to 'Table I' for the parameter settings of the 12 cases, but the displayed table is Table II; please correct the cross-reference.
  2. [Abstract and Table III] The abstract states that the alternative formulation reduces computing time to 1.5 to 3.5 times of that for KF; this wording is logically inverted, since Table III reports VIKF computing time as 1.51 to 3.46 times that of KF (i.e., slower). Please rephrase to say the computing time is 1.5-3.5 times that of KF.
  3. [VI, Eq. (51)] Equation (51) defines alpha_k = gamma * ||X_hat_{k|k}^KF|| with a norm, but the experiments in Fig. 4 use alpha_k = gamma * |X_hat_{k|k}^KF| for the scalar case; please define the norm used and clarify the relationship for m>1.
  4. [II, Eq. (10)] The word 'scaler' in Eq. (10) should be 'scalar'.
  5. [General typography] Several equations and inline math expressions appear garbled in the submitted text (for example, the definition of Type-II CB in Section II and parts of Eqs. (4) and (5)). Please ensure all mathematical notation is typeset correctly so that the derivation is fully readable.

Circularity Check

2 steps flagged · score 6.0 of 10

The 20-30% tail-RMSE headline is produced by per-group gamma values hand-picked on the same evaluation cases; the adaptive improvement is an in-sample fit rather than an out-of-sample prediction.

  1. fitted input called prediction [Section VI, Eq. (51) and Fig. 4a]
    "we employed the follow ing model for time-varying 𝛼: 𝛼𝑘 = 𝛾‖𝑋̂𝑘|𝑘 𝐾𝐹 ‖ ... The γ values used were 3.0, 1.0 and 0.5 for Groups 1, 2 and 3 in Table II, respectively. The figure shows that adaptive CBPKF performs comparably to KF in the unconditional sense while substantially improving performance in the tails."

    The headline 20-30% tail-RMSE improvement is generated by the adaptive rule α_k = γ‖X̂_KF‖ with γ = 3.0/1.0/0.5 chosen per group on the same 12 cases of Table II that are then used to compute the reported RMSE reductions. No selection criterion, cross-validation, or independent test set is provided, so the improvement is an in-sample fit of γ to the evaluation design rather than an out-of-sample prediction. The Conclusions' admission that 'additional research is needed ... to prescribe the weight for the CB penalty more skillfully' confirms that the prescription of γ is unresolved.

  2. fitted input called prediction [Section V, Evaluation and Results (paragraph following Table I)]
    "the VIKF approximation with 𝛼 increased by a factor of 1.25 to 1.90 differ from CBPKF only by 1% or less for all 12 cases in Table II with m=1 and n=10."

    The closeness of the VIKF approximation to CBPKF is obtained by multiplying α by a factor of 1.25-1.90, a factor fitted to the same 12 cases on which the agreement is then reported. Thus 'differ from CBPKF only by 1% or less' is a property of the calibrated factor, not an independent test of the approximation; the computational-advantage claim is not invalidated, but the reported agreement is partly by construction.

full rationale

The Sections II-IV derivation is largely self-contained: CBPKF is derived from a penalized Fisher-like estimator, and the VIKF form follows from an explicitly stated approximation C≈H with a 1D analytical comparison. Use of the authors' prior CBPKF papers [23,24] is normal and not load-bearing here because the present paper re-derives the filter and does not invoke their results as a uniqueness theorem. The circularity is in the empirical headline claim: the adaptive gain γ in Eq. (51) is selected per group on the same 12 synthetic cases that are then used to compute the RMSE reductions, so the reported 20-30% tail improvement is a fitted outcome rather than a validated prediction. Similarly, the 1.25-1.90 factor used to equate VIKF with CBPKF is calibrated in-sample on the same 12 cases, making the 'very closely approximate' conclusion partly a statement about the fitted factor. These are missing-validation issues rather than mathematical tautologies, but under the fitted-input-called-prediction rule they constitute partial circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim depends on two fitted constants: the adaptive penalty constant γ (3.0, 1.0, 0.5 for Groups 1-3) and the VIKF α-matching factor (1.25-1.90). The derivation assumes linear-Gaussian dynamics with known statistics, imposes unbiasedness W H = I, sets the a priori covariance to the forecast covariance, and above all assumes the CB-penalty gain C is linearly approximable by H. These are reasonable within the paper's scope, but the C≈H approximation is the weakest link and is only demonstrated in 1D.

free parameters (3)
  • gamma (γ) = 3.0, 1.0, 0.5 (Groups 1-3) in Fig. 4a; 3.0, 1.5, 1.0 in Fig. 4b
    Proportionality constant in adaptive alpha_k = γ||X̂_KF||, hand-picked per group on the same synthetic experiments used for evaluation; no tuning procedure or sensitivity analysis.
  • alpha (α) = 0.5-0.7 for best tail performance in non-adaptive CBPKF; iteratively reduced if Σ_{k|k} > Σ_{k|k-1}
    CB penalty weight chosen by user; the paper explores a range and reports improvements at specific values.
  • VIKF alpha adjustment factor = 1.25-1.90
    Multiplicative factor applied to α in the VIKF approximation to match CBPKF within 1% for m=1, n=10; appears to be fitted from experiments.
assumptions (5)
  • domain assumption State and observation models are linear and Gaussian with perfectly known statistics (Eqs. 46-47, Section V)
    The experiments and derivation assume this; the authors acknowledge in the conclusion that non-normal/nonlinear cases are not assessed.
  • ad hoc to paper The CB-penalty regression matrix C is linearly approximable by the observation matrix H (Section IV, Eq. 42)
    This is the load-bearing approximation that turns CBPKF into variance inflation; it is shown only for the 1D case.
  • standard math The unbiasedness condition W H = I is imposed after deriving the penalized solution (Section II, near Eq. 18)
    Standard for linear estimators; but it makes the conditional bias zero if E[Z|X]=HX, which complicates the meaning of the penalty.
  • domain assumption The a priori error covariance ΨXX is set to the forecast covariance Σ_{k|k-1} (Section III)
    Standard in Kalman filtering.
  • ad hoc to paper U^T is chosen as H^T to ensure invertibility in Eq. (6)
    Arbitrary choice; other choices could change C and the approximation.

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Cite this review

Pith. "Pith review of Adaptive Conditional Bias-Penalized Kalman Filter for Improved Estimation of Extremes and its Approximation for Reduced Computation." pith.science (2026). https://pith.science/paper/Q3NHGIWC

@misc{pith2026190800482,
  author       = {Pith},
  title        = {Pith review of: Adaptive Conditional Bias-Penalized Kalman Filter for Improved Estimation of Extremes and its Approximation for Reduced Computation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q3NHGIWC}},
  note         = {Machine review of arXiv:1908.00482}
}
read the original abstract

In many signal processing applications of Kalman filter (KF) and its variants and extensions, accurate estimation of extreme states is often of great importance. When the observations used are uncertain, however, KF suffers from conditional bias (CB) which results in consistent under- and overestimation of extremes in the right and left tails, respectively. Recently, CB-penalized KF, or CBPKF, has been developed to address CB. In this paper, we present an alternative formulation based on variance-inflated KF to reduce computation and algorithmic complexity, and describe adaptive implementation to improve unconditional performance. For theoretical basis and context, we also provide a complete self-contained description of CB-penalized Fisher-like estimation and CBPKF. The results from 1-dimensional synthetic experiments for a linear system with varying degrees of nonstationarity show that adaptive CBPKF reduces root mean square error at the extreme tail ends by 20 to 30% over KF while performing comparably to KF in the unconditional sense. The alternative formulation is found to approximate the original formulation very closely while reducing computing time to 1.5 to 3.5 times of that for KF depending on the dimensionality of the problem. Adaptive CBPKF hence offers a significant addition to the dynamic filtering methods for general application in signal processing when accurate estimation of extremes is of importance.

Figures

Figures reproduced from arXiv: 1908.00482 by the authors.

Figure 1
Figure 1. Comparison of 𝜅𝑘 and 𝜎𝑘|𝑘 2 for KF, the VIKF approximation and CBPKF for three different cases: 𝜎𝑘|𝑘−1 2 = 1 and 𝜎𝑍 2 = 1 (left), 𝜎𝑘|𝑘−1 2 = 1 and 𝜎𝑍 2 = 4 (middle), 𝜎𝑘|𝑘−1 2 = 4 and 𝜎𝑍 2 = 1 (right). TABLE I COMPARISON OF GAIN AND FILTERED ERROR VARIANCE AMONG KF, THE VIKF APPROXIMATION, AND CBPKF. Gain, 𝜿𝒌 Filtered error variance, 𝝈𝒌|𝒌 𝟐 KF ℎ𝜎𝑘|𝑘−1 2 ℎ 2𝜎𝑘|𝑘−1 2 + 𝜎𝑍 2 𝜎𝑍 2 ℎ 2𝜎𝑘|𝑘−1 2 + 𝜎𝑍 2 𝜎𝑘|𝑘−1 2 VIKF approx.… view at source ↗

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Works this paper leans on

39 extracted references · 34 canonical work pages

  1. [1]

    Nonlinear Kalman filtering algorithms fo r on-Line calibration of dynamic traffic assignment models,

    C. Antoniou, M. Ben -Akiva, and H.N. Koutsopoulos, "Nonlinear Kalman filtering algorithms fo r on-Line calibration of dynamic traffic assignment models," IEEE Trans . Intell. Transp. Syst., vol. 8, pp. 661–670, 2007 . DOI:10.1109/TITS.2007.908569

    work page arXiv 2007

  2. [2]

    Constant modulus blind adaptive beamforming based on unscented Kalman filtering,

    M.Z.A. Bhotto, and I.V. Bajić, "Constant modulus blind adaptive beamforming based on unscented Kalman filtering," IEEE Signal Process . Lett., vol. 22 pp. 474–478, 2015. DOI:10.1109/LSP.2014.2362932

    arXiv 2015

  3. [3]

    Ensemble Kalman filter for the reconstruction of the Earth’s mantle circulation,

    M. Bocher, A. Fournier, and N. Coltice, "Ensemble Kalman filter for the reconstruction of the Earth’s mantle circulation," Nonlinear Process. Geophys., vol. 25, pp. 99–123, 2018, DOI:https://doi.org/10.5194/npg-25-99-2018

    work page doi:10.5194/npg-25-99-2018 2018

  4. [4]

    Improving soil moisture estimation with a dual ensemble Kalm an smoother by jointly assimilating AMSR -E brightness temperature and MODIS LST,

    W. Chen, H. Shen, C. Huang, and X. Li, "Improving soil moisture estimation with a dual ensemble Kalm an smoother by jointly assimilating AMSR -E brightness temperature and MODIS LST, " Remote Sens ., vol. 9, 2017, DOI:10.3390/rs9030273

    work page doi:10.3390/rs9030273 2017

  5. [5]

    Application of helmert variance component based adaptive Kalman filter i n multi-GNSS PPP/INS tightly coupled integration,

    Z. Gao, W. Shen, H. Zhang, M. Ge, and X. Niu, "Application of helmert variance component based adaptive Kalman filter i n multi-GNSS PPP/INS tightly coupled integration," Remote Sens ., vol. 8, 2016, DOI:10.3390/rs8070553

    work page doi:10.3390/rs8070553 2016

  6. [6]

    Review of the ensemble Kalman filter for atmospheric data assimilation,

    P.L. Houtekamer, and F. Zhang, "Review of the ensemble Kalman filter for atmospheric data assimilation," Mon. Weather Rev., vol. 144, pp. 4489–4532, 2016, DOI:10.1175/MWR-D-15-0440.1

    doi:10.1175/mwr-d-15-0440.1 2016

  7. [7]

    Phase noise tracking and compensation in coherent optical systems using Kalman filter,

    A. Jain, and P.K. Krishnamurthy, "Phase noise tracking and compensation in coherent optical systems using Kalman filter," IEEE Commun. Lett., vol. 20, pp. 1072–1075, 2016, DOI:10.1109/LCOMM.2016.2550429

    arXiv 2016

  8. [8]

    Landslide deformation analysis by coupling deformation time series from SAR data with hydrological factors through data assimilation,

    Y. Jiang, M. Liao, Z. Zhou, X. Shi, L. Zhang, and T. Balz, "Landslide deformation analysis by coupling deformation time series from SAR data with hydrological factors through data assimilation," Remote Sens., vol. 8, 2016, DOI:10.3390/rs8030179

    work page doi:10.3390/rs8030179 2016

Show all 39 references
  1. [9]

    Identification of time - variant river bed properties with the ensemble Kalman filter,

    W. Kurtz, H. -J.H. Franssen, and H. Vereecken, "Identification of time - variant river bed properties with the ensemble Kalman filter, " Water Resour. Res., vol. 48, 2012, DOI:10.1029/2011WR011743

    2012 doi

  2. [10]

    Kalman filtering for delayed singular systems with multiplicative noise,

    X. Lu, L. Wang, H. Wang, and X. Wang, "Kalman filtering for delayed singular systems with multiplicative noise, " IEEE/CAA J. Automatica Sinica, vol. 3, pp. 51–58, 2016, DOI:10.1109/JAS.2016.7373762

    2016

  3. [11]

    Improved detection of human respiration using data fusion based on a multistatic UWB radar,

    H. Lv, F. Qi, Y. Zhang, T. Jiao, F. Liang, Z. Li, and J. Wang, "Improved detection of human respiration using data fusion based on a multistatic UWB radar," Remote Sens., vol. 8, 2016, DOI:10.3390/rs8090773

    2016 doi

  4. [12]

    Assimilation of remotely-sensed leaf area index into a dynamic vegetation model for gross primary productivity estimation,

    R. Ma, L. Zhang, X. Tian, J. Zhang, W. Yuan, Y. Zheng, X. Zhao, and T. Kato, "Assimilation of remotely-sensed leaf area index into a dynamic vegetation model for gross primary productivity estimation," Remote Sens., vol. 9, 2017, DOI:10.3390/rs9030188

    2017 doi

  5. [13]

    Incorporation of passive microwave brightness temperatures in the ECMWF soil moisture analysis,

    J. Muñoz -Sabater, "Incorporation of passive microwave brightness temperatures in the ECMWF soil moisture analysis," Remote Sens., vol. 7, pp. 5758–5784, 2015, DOI:10.3390/rs70505758

    2015 doi

  6. [14]

    Nair, and J

    A. Nair, and J. Indu, "Enhancing Noah land surface model prediction skill over Indian subcontinent by assimilating SMOPS blended soil moisture, Remote Sens., vol. 8, 2016, DOI:10.3390/rs8120976

    2016 doi

  7. [16]

    Development of a UAV-LiDAR system with application to forest inventory,

    L. Wallace, A. Lucieer, C. Watson, and D. Turner, "Development of a UAV-LiDAR system with application to forest inventory," Remote Sens., vol. 4, pp. 1519–1543, 2012, DOI:10.3390/rs4061519

    2012 doi

  8. [17]

    Crop model data assimilation with the ensemble Kalman filter for improving regional crop yield forecasts,

    A.J.W. de Wit, and C.A. van Diepen, "Crop model data assimilation with the ensemble Kalman filter for improving regional crop yield forecasts," Agric. For. Meteorol., vol. 146, pp. 38–56, 2007, DOI:10.1016/j.agrformet.2007.05.004

    2007 doi

  9. [18]

    Simulation of forest carbon fluxes using model incorporation and data assimilation,

    M. Yan, X. Tian, Z. Li, E. Chen, X. Wang, Z. Han, and H. Sun, "Simulation of forest carbon fluxes using model incorporation and data assimilation," Remote Sens., vol. 8, 2016, DOI:10.3390/rs8070567

    2016 doi

  10. [19]

    An adaptive Kalman filter for dynamic harmonic state estimation and harmonic injection tracking,

    K.K.C. Yu, N.R. Watson, and J. Arrillaga, "An adaptive Kalman filter for dynamic harmonic state estimation and harmonic injection tracking," IEEE Trans. Power Del ., vol. 20, pp. 1577–1584, 2005, DOI:10.1109/TPWRD.2004.838643

    2005

  11. [20]

    Finite-horizon robust Kalman filtering for uncertain discrete time -varying systems with uncertain -covariance white noises,

    Z. Dong, and Z. You, "Finite-horizon robust Kalman filtering for uncertain discrete time -varying systems with uncertain -covariance white noises," IEEE Signal Process . Lett., vol. 13, pp. 493–496, 2006, DOI:10.1109/LSP.2006.873148

    2006

  12. [21]

    Adaptive unscented Kalman filter for target tracking in the presence of nonlinear systems involving model mismatches,

    H. Zhou, H. Huang, H. Zhao, X. Zhao, and X. Yin, "Adaptive unscented Kalman filter for target tracking in the presence of nonlinear systems involving model mismatches," Remote Sens., vol. 9, 2017, DOI:10.3390/rs9070657

    2017 doi

  13. [22]

    Conditional bias in radar rainfall estimation,

    G.J. Ciach, M.L. Morrissey , W.F. Krajewski, G.J. Ciach, M.L. Morrissey, and W.F. Krajewski, "Conditional bias in radar rainfall estimation," J. Appl. Meteorol., vol. 39, pp. 1941–1946, 2000, DOI:10.1175/1520- 0450(2000)039<1941:CBIRRE>2.0.CO;2

    2000 doi

  14. [23]

    Erratum: conditional bias- penalized Kalman filter for improved estimation and prediction of extremes,

    D.J. Seo, M. m. Saifuddin, and H. Lee, "Erratum: conditional bias- penalized Kalman filter for improved estimation and prediction of extremes," Stochastic Environ. Res. Risk Assess., 2018

    2018

  15. [24]

    Conditional bias -penalized Kalman filter for improved estimation and prediction of extremes,

    D.-J. Seo, M.M. Saifuddin, and H. Lee, "Conditional bias -penalized Kalman filter for improved estimation and prediction of extremes," Stochastic Environ. Res. Risk Assess., vol. 32, pp. 183–201, 2018, DOI:10.1007/s00477- 017-1442-8

    2018 doi

  16. [25]

    Jolliffe, and D.B

    I.T. Jolliffe, and D.B. Stephenson, Forecast verification: a practitioner’s guide in atmospheric science, John Wiley & Sons, 2003

    2003

  17. [26]

    A nonparametric postprocessor for bias correction of hydrometeorological and hydrologic ensemble forecasts,

    J.D. Brown, D. -J. Seo, J.D. Brown, and D.-J. Seo, "A nonparametric postprocessor for bias correction of hydrometeorological and hydrologic ensemble forecasts," J. Hydrometeorol., vol. 11, pp. 642–665, 2010, DOI:10.1175/2009JHM1188.1

    2010 doi

  18. [27]

    Conditional bias -penalized kriging (CBPK),

    D.-J. Seo, "Conditional bias -penalized kriging (CBPK), " Stochastic Environ. Res. Risk Assess., vol. 27, pp. 43-58, 2013, DOI:10.1007/s00477-012- 0567-z

    2013 doi

  19. [28]

    Improving real-time estimation of heavy -to-extreme precipitation using rain gauge data via conditional bias-penalized optimal estimation,

    D.-J. Seo, R. Siddique, Y. Zhang, and D. Kim, "Improving real-time estimation of heavy -to-extreme precipitation using rain gauge data via conditional bias-penalized optimal estimation," J. Hydrol., vol. 519, pp. 1824– 1835, 2014, DOI:10.1016/J.JHYDROL.2014.09.055

    2014 doi

  20. [29]

    Improving multisensor estimation of heavy-to-extreme precipitation via conditional bias - penalized optimal estimation,

    B. Kim, D. -J. Seo, S.J. Noh, O.P. Prat, and B.R. Nelson, "Improving multisensor estimation of heavy-to-extreme precipitation via conditional bias - penalized optimal estimation, " J. Hydrol., vol. 556, pp. 1096–1109, 2018, DOI:10.1016/j.jhydrol.2016.10.052

    2018 doi

  21. [30]

    Improving flood forecasting using conditional bias-penalized ensemble Kalman filter,

    H. Lee, S. J. Noh, S. Kim, H. Shen, D.-J. Seo, and Y. Zhang, "Improving flood forecasting using conditional bias-penalized ensemble Kalman filter," Submitted to J. Hydrol., 2018

    2018

  22. [31]

    Schweppe, Uncertain dynamic systems , Prentice -Hall, 1973

    F.C. Schweppe, Uncertain dynamic systems , Prentice -Hall, 1973. [Online]. Available: https://openlibrary.org/books/OL5291577M/Uncertain_dynamic_systems

    1973

  23. [32]

    Woodbury, Inverting modified matrices , Princeton University, Princeton, N

    M.A. Woodbury, Inverting modified matrices , Princeton University, Princeton, N. J., 1950

    1950

  24. [33]

    Mismeasured variables in econometric analysis: problems from the right and problems from the left,

    J. Hausman, "Mismeasured variables in econometric analysis: problems from the right and problems from the left," J. Econ. Perspect., vol. 15, pp. 57– 67, 2001

    2001

  25. [34]

    locfit: local regression, likelihood and density estimation,

    Catherine Loader, "locfit: local regression, likelihood and density estimation," 2013, [Online]. Available: https://CRAN.R- project.org/package=locfit

    2013

  26. [35]

    Assimilation of hydrologic and hydrometeorological data into distributed hydrologic model: effect of adjusting mean field bias in radar-based precipitation estimates,

    H. Lee, and D.-J. Seo, "Assimilation of hydrologic and hydrometeorological data into distributed hydrologic model: effect of adjusting mean field bias in radar-based precipitation estimates," Adv. in Water Resour., vol. 74, pp. 196–211, 2014, DOI:10.1016/j.advwatres.2014.09.002

    2014 doi

  27. [36]

    Lee, D.-J

    H. Lee, D.-J. Seo, and V. Koren, "Assimilation of streamflow and in situ soil moisture data into operational distributed hydrologic models: effects of uncertainties in the data and initial model soil moisture states, " Adv. in Water Resour., vol. 34, pp. 1597–1615, 2011, DOI:1...

    2011 doi

  28. [37]

    Variational assimilation of streamflow into operational distributed hydrologic models: effect of spatiotemporal scale of adjustment,

    H. Lee, D. -J. Seo, Y. Liu, V. Koren, P. McKee, and R. Corby, "Variational assimilation of streamflow into operational distributed hydrologic models: effect of spatiotemporal scale of adjustment," Hydrol. Earth Syst. Sci., vol. 16, pp. 2233–2251, 2012, DOI:https://doi.org/10.5...

    2012 doi

  29. [38]

    Utilizing satellite precipitation estimates for streamflow forecasting via adjustment of mean field bias in precipitation data and assimilation of streamflow observations,

    H. Lee, Y. Zhang, D.-J. Seo, and P. Xie, "Utilizing satellite precipitation estimates for streamflow forecasting via adjustment of mean field bias in precipitation data and assimilation of streamflow observations," J. Hydrol., vol. 529, pp. 779–794, 2015, DOI:10.1016/j.jhydrol...

    2015 doi

  30. [39]

    Comparative evaluation of maximum likelihood ensemble filter and ensemble Kalman filter for real - time assimilation of stre amflow data into operational hydrologic models,

    A. Rafieeinasab, D.-J. Seo, H. Lee, and S. Kim, "Comparative evaluation of maximum likelihood ensemble filter and ensemble Kalman filter for real - time assimilation of stre amflow data into operational hydrologic models, " J. Hydrol., vol. 519, pp. 2663–2675, 2014, DOI:10.101...

    2014 doi

  31. [40]

    Real-time variational assimilation of hydrologic and hydrometeorological data into operational hydrologic forecasting,

    D.-J. Seo, V. Koren, and N. Cajina, "Real-time variational assimilation of hydrologic and hydrometeorological data into operational hydrologic forecasting," J. Hydrometeor., vol. 4, pp. 627–641, 2003, DOI:10.1175/1525- 7541(2003)004<0627:RVAOHA>2.0.CO;2

    2003 doi

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.