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arxiv: 2604.26803 · v2 · submitted 2026-04-29 · 📡 eess.SY · cs.SY

PM-EKF: A Physiological Model-Based Extended Kalman Filter for Daily-Life Physical Activity Energy Expenditure Estimation

Shuhao Que , Remco Poelarends , Valentina Breschi , Ying Wang This is my paper

Pith reviewed 2026-05-08 03:06 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords physical activity energy expenditureextended Kalman filterphysiological modelinertial measurement unitswearable sensorsmetabolic estimationdaily life monitoringstate-space filtering
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The pith

A simplified physiological model inside an extended Kalman filter estimates daily physical activity energy expenditure from IMU motion and heart rate measurements.

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

The paper builds a model that directly connects measured body movements to the metabolic processes that produce energy expenditure during everyday activities. This model is expressed as a nonlinear state-space system and processed with an extended Kalman filter to generate ongoing estimates while accounting for noise and uncertainty. The goal is to deliver personalized results that remain understandable rather than relying on black-box machine learning. Validation used nine participants performing roughly fifty minutes of activities each in a lab setup that mimicked free-living conditions. The resulting estimates explained a median of 72 percent of the variation seen in reference respiratory measurements and exceeded the performance of both linear regression and a CNN-LSTM baseline.

Core claim

The central claim is that a simplified physiological model explicitly linking IMU-captured body-center-of-mass motion to time-varying cardiac output and metabolic gas-exchange processes, when formulated as a nonlinear state-space system and embedded in an EKF, produces PAEE estimates with median R² of 0.72 (range 0.60-0.87) against COSMED K5 reference data and outperforms linear regression (median R² 0.52) and CNN-LSTM (median R² 0.65) on the same nine-subject dataset while remaining interpretable.

What carries the argument

The simplified physiological model that links three-IMU body-center-of-mass motion to measured heart-rate cardiac output and underlying metabolic gas-exchange processes, cast as a nonlinear state-space system for EKF state estimation.

If this is right

  • PAEE estimates become available in real time with explicit handling of sensor noise and model mismatch.
  • IMU mechanical workload dominates accuracy, so heart-rate data may be dropped without major loss in similar protocols.
  • Estimates remain personalized and physiologically interpretable rather than opaque.
  • The framework supports continuous daily-life monitoring without laboratory equipment.
  • Performance exceeds both linear and recurrent neural baselines on the tested dataset.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Wearable devices could adopt this approach to give users ongoing, explainable feedback on energy expenditure during normal routines.
  • Extending the model to include additional signals such as skin temperature or breathing rate might further improve robustness outside controlled settings.
  • The dominance of motion data suggests prioritizing improvements in IMU placement and signal quality for broader applicability.
  • Similar state-space physiological modeling could be tested for related quantities such as fatigue or recovery estimation.

Load-bearing premise

The simplified physiological model accurately represents the relationship between measured body movements and actual metabolic energy expenditure across the range of daily activities.

What would settle it

A larger free-living study collecting simultaneous IMU, heart-rate, and indirect-calorimetry data over full days of varied activities where the model's median R² falls substantially below 0.6 would falsify the reliability claim.

Figures

Figures reproduced from arXiv: 2604.26803 by Remco Poelarends, Shuhao Que, Valentina Breschi, Ying Wang.

Figure 1
Figure 1. Figure 1: A system-level representation of the respiratory control loop and view at source ↗
Figure 2
Figure 2. Figure 2: Placement of the used sensors, including three Movella Xsens DOT view at source ↗
Figure 3
Figure 3. Figure 3: PAEE estimation results using the PM-EKF, CNN-LSTM, and LR models on two subjects in the time domain. The left and right figures correspond view at source ↗
read the original abstract

Monitoring physical activity energy expenditure (PAEE) in daily life is essential for characterizing individual health and metabolic status. Although indirect calorimetry provides gold-standard PAEE measurements, it is impractical for continuous daily-life monitoring. Consequently, wearable sensing approaches using inertial measurement units (IMUs) and heart rate (HR) sensors have attracted substantial interest. However, most existing IMU- and HR-based methods are purely data-driven and offer limited physiological interpretability. In this work, we propose a simplified physiological model that explicitly links body movement during activities of daily living to the underlying metabolic gas-exchange processes governing PAEE. The model is formulated as a nonlinear state-space system and embedded within an Extended Kalman Filter (EKF), enabling principled handling of measurement noise, model uncertainty, and system nonlinearities. The proposed framework provides personalized, interpretable PAEE estimates without employing black-box models. Our model was validated using a dataset, including 9 subjects with around 50 minutes of measurements per subject, collected in our lab simulating a free-living condition. Using the respiratory data measured by COSMED K5 as reference and explained variance (R^2) as evaluation metric, our model's predicted PAEE yielded median (min-max) R^2 = 0.72 (0.60--0.87), using three IMUs (pelvis and two thighs) for capturing the body-center-of-mass motion and measured HR for the time-varying cardiac output. Our model outperformed a linear regression (LR) model (R^2 = 0.52 (0.23--0.92)) and CNN-LSTM model (R^2 = 0.65 (0.46--0.78)) on the same dataset. Notably, excluding the sensory HR measurement did not significantly degrade PAEE estimation of all three models, indicating that IMU-captured mechanical workload dominated PAEE estimation performance in our protocol.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes PM-EKF, a nonlinear state-space physiological model of physical activity energy expenditure (PAEE) embedded in an Extended Kalman Filter. The model explicitly links IMU-derived body center-of-mass kinematics (pelvis + bilateral thighs) and heart-rate measurements to time-varying cardiac output and oxygen uptake. On a 9-subject dataset of ~50 min lab-simulated ADL per subject, the filter yields median R² = 0.72 (range 0.60–0.87) against COSMED K5 reference, outperforming linear regression (0.52) and CNN-LSTM (0.65). The authors note that removing HR input does not significantly degrade performance.

Significance. A correctly specified physiological state-space model would supply an interpretable, parameter-light alternative to black-box regressors for wearable PAEE monitoring and could enable principled uncertainty propagation. The reported dominance of IMU kinematics over HR is a practically useful observation for sensor-minimization studies.

major comments (2)
  1. [§3 and §4] §3 (Physiological Model) and §4 (EKF Formulation): the central justification for using an EKF rather than a generic regressor is that the state equations correctly encode the IMU-to-metabolic linkage. No ablation that disables individual physiological terms (e.g., the cardiac-output or mechanical-work sub-models) or direct comparison of internal filter states (predicted VO₂, stroke volume) against the COSMED reference is presented; only end-to-end PAEE R² is reported. This leaves the load-bearing modeling assumption untested.
  2. [§5] §5 (Experiments): the evaluation uses only 9 subjects and laboratory-simulated ADL. No subject-independent cross-validation statistics, no hold-out free-living recordings, and no power analysis for the reported median R² difference are provided. With such a small cohort the performance gap versus CNN-LSTM could be driven by overfitting or protocol-specific artifacts rather than model fidelity.
minor comments (2)
  1. [Table 1 and §5.2] Table 1 and §5.2: clarify whether the linear-regression and CNN-LSTM baselines received identical IMU + HR feature sets and whether their hyperparameters were tuned on the same cross-validation folds as the EKF.
  2. [§2] §2 (Related Work): several recent IMU-only PAEE papers using biomechanical energy models are cited only in passing; a brief quantitative comparison of their reported R² ranges would strengthen the positioning.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive comments and the positive evaluation of the work's significance. We address each major comment point by point below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [§3 and §4] §3 (Physiological Model) and §4 (EKF Formulation): the central justification for using an EKF rather than a generic regressor is that the state equations correctly encode the IMU-to-metabolic linkage. No ablation that disables individual physiological terms (e.g., the cardiac-output or mechanical-work sub-models) or direct comparison of internal filter states (predicted VO₂, stroke volume) against the COSMED reference is presented; only end-to-end PAEE R² is reported. This leaves the load-bearing modeling assumption untested.

    Authors: We agree that targeted ablations would strengthen the justification for the physiological structure. In the revised manuscript we will add results from two ablations: (i) disabling the cardiac-output sub-model (setting cardiac output to a constant) and (ii) disabling the mechanical-work term, reporting the resulting degradation in PAEE R² for each case. For internal states, COSMED K5 directly measures VO₂, so we will add a comparison of the filter's predicted VO₂ time series against the reference VO₂ in a new figure and subsection of §4. Stroke volume and cardiac output are not measured by the reference system; we will therefore report the estimated cardiac-output trajectories and discuss their physiological plausibility against literature values for ADL rather than claiming direct validation. These changes will be incorporated as a partial revision. revision: partial

  2. Referee: [§5] §5 (Experiments): the evaluation uses only 9 subjects and laboratory-simulated ADL. No subject-independent cross-validation statistics, no hold-out free-living recordings, and no power analysis for the reported median R² difference are provided. With such a small cohort the performance gap versus CNN-LSTM could be driven by overfitting or protocol-specific artifacts rather than model fidelity.

    Authors: We accept that the current evaluation is limited by cohort size and protocol. We will re-run the experiments with leave-one-subject-out cross-validation, reporting mean ± std R² across the nine folds for PM-EKF, LR, and CNN-LSTM. A post-hoc power analysis will be added to quantify the statistical reliability of the median R² differences. The dataset contains only laboratory-simulated ADL and no free-living recordings, so we cannot supply hold-out free-living results; this limitation will be stated more explicitly in §5 and the conclusions. revision: partial

standing simulated objections not resolved
  • The study does not contain free-living recordings, preventing any hold-out validation on unconstrained daily-life data.

Circularity Check

0 steps flagged

No significant circularity detected; derivation remains self-contained against external reference

full rationale

The paper constructs a simplified physiological model linking IMU-captured body-center-of-mass motion and HR to metabolic gas-exchange processes, casts it as a nonlinear state-space system, and applies EKF for state estimation. PAEE predictions are evaluated via R^2 against independent COSMED K5 indirect calorimetry measurements on held-out lab-simulated ADL data from 9 subjects; this reference is external to the model inputs and not used for fitting the core physiological equations. The model also outperforms purely data-driven LR and CNN-LSTM baselines on identical data, and the note that HR removal does not degrade performance is reported as an empirical observation rather than a definitional necessity. No self-citations, parameter-fitting loops that rename fits as predictions, ansatzes smuggled via prior work, or uniqueness theorems appear in the derivation chain. The approach is therefore grounded in first-principles physiological relations plus external validation rather than reducing to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Since only the abstract is available, specific free parameters, axioms, or invented entities in the physiological model cannot be identified. The model is described as simplified and linking movement to gas-exchange, likely involving assumptions about metabolic processes and state variables for the EKF, but details are absent.

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