Two-Stage Least Squares for Equivalent-Circuit Model Parameter Estimation of Li-Ion Batteries Using Pulse-Relaxation Excitation
Bibliographic record
Abstract
This paper proposes a two-stage linear least squares (LS) approach for estimating the parameters of a battery equivalent circuit model (ECM) using a simple pulse-relaxation excitation. Unlike conventional approaches that require long relaxation periods or pre-characterized open-circuit voltage (OCV) models to determine the battery OCV, the proposed approach jointly estimates the OCV and the ECM parameters directly from the input-output response. The estimation process is carried out in two sequential LS stages: the first stage estimates the RC time constant from the voltage relaxation response, and the second stage uses the estimated time constant and the entire pulse-relaxation response to estimate the remaining ECM parameters including OCV. A key theoretical contribution is the derivation and Monte Carlo validation of the Cramér–Rao lower bounds for both stages, establishing the lower bound on estimation performance. Using simulations and a newly introduced metric, the rest-to-time-constant ratio, we provide a generalized analytical insights into how signal-to-noise ratio, sampling rate, and the pulse characteristics impact estimation accuracy. The results reveal important principles for excitation signal design in battery ECM parameter estimation, a topic often overlooked in the literature. Finally, experimental validation on a cylindrical Li-ion cell demonstrates that the two-stage LS approach achieves less than 1% relative voltage fitting error over the typical battery operational range.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".