Residual Bias Compensation Dual Extended Kalman Filter for Physics-Based SOC Estimation in Lithium Iron Phosphate Batteries

arXiv:2510.22813 · eess.SY, cs.SY · Submitted 2025-10-26 · Read on arXiv

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Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: Today's paper: "Residual Bias Compensation Dual Extended Kalman Filter for Physics-Based SOC Estimation in Lithium Iron Phosphate Batteries".

Dev: A residual bias compensation dual extended Kalman filter (RBC-DEKF) is developed to address state of charge (SOC) estimation challenges in lithium iron phosphate (LFP) batteries,

Rosa: First, who's behind it and why it matters.

Title and authors: Rosa: So we're looking at the paper titled "Residual Bias Compensation Dual Extended Kalman Filter for Physics-Based SOC Estimation in Lithium Iron Phosphate Batteries" by Guo, Couto, Trad, Hu, and Safari. It sounds like they are tackling a really specific problem within battery estimation. Dev That title tells us immediately that they are using a dual extended Kalman filter to handle residual bias compensation while estimating the state of charge in LFP batteries. Rosa Exactly; the focus is clearly on overcoming the observability issues that come with LFP batteries having a relatively flat open-circuit voltage to state of charge characteristic. Dev It seems like they’re proposing a decoupled structure where one filter handles the actual electrochemical states and another filter specifically estimates the residual bias to correct measurement deviations in real time. Rosa That decoupling is what caught my attention; it suggests they're trying to solve a problem that usually requires treating the bias as just another part of the main state, which can get messy. Dev Right, and if they succeed in this decoupling, it means we could potentially refine the voltage prediction without messing up the core electrochemical dynamics of the battery model.

Taro: From an autonomy perspective, I'm curious how robust this estimation is when things go wrong outside of a perfectly controlled lab environment. Rosa That’s a fair question; I was thinking about that right away—how long can this system actually operate reliably in the field? Dev The paper focuses heavily on the filtering mechanism itself, so it doesn't explicitly detail field deployment times, but its performance validation included tests across several temperatures, which gives us some clues about its stability. Taro I want to know what happens when the world misbehaves; does this dual filter handle unexpected sensor noise or sudden changes in the battery’s internal resistance that we don't expect?

Rosa: Well, it seems like the researchers focused on demonstrating its performance across a range of conditions, which hints at some real-world applicability beyond just idealized lab settings. Dev If you look at their methodology, they use a physics-based model—specifically the CPG-SPMT—which grounds the estimation in known electrochemical principles rather than relying purely on data patterns. Taro That reliance on a physics model is interesting because it suggests that if the underlying physical assumptions about diffusion or kinetics are sound, this dual filter approach should hold up better than purely data-driven methods when the OCV-SOC curve is flat.

Rosa: It’s a strong point; they are trying to anchor the estimation in known physics, which helps when the measurement characteristics, like that flat OCV–SOC curve in LFP batteries, make it hard for simpler filters to see what's happening. Dev That flatness is definitely the core challenge they are addressing with this specific paper. It sets up a situation where standard methods struggle because the state estimation becomes unobservable with just one filter. Taro So, the implication here is that we might see more reliable SOC tracking in batteries that have challenging voltage profiles, not just those with steep curves like NMC ones which they mention in prior work twelve <ref:2510.22813#pg0>.

The paper's summary: Rosa: Moving on to what the paper actually summarizes, the core idea of this work is developing the Residual Bias Compensation Dual Extended Kalman Filter for Physics-Based SOC Estimation in Lithium Iron Phosphate Batteries. Essentially, they are presenting a method where they use two separate extended Kalman filters instead of one combined filter to estimate both the electrochemical states and an unknown residual bias simultaneously. Dev That summary highlights that the dual structure is key because it separates the estimation of the physical battery dynamics from the correction of measurement errors like sensor biases. Rosa Yes, and they explain that one EKF estimates those internal electrochemical states using a model based on thermal effects, while the second EKF independently tracks a residual bias to continuously adjust how they interpret the voltage observation equation. Dev That means instead of coupling everything into one large covariance matrix which can become unstable when observability is poor, this paper proposes separating those estimation tasks. Rosa It seems like the main takeaway from their summary is that this decoupling allows them to refine the model-predicted voltage in real time without disturbing the actual evolution of the electrochemical states themselves.

Taro: If I were to summarize what that means for a robot or an autonomous system, it suggests a more resilient way to handle noisy sensor data where you have multiple sources of error layered on top of each other. Dev Precisely; if one part of the measurement equation is persistently offset by a bias, this dual filter structure lets the second filter hunt down that bias separately, which keeps the first filter focused on tracking what's actually happening chemically. Rosa It gives us a mechanism for better handling those unmodeled dynamics and sensor biases that plague complex systems like batteries. Taro It really pushes the idea of separating estimation tasks to handle system complexity rather than trying to force a single, overly complicated model to account for everything at once.

Dev: I think what they emphasize is that this approach improves the model accuracy and thus the SOC estimation performance by accounting for things like sensor biases and unmodeled dynamics, which adjusting parameters alone just can't fix on its own Rosa. It’s about refining the voltage observation equation in real time, not just guessing a better parameter set beforehand.

Rosa: So, to put it simply, they are using this dual filter approach to get a more accurate SOC estimate by treating the systematic measurement error as an explicit state that gets corrected alongside the true battery state. Taro It sounds like they are building a system that can be more forgiving of imperfect models, which is crucial when deploying autonomous systems in unpredictable environments.

The paper's improvements: Dev: Now let's talk about the specific improvements they suggest in the "Residual Bias Compensation Dual Extended Kalman Filter for Physics-Based SOC Estimation in Lithium Iron Phosphate Batteries." They highlight that this dual structure improves performance over conventional bias-augmented single-filter schemes which treat the bias as an augmented state within a single filter. Rosa That’s a direct comparison to existing methods, showing that decoupling the bias estimation from the main state estimation doesn't just offer marginal gains; it leads to significant improvements in SOC accuracy and voltage prediction compared to those coupled approaches. Dev The paper shows that by separating these estimations, they avoid perturbing the electrochemical state dynamics with the bias estimator, which is a major technical advantage when dealing with highly sensitive systems. Rosa And their validation results are quite compelling; for instance, they reported reducing the average SOC Root Mean Square Error from three point seven five percent down to about zero point two zero percent, and they also saw a massive reduction in voltage estimation errors, cutting the voltage RMSE from thirty-two point eight mV down to less than zero point eight mV across different operating temperatures of the A123 LFP eighteen thousand six hundred fifty cell Rosa.

Taro: That drop in SOC RMSE, going from nearly four percent error down to about two percent, is substantial for battery monitoring systems in practice; that level of accuracy is something you really need when you're trying to monitor health accurately. Dev And the voltage error reduction from thirty-two point eight mV to under zero point eight mV shows a huge leap in predictive capability, meaning the filtered model voltage is much closer to what the sensors are actually reading. Rosa It’s impressive how they managed to achieve these kinds of reductions in error metrics across varying temperature conditions, including those tested at zero degrees Celsius, twenty-five degrees Celsius, and fifty degrees Celsius.

Dev: The robustness across that wide temperature spectrum is particularly noteworthy because it confirms the method isn't just working in a narrow band but can handle the thermal effects modeled in their CPG-SPMT model effectively Rosa.

Taro: That’s exactly what I was wondering about earlier; if this works across different temperatures, it suggests that the compensation mechanism is fundamentally sound and not just a fluke for one specific operating point.

Conclusion: Rosa: So, wrapping up our discussion on the Residual Bias Compensation Dual Extended Kalman Filter for Physics-Based SOC Estimation in Lithium Iron Phosphate Batteries. Essentially, this paper presents a dual filter approach that successfully decouples the residual bias estimation from electrochemical state estimation using a physics-based model. Dev The main implication is that this method offers a way to get high-precision SOC estimates even in batteries with tricky voltage characteristics like LFP’s flat OCV–SOC curve. Rosa It moves beyond just fixing parameters and shows how separating the bias correction can lead to much tighter error bounds for both state tracking and voltage prediction. Dev And the validation data, showing those substantial reductions in SOC RMSE and voltage RMSE, really supports the idea that this is a viable technique for improving estimation accuracy in these types of systems.

Taro: For me, I see the biggest implication being about building more reliable autonomous systems that can operate when sensor performance isn't perfect. Rosa That makes sense; if we can build systems whose state estimation is less sensitive to systematic measurement errors, they become much more trustworthy in complex scenarios. Dev And for a control engineer like me, the decoupling of the filter structure means we have a cleaner way to manage latency and potential failure modes in the loop rate, since the bias correction isn't constantly fighting with our primary state update.

Rosa: It’s encouraging to see this kind of refinement in how we handle estimation challenges in battery monitoring. Taro I just think if we can apply this concept of separating estimation tasks to other areas, like sensor tracking or autonomous navigation, it could open up new ways to handle system uncertainty that we're currently ignoring.

Dev: Indeed, the Residual Bias Compensation Dual Extended Kalman Filter for Physics-Based SOC Estimation in Lithium Iron Phosphate Batteries is a solid piece of work showing how careful modeling and filtering structure can tackle complex estimation problems.

Institute for Materials Research (IMO-imomec), Hasselt University (UHasselt) · WET, VITO

eess.SY, cs.SY

Submitted: 2025-10-26

Updated: 2026-10-05

Comments: 6 pages, 4 figures. Published in the Proceedings of the 2026 European Control Conference (ECC). This is the authors' accepted version. The official published version is available on IEEE Xplore: https://ieeexplore.ieee.org/document/11625570

Journal ref: Proceedings of the 2026 European Control Conference (ECC), 2026, pp. 1708-1713

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 90/100

The gist: A residual bias compensation dual extended Kalman filter (RBC-DEKF) is developed to address state of charge (SOC) estimation challenges in lithium iron phosphate (LFP) batteries, where the relatively

Key concepts

Flat OCV–SOC Characteristic: In LFP batteries, the relationship between open-circuit voltage (OCV) and State of Charge (SOC) is relatively flat. This flatness makes it difficult for standard estimation methods to reliably determine the battery's charge level because small changes in SOC do not cause large, easily measurable changes in voltage.
Residual Bias Compensation Dual Extended Kalman Filter (RBC-DEKF): This is a novel filtering approach that uses two separate extended Kalman filters. One filter estimates the battery's internal states, while the second filter specifically estimates and compensates for residual bias errors. Separating these tasks leads to more robust and accurate state estimation.
Physics-Based Model (CPG-SPMT): The system uses a detailed physics model based on particle dynamics with thermal effects. This model describes how the internal physical states of the positive and negative electrodes change over time, providing a realistic foundation for predicting battery behavior.

Terminology

Accuracy — 18× in this paper · explained in 1 episode
Decoupling — 5× in this paper · explained in 2 episodes
Robustness — 4× in this paper · explained in 5 episodes
Consistency — 3× in this paper · explained in 3 episodes
Core — 3× in this paper · explained in 2 episodes
Interpretability — 2× in this paper · explained in 15 episodes
Adaptability — 1× in this paper · explained in 1 episode
European Control Conference — 1× in this paper
Failure Modes — 1× in this paper · explained in 3 episodes
Generalizability — 1× in this paper · explained in 6 episodes
Generalization — 1× in this paper · explained in 13 episodes
Hysteresis — 1× in this paper · explained in 3 episodes
Verification — 1× in this paper · explained in 2 episodes

Summary

A residual bias compensation dual extended Kalman filter (RBC-DEKF) is developed to address state of charge (SOC) estimation challenges in lithium iron phosphate (LFP) batteries, where the relatively flat open-circuit voltage (OCV)–SOC characteristic reduces observability. This method decouples residual bias estimation from electrochemical state estimation using a dual-filter structure, leading to significant improvements in SOC accuracy and voltage prediction compared to conventional methods.

The gist

Electrochemical Model and System Formulation

The work employs a physics-based model based on the control-oriented parameter-grouped single particle model with thermal effects (CPG-SPMT). This model is formulated in a state-space form to satisfy controllability and observability conditions, where the normalized state vector is denoted by χ = [χ p n]⊤, corresponding to internal dynamic states of the positive and negative electrodes. The system dynamics are described by:

State equation: χ˙(t) = Aχ˜ (t) + Bu˜ (t), with the initial condition χ(0) = χ0.
Output equation: ψ(t) = Cχ˜ (t) + Du˜ (t).

The terminal voltage predicted by the SPM is formulated as:

VSPM(t) = OCPp c ss,p(t − OCPn c ss,n(t − ηp c ss,p(t − I(t) - ηn c ss,n(t − I(t)) - R0I(t)).

Residual Bias Compensation Dual Extended Kalman Filter (RBC-DEKF)

The proposed method utilizes a dual extended Kalman filter structure to decouple residual bias estimation from electrochemical state estimation. Unlike conventional bias-augmented single-filter schemes that treat the bias as an augmented state within a single filter, the RBC-DEKF separates these estimations.

The first EKF estimates the system states χ using prediction step: χˆkk−1 = Adχˆk−1k−1 + Bduk−1 (Eq. 19).
The second scalar EKF updates the residual bias state θ using prediction step: ˆθkk-1 = ˆθk-1k-1 (Eq. 28).

The measurement equation incorporates the estimated residual bias:

zk = h(χk, uk, θk) + vk = V(ψk, uk) + θk + vk (Eq. 18).

Filter Updates and State Estimation

The state filter update uses the innovation yx k = zk − Vˆ SPM,k + ˆθk−1k−1 (Eq. 23), followed by Kalman gain calculation Kx k = Px kk−1(Hx k)⊤ Sxk − Rx (Eq. 25). The covariance update adopts the Joseph stabilized form for numerical consistency.

The residual bias filter update uses the innovation yθ k = zk − Vˆ xSPM,k + ˆθkk−1 (Eq. 32), with Kalman gain Kθ k = Pθ kk−1(Hθ k)⊤ Sθ k − Stheta-1 (Eq. 34).

SOC Estimation and Performance Validation

After each iteration, the estimated state vector χˆkk is used to reconstruct normalized lithium concentrations, which are then used to calculate electrode-level SOC:

SOCi,k = ˜cs i,k − ˜cs i,min / (˜cs i,max − ˜cs i,min), i ∈ p, n (Eq. 37). The overall cell SOC is the mean of the positive and negative electrode SOCs:

SOCk = 1/2(SOCp,k + SOCn,k) (Eq. 38).

Validation on an A123 LFP 18650 cell under three conditions (US06 at 0 °C, DST at 25 °C, and FUDS at 50 °C) demonstrated substantial improvements over a conventional EKF. The RBC-DEKF reduced the average SOC RMSE from 3.75% to 0.20% and the voltage RMSE between the filtered model voltage and the measured voltage from 32.8 mV to 0.8 mV, confirming its effectiveness across a wide temperature range, particularly in the mid-SOC range where OCV–SOC is flat.

Improvements for AI systems

Here are the specific improvements that can be made to AI systems by leveraging the proposed Residual Bias Compensation Dual Extended Kalman Filter (RBC-DEKF) framework, and what these improved systems can achieve:

The core improvement is moving from a single-filter approach (which suffers when model observability is poor, as in LFP batteries) to a decoupled, dual-filter architecture that explicitly separates electrochemical state estimation from residual bias correction.

Here are the specific improvements and resulting capabilities:

Mitigation of Model-Induced Observability Issues in Non-Linear Systems (LFP Batteries):
Enhanced Real-Time State Estimation Accuracy Under Flat OCV–SOC Regions:
Robustness to Sensor Biases and Model Mismatches via Decoupling:

The improved AI system (the RBC-DEKF implementation) can achieve the following specific capabilities:

Provide highly accurate, continuous State of Charge (SOC) estimation for Lithium Iron Phosphate (LFP) batteries across a wide temperature range, overcoming the inherent challenges posed by their relatively flat Open Circuit Voltage (OCV)–SOC characteristic.
Achieve significantly reduced error metrics compared to conventional Extended Kalman Filters (EKF). Specifically:
Minimize SOC Root Mean Square Error (RMSE), reducing it from an average of 3.75% to approximately 0.20%.
Drastically reduce voltage estimation errors, narrowing the gap between filtered model voltage and measured voltage, reducing the RMSE from 32.8 mV to under 0.8 mV (a reduction of over 97%).
Maintain superior performance during dynamic operating conditions (e.g., US06 at 0°C, DST at 25°C, and FUDS at 50°C), where conventional methods suffer from observable drift or large transient errors in the mid-SOC range.
Effectively compensate for unmodeled dynamics, sensor biases, and model parameter inaccuracies in real time by treating the residual bias as an independent state variable rather than coupling it into the primary state estimation covariance matrix.