State of charge (SOC) estimation is a critical function in battery management systems, enabling accurate monitoring of remaining energy in a cell or pack. Traditional methods rely on multiple sensor inputs, including voltage, current, and temperature, to achieve high precision. However, in cost-sensitive or space-constrained applications, only limited sensor data may be available, such as voltage-only measurements. This constraint demands advanced estimation techniques that compensate for missing information while maintaining robustness.

One approach to SOC estimation under limited sensing involves compressive sensing, a signal processing technique that reconstructs sparse or incomplete data sets. Batteries exhibit predictable voltage relaxation behavior under steady-state conditions, allowing voltage-only measurements to be processed using sparse recovery algorithms. By leveraging the inherent structure of battery discharge curves, compressive sensing can approximate SOC even when dynamic current profiles are unavailable. Key to this method is the assumption that the true SOC trajectory lies within a low-dimensional subspace, enabling accurate reconstruction from limited samples. The effectiveness of this approach depends on the battery's open-circuit voltage (OCV) characteristics, with chemistries like lithium iron phosphate (LFP) posing greater challenges due to their flat voltage-SOC relationship.

Observer-based techniques provide another pathway for SOC estimation with restricted inputs. Model-based observers, such as Luenberger or sliding mode observers, use a reduced-order electrochemical or equivalent circuit model to infer SOC from voltage measurements. These methods rely on designing a stable observer gain that minimizes estimation error despite uncertainties in initial conditions or model parameters. For example, a sliding mode observer can enforce convergence to the true SOC by forcing the system trajectory onto a predefined sliding surface, even with parametric inaccuracies. The observer's robustness is often enhanced by adaptive laws that tune model parameters online, compensating for aging or temperature effects without direct measurement.

Robustness to missing or noisy data is essential when relying on limited sensor inputs. Techniques from robust control theory, such as H-infinity filtering or set-membership estimation, can bound SOC errors despite incomplete information. H-infinity filters minimize the worst-case estimation error caused by disturbances, making them suitable for systems where sensor reliability is uncertain. Set-membership approaches, on the other hand, maintain SOC estimates within dynamically adjusted bounds based on voltage measurement residuals. These methods trade off computational complexity for improved reliability in real-world conditions where voltage readings may be intermittent or corrupted.

Data-driven approaches have also gained traction for SOC estimation under sensing constraints. Machine learning models, particularly recurrent neural networks (RNNs) and support vector regression (SVR), can learn voltage-SOC mappings from historical data without explicit knowledge of battery dynamics. These models are trained offline using diverse cycling data and then deployed for real-time inference. While data-driven methods avoid the need for precise physical models, their performance depends heavily on the representativeness of training data across operating conditions. Hybrid approaches that combine model-based observers with data-driven corrections offer a middle ground, leveraging physics where possible and learning residual patterns.

The choice of battery model significantly impacts the performance of voltage-only SOC estimators. Simplified models, such as the single-particle model or first-order equivalent circuits, reduce computational overhead but may sacrifice accuracy during high-rate transients. Higher-fidelity models improve estimation but require careful parameterization to avoid overfitting when only voltage is observable. Techniques like sensitivity analysis help identify the most critical parameters to calibrate, ensuring model outputs remain aligned with sparse voltage measurements.

Practical implementation must address challenges such as sensor drift and sampling rate limitations. Voltage measurements are susceptible to noise and bias, particularly in low-cost systems. Recursive filtering techniques, including moving average or median filters, can suppress high-frequency noise without introducing significant lag. For applications where voltage sampling is sporadic, event-triggered estimation strategies update SOC only when new measurements arrive, conserving computational resources. These strategies often incorporate model predictions between measurement updates, with correction steps applied upon receiving new data.

Validation of voltage-only SOC estimators requires rigorous testing across diverse operating scenarios. Standardized protocols, such as dynamic stress test (DST) or urban dynamometer driving schedule (UDDS) profiles, assess performance under realistic load variations. Benchmarks typically include metrics like mean absolute error (MAE) and root mean square error (RMSE) relative to ground truth SOC determined through coulomb counting with high-precision instrumentation. Results vary by chemistry, with lithium nickel manganese cobalt oxide (NMC) cells generally permitting more accurate voltage-only estimation than LFP due to steeper OCV-SOC gradients.

Emerging research explores the integration of physics-informed neural networks and probabilistic estimation frameworks to further enhance robustness. These advanced methods embed known physical constraints into learning algorithms, preventing unrealistic SOC predictions while retaining adaptability to new operating conditions. Probabilistic approaches, such as Gaussian process regression or particle filters, quantify estimation uncertainty explicitly, enabling risk-aware decision-making in battery management.

The development of reliable SOC estimation under sensing constraints remains an active area of innovation, balancing accuracy, computational efficiency, and implementation cost. As battery applications diversify, from grid storage to portable electronics, tailored solutions will continue to evolve for specific operational environments and performance requirements. Future advancements may leverage embedded intelligence at the cell level, where integrated voltage sensing and local processing enable decentralized SOC estimation without relying on external current measurements.