This paper presents a symbolic dynamic method for real-time estimation of battery state-of-charge (SOC). In the proposed method, symbol strings are generated by partitioning (finite-length) time windows of synchronized input-output (e.g., current-voltage) pairs in the respective two-dimensional space. Then, a special class of probabilistic finite state automata (PFSA), called D-Markov machine, is constructed from the symbol strings to extract pertinent features. The SOC estimation is formulated as a sequential estimation scheme with adaptive acceptance of new features to circumvent the problem of having potential outliers. A major challenge is that SOC value is continuously varying during the operation. While modeling and analysis of such time-varying problems is computationally intensive, the data-driven approach requires adequate length of time series data for statistically significant analysis. From these perspectives, a critical aspect is to determine an optimal (or suboptimal) length of the analysis window to make a tradeoff between estimation accuracy and dynamic sensitivity. The proposed method has been validated on experimental data of a commercial-scale lead-acid battery.