We propose an online algorithm to estimate the state of charge (SOC) and parameters of lithium-ion batteries suitable for wireless battery management systems with low requirements on data transmission rates. We assume the voltage measurement of each battery cell and the battery pack current are quantized before being sent to the battery management system. A conventional equivalent circuit model of batteries is augmented with system parameters, and we analyzed its observability. We found although this augmented model is not observable in linear sense, it is fully observable based on a nonlinear observability analysis. Hence, two nonlinear observers are designed, based on the unscented Kalman filter and the ensemble Kalman filter, respectively. Using the experimental data, we show that based on the designed algorithms, the requirements on transmitting voltage measurement data for estimating battery SOC and parameters can be reduced from 11 bits per sample to 4 bits per sample, while the error of battery SOC estimation can be limited to 0.5%.