Accurate and precise online estimation of the state of health (SOH) is crucial when managing lithium-ion batteries. Most existing SOH estimation methods rely on supervised learning algorithms utilizing large amounts of labeled data. However, lithium-ion batteries are typically operated under dynamic conditions, including significant amounts of unlabeled charging or discharging data in online application scenarios. To fully utilize these data, we propose an adaptive semi-supervised self-learning teacher-student model (AS3LTSM) method for online SOH estimation. First, four physically interpretable health indicators (PIHIs) are extracted from the voltage and current data. The Pearson correlation coefficient (PCC) is used to assess significant associations between PIHIs and the SOH. Regressive and autoregressive long short-term memory (LSTM) models are selected as the teacher and student networks. Knowledge is transferred from the teacher to the student through pseudolabels, which guide the updating and evolution of the student network. Furthermore, a self-learning strategy and a retraining process for improving the long-term estimation accuracy are proposed. Two public datasets are used for comparison and ablation experiments. Experimental analysis validates the improved effectiveness and performance of the proposed method, with the RMSE and MAPE of the three experimental groups all within 1.3 % and 1.29 %, respectively.