Although positioning in both indoor and outdoor environments has been investigated in-depth individually by various means, little attention has been paid to the intersected areas of both environments and the positioning accuracy in these boundary areas remains concern. For indoor positioning, several recent studies have applied machine learning algorithms based on WiFi signals. However, these methods may not be applicable to solve the boundary localization problem which is faced for positioning in boundary areas around a building. In this paper, we propose a deep learning model which concatenates auto-encoders with LSTM networks to perform multi-sensor multi-task fingerprint positioning. The adopted sensors include WiFi, GPS, cellular (fused with GPS), and magnetometer. In our model, we first employ a dense block-based auto-encoder to extract representative latent codes of fingerprints. Such latent codes are proven to be more distinguishable since they are revertible to their original inputs. Then, a sequence of latent codes are injected into an LSTM network performing three output tasks, responsible for location estimation, most suitable sensor selection, and indoor/outdoor classification, respectively. Extensive real-life experiments are performed on two campuses and the results demonstrate that our model achieves high positioning accuracy with an average Euclidean distance estimation error of about 0.43 meter.