Small object tracking in low-resolution remote sensing images presents numerous challenges. Targets are relatively small compared to the field of view, do not present distinct features, and are often lost in cluttered environments. In this paper, we propose a track-by-detection approach to detect and track small moving targets by using a convolutional neural network and a Bayesian tracker. Our object detection consists of a two-step process based on motion and a patch-based convolutional neural network (CNN). The first stage performs a lightweight motion detection operator to obtain rough target locations. The second stage uses this information combined with a CNN to refine the detection results. In addition, we adopt an online track-by-detection approach by using the Probability Hypothesis Density (PHD) filter to convert detections into tracks. The PHD filter offers a robust multi-object Bayesian data-association framework that performs well in cluttered environments, keeps track of missed detections, and presents remarkable computational advantages over different Bayesian filters. We test our method across various cases of a challenging dataset: a low-resolution satellite video comprising numerous small moving objects. We demonstrate the proposed method outperforms competing approaches across different scenarios with both object detection and object tracking metrics.