We propose a new approach for securely verifying sequences of location claims from mobile nodes. The key idea is to exploit the inherent mobility of the nodes in order to constrain the degree of freedom of an attacker when spoofing consecutive location updates along a claimed track. We show that in the absence of noise, our approach is able to securely verify any 2-D track with a minimum of three verifiers or any 3-D track with four verifiers. Our approach is lightweight in the sense that it considerably relaxes the system requirements compared to previous secure location verification schemes which are all agnostic to mobility. As opposed to previous schemes, our track verification solution is at the same time (i) passive, (ii) does not require any time synchronization among the verifiers, (iii) does not need to keep the location of the verifiers secret, (iv) nor does it require specialized hardware. This makes our solution particularly suitable for large-scale deployments. We have evaluated our solution in a realistic air traffic monitoring scenario using real-world data. Our results show that 25 position claims from a track are sufficient to detect spoofing attacks with a false positive rate of 1.4% and a false negative rate of 1.2%. For tracks with more than 40 claims, the false positive and false negative rates drop to zero.