Currently, indoor navigation software is typically embedded in smartphones as mobile applications. These apps enable users to access cloud-based data while retrieving indoor navigation information. However, cloud data faces risks of tampering and deletion, necessitating verification of its integrity by users. While smartphones possess certain computational capabilities, prolonged execution of computationally intensive tasks can lead to rapid battery depletion. Additionally, excessive storage demands may prompt users to frequently close or even uninstall the apps to free up memory. This paper presents a blockchain-based data integrity verification scheme tailored for indoor navigation. To address storage overhead, we introduce a user-frequency-based selection technique that designates certain blockchain nodes as light nodes. We further propose a Merkle Hash Tree-based proof extraction method to facilitate efficient proof transfer between different types of nodes. Our approach incorporates an efficient Zhang-Safavi-Susilo (ZSS) signature-based data auditing protocol. By leveraging a data label placement mechanism during signature generation, our scheme supports tamper-proof batch verification, significantly reducing computational overhead. To enable dynamic data updates, we design a novel dynamic data structure, the Red-Black Hash Table, which enhances efficiency in handling updates. Through rigorous security analysis, we demonstrate that our scheme effectively defends against forgery, replay, and replacement attacks. We implemented and simulated our solution on smartphones and indoor navigation apps, conducting experimental evaluations using indoor positioning data. We take audit initialization overhead, audit verification computation overhead, evidence storage overhead, consensus computation overhead, etc. as important experimental indicators. Performance results indicate that our scheme, Efficient and Secure Data Integrity (ESDI), improves auditing efficiency by approximately 54% on average compared to existing approaches.