Real-time data processing is one of the central processes of particle physics experiments which require large computing resources. The LHCb (Large Hadron Collider beauty) experiment will be upgraded to cope with a particle bunch collision rate of 30 million times per second, producing 10$^{9}$ particles/s. 40 Tbits/s need to be processed in real-time to make filtering decisions to store data. This poses a computing challenge that requires exploration of modern hardware and software solutions. We present Compass, a particle tracking algorithm and a parallel raw input decoding optimized for GPUs. It is designed for highly parallel architectures, data-oriented, and optimized for fast and localized data access. Our algorithm is configurable, and we explore the trade-off in computing and physics performance of various configurations. A CPU implementation that delivers the same physics performance as our GPU implementation is presented. We discuss the achieved physics performance and validate it with Monte Carlo simulated data. We show a computing performance analysis comparing consumer and server-grade GPUs, and a CPU. We show the feasibility of using a full GPU decoding and particle tracking algorithm for high-throughput particle trajectories reconstruction, where our algorithm improves the throughput up to 7.4 × compared to the LHCb baseline.