  Real-time data processing is a central aspect of particle physics experiments
with high requirements on computing resources. The LHCb experiment must cope
with the 30 million proton-proton bunches collision per second rate of the
Large Hadron Collider (LHC), producing $10^9$ particles/s. The large input data
rate of 32 Tb/s needs to be processed in real time by the LHCb trigger system,
which includes both reconstruction and selection algorithms to reduce the
number of saved events. The trigger system is implemented in two stages and
deployed in a custom data centre.
  We present Looking Forward, a high-throughput track following algorithm
designed for the first stage of the LHCb trigger and optimised for GPUs. The
algorithm focuses on the reconstruction of particles traversing the whole LHCb
detector and is developed to obtain the best physics performance while
respecting the throughput limitations of the trigger. The physics and computing
performances are discussed and validated with simulated samples.
