Timing newly discovered pulsars requires gradually building up a timing model that connects observations taken days to months apart. This sometimes can be challenging when our initial knowledge of the pulsar's position is arcminutes off from its true position. Such a position error leads to significant arrival time shifts as a result of the Earth's orbital motion. Traditional down-hill fitting timing algorithms become ineffective when our model predicts the wrong pulse rotations for our next observation. For some pulsars whose model prediction is not too far off, the correct rotation number could be found by trial-and-error methods. For the remaining challenging pulsars, a more generalized method is called for. This paper proposes a GPU-based algorithm that could exhaustively search a large area of trail positions for probable timing solutions. This could help find phase-connected timing solutions for new pulsars using brute force.

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