Swarm-optimized low-dimensional joint position–velocity estimation method for Crab pulsar

In traditional pulsar joint position-velocity estimation, the estimation is in sensitive directions, whose three-dimensional and lower sensitive directions are constrained by onboard computational resources. However, large errors in non-sensitive directions can affect the accuracy of estimations in sensitive directions. To achieve real-time high-precision estimation, we propose a swarm-optimized low-dimensional joint position-velocity estimation; this new swarm intelligence algorithm is Electric Eel Foraging Optimization (EEFO). Six-dimensional estimation is performed to mitigate the influence of large errors in non-sensitive directions, thereby achieving high-precision low-dimensional estimation in sensitive directions. First, we use differential geometry to construct a sensitivity-based coordinate framework in the six-dimensional position-velocity space. That is, the coordinate framework is determined based on sensitivity to define its axes. Subsequently, we utilize super-resolution estimation to determine the search center, adaptively determine the search range based on the sensitivity of the coordinate axes, and use it to initialize the population. Finally, with the chi-square value of an accumulative pulsar profile as the optimization objective, we employ EEFO to estimate the six-dimensional position-velocity and propose an energy factor strategy for the Target Fitness Guidance (TFG) to enhance accuracy and accelerate convergence speed. Experimental results demonstrate that compared to the three-dimensional grid search method and the grouping bi-chi-square inversion method, when the computation time of TFG-EEFO is comparable to that of the three-dimensional grid search method, the sensitive direction joint position-velocity error is reduced by more than 71.9% and 28.5%, respectively.