Extreme-mass-ratio inspirals (EMRIs) are significant observational targets for spaceborne gravitational wave detectors, namely, LISA, Taiji, and Tianqin, which involve the inspiral of stellar-mass compact objects into massive black holes (MBHs) with a mass range of approximately 104∼107M⊙. EMRIs are estimated to produce long-lived gravitational wave signals with more than 105 cycles before plunge, making them an ideal laboratory for exploring the strong-gravity properties of the spacetimes around the MBHs, stellar dynamics in galactic nuclei, and properties of the MBHs itself. However, the complexity of the waveform model, which involves the superposition of multiple harmonics, as well as the high-dimensional and large-volume parameter space, make the fully coherent search challenging. In our previous work, we proposed a 10-dimensional search using Particle Swarm Optimization (PSO) with local maximization over the three initial angles. In this study, we extend the search to an 8-dimensional PSO with local maximization over both the three initial angles and the angles of spin direction of the MBH, where the latter contribute a time-independent amplitude to the waveforms. Additionally, we propose a 7-dimensional PSO search by using a fiducial value for the initial orbital frequency and shifting the corresponding 8-dimensional Time Delay Interferometry responses until a certain lag returns the corresponding 8-dimensional log-likelihood ratio’s maximum. The reduced dimensionality likelihoods enable us to successfully search for EMRI signals with a duration of 0.5 years and signal-to-noise ratio of 50 within a wider search range than our previous study. However, the ranges used by both the LISA Data Challenge (LDC) and Mock LISA Data Challenge (MLDC) to generate their simulated signals are still wider than the those we currently employ in our direct searches. Consequently, we discuss further developments, such as using a hierarchical search to narrow down the search ranges of certain parameters and applying Graphics Processing Units to speed up the code. These advances aim to improve the efficiency, accuracy, and generality of the EMRI search algorithm.
