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Once a gravitational wave signal is detected, the measurement of its sourceparameters is important to achieve various scientific goals. This is donethrough Bayesian inference, where the analysis cost increases with the modelcomplexity and the signal duration. For typical binary black hole signals withprecession and higher-order modes, one has 15 model parameters. With standardmethods, such analyses require at least a few days. For strong gravitationalwave lensing, where multiple images of the same signal are produced, the jointanalysis of two data streams requires 19 parameters, further increasing thecomplexity and run time. Moreover, for third generation detectors, due to thelowered minimum sensitive frequency, the signal duration increases, leading toeven longer analysis times. With the increased detection rate, such analysescan then become intractable. In this work, we present a fast and preciseparameter estimation method relying on relative binning and capable ofincluding higher-order modes and precession. We also extend the method toperform joint Bayesian inference for lensed gravitational wave signals. Then,we compare its accuracy and speed to those of state-of-the-art parameterestimation routines by analyzing a set of simulated signals for the current andthird generation of interferometers. Additionally, for the first time, weanalyze some real events known to contain higher-order modes with relativebinning. For binary black hole systems with a total mass larger than $50\,M_{\odot}$, our method is about 2.5 times faster than current techniques. Thisspeed-up increases for lower masses, with the analysis time being reduced by afactor of 10 on average. In all cases, the recovered posterior probabilitydistributions for the parameters match those found with traditional techniques.

Relative binning for complete gravitational-wave parameter estimation  with higher-order modes and precession, and applications to lensing and  third-generation detectors