  In future gravitational-wave (GW) detections, a large number of overlapping
GW signals will appear in the data stream of detectors. When extracting
information from one signal, the presence of other signals can cause large
parameter estimation biases. Using the Fisher matrix (FM), we develop a bias
analysis procedure to investigate how each parameter of other signals affects
the inference biases. Taking two-signal overlapping as an example, we show
detailedly and quantitatively that the biases essentially originate from the
overlapping of the frequency evolution. Furthermore, we find that the behaviors
of the correlation coefficients between the parameters of the two signals are
similar to the biases. Both of them can be used as characterization of the
influence between signals. We also corroborate the bias results of the FM
method with full Bayesian analysis. Our results can provide guidance for the
development of new PE algorithms on overlapping signals, and the analysis
methodology has the potential to generalize.
