This is a question about how to determine if two different output signals represent the same process with different random inputs. This is related to validating ship motion modeling. When ship motion is modeled, using inertia and hydrodynamic equations, the resulting motion can be evaluated for a specified time history of a wave field. The question is how to determine if the ship model motion represents an actual ship where the ocean wave motion is not known and only the ship motion is measured? There are two sets of motion data, one set is output from ship model simulation, and the second set is measurements of the ship motion at sea. Is there a way to determine if these two sets of motion represent the same ship response, just driven by different forcing? Let's assume that the ship motion is a linear operator.
This is not a navigation problem about the change in speed or heading due to propeller or rudder inputs. The question is for the case of fixed speed and heading, what is the ship motion that results primarily due to ocean waves. The model has fixed propeller speed with rudder feedback to maintain course. The model also has an ocean wave spectrum with a prescribed wave heading. The measurements on the ship are the inertia measurements of pitch, roll, heave, and heave velocity, and long/lat. Previously significant motion values were used to compare two different models, but the significant motion (mean top 1/3) don't compare very well. I was thinking of comparing the histogram of motion and/or the frequency content, for a fixed time period, like five minutes.
Given two linear processes, L1, and L2, with measured outputs X1 and X2, to unknown random inputs Y1, Y2. Can the similarity of L1 and L2 be determined from the outputs X1 and X2?