From Memory Alpha:

The Picard Maneuver was born out of desperation during the battle. The Stargazer, which was damaged, suddenly accelerated into high warp directly towards the Ferengi ship. By doing so the Stargazer appeared to ship's sensors, for an instant, to be in two places at once. When data from the newly-moved ship reached the Ferengi ship's sensors, data from its previous position was still arriving, so the Ferengi effectively "saw" two Stargazers in different locations.

As I have recalled, the text is correct. This was told by Picard in an episode of Star Trek: The Next Generation TV series. And, in the end of that episode, when Picard tried to apply Picard Maneuver to attack USS Enterprise D, it was shown on screen of Enterprise D that Stargazer was at two places for an instant before it was stopped by tractor beam. The images from Memory Alpha:

How could the Picard Maneuver work to confuse sensors from the Warp Era? Isn't it like we rely on light waves to see the warping ship?

When data from the newly-moved ship reached the sensors, data from its previous position was still arriving.

It seems as if data transmission wasn't FTL. If it was, the sensors would never have been able to lock a warping ship's exact location. But, we have seen battles at warp speed and sensors detect something from light years away. What's special with Picard Maneuver which screws sensor readings (even that of a Galaxy-class starship)?