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We describe the development and implementation of a method for extracting altimetric information using the Passive Reflectometry and Interferometry System (PARIS), i.e., from GPS signals after their reflection off the sea surface. We have formalized one idea laid out in the description of a bistatic system for ocean altimetry using the GPS signal, by Hajj and Zuffada (Jet Propulsion Laboratory), and have extended it to real situations encountered in PARIS aircraft experiments. Second, we have developed the corresponding algorithms to produce real-time altimetric observables to be used in dedicated digital signal processors. Finally, we have applied this method to estimate sea-surface height from one flight experiment in the North Sea off the coast of Norway.