Leibniz bragged as early as 1671 about solving the problem of longitude, among a long list of other major problems, with the help of his "combinatory art" At the time he was euphoric about the sweeping capabilities of his "characteristica universalis" to solve any intellectual problems. Unfortunately, his letter does not give many details:
"I will demonstrate how to find longitudes completely, and provide a way for a person on a ship to know what his location is without the help of the sun, moon and stars which can not always be observed (yet Huygens's famous invention depends on them alone)". [quoted from Leibniz and the Kabbalah by Coudert, p. 154]
He published one solution in the Journal des Scavans in 1675, it was based on a clockwork with a new escapement mechanism. It is described, and pictured, in Matthews's Time for Science Education, p.170:
"He proposed using two balances and two spiral springs. Each spring was wound in tum by the train and then allowed to run down freely, controlled only by the inertia of the balance, the other spring being meanwhile wound. When the first spring had run down, it unlocked the second and so the cycle was to be repeated. He was oblivious to the fact, well known to Hooke, that as the spring unwound its motive power decreased."
The clockwork idea for the measurement of longitude was of course suggested already by Huygens. Leibniz's own comments show that he was a big idea man, and not a good fit for the problem of longitude which was largely practical.
"all these defects, that proceed from the imperfection of the matter, may be
surmounted by a general remedy, without examining them here in particular. And that is, that for executing it in great, we may make use of massy springs, as are those of cross-bows, we being the masters of them, not wanting force or place in a ship to govern a great weight that may serve to bend them continually again... And it is easy to demonstrate, that by augmenting the size of the engine, and the force of the massy springs, we may make the error as small as we please..."
"It is easy to demonstrate" will have a long life in mathematical literature, and as Hooke put it on another occasion "as a clockmaker, Leibniz made a great mathematician."
Later Leibniz did get involved with something more perhaps in the spirit of the OP, but as usual with practical matters he did not pursue it too far. It was longitude measurement based on measuring magnetic inclination. In 1676 a British instrument maker and teacher of mathematics Henry Bond had claimed that magnetic inclinators can be used for measuring longitude. The Royal Society got interested, and Oldenbourg, its secretary, sent a copy of Bond’s book to Leibniz:
"As Leibniz explained, magnets were also “inclined toward the horizon,” and since these inclinations were also inconsistent when measured in a single location over time, it made sense to study this phenomenon too. Yet this required the use of a different kind of instrument, an “Instrumentum inclinatorium,” Leibniz wrote, “so that Inclinati Magnetis, which is different from declination, could be observed.”" [from Halle Orphanage as Scientific Community by Whitmer]
But it is possible that "instrumentum longitudinum" mentioned in Kempe's book, that "could record the course of a ship and automatically transmit these records to the map", was yet another of Leibniz's big ideas from 1700s. Indeed it sounds like an automated version of the oldest method in history, the dead reckoning, still in use until Harrison finally solved the problem of longitude with his marine chronometer in 1730s.
