Marcel,
There are probably as many ways to measure a canoe as there are people with a tape measure. That being said, it was explained to me that measurements should reflect how the water sees the canoe, that is the outside surface of the canoe.
To measure the length, most people stretch a tape measure from stem to stem. Ideally, two people should stretch a tape measure with a plumb bob hanging from the tape at each end so the plumb bob string just kisses the furthest reach of the stem. (the way surveyors measured an irregular surface before electronics) Most people just stretch the tape and eyeball the longest length.
To measure the width, it is supposed to be from outside of canvas to outside of canvas at the widest part of the canoe, generally at the center thwart. That being said, a lot of people measure from the inside of the outer gunwale to the inside of the outer gunwale, sometimes adding something for planking and canvas, sometimes not. A few people just measure from outside gunwale to outside gunwale, but that does not really reflect the hull of the canoe and is just good for figuring whether it will go through the door or not. Ideally, one would have a super large caliper like timber scalers used to use and measure the widest part from canvas to canvas. This would handle questions of tumblehome, etc.
Unfortunately, the measurements in the catalogs are no more consistent or accurate than the ones taken by the average canoeist.
In your case, 15'9" is usually reported at 16 feet. The depth may be the most revealing measurement and may indicate a Chestnut Prospector. In Bill Mason's book, Song of the Paddle, page 145, is a drawing and picture of a Prospector with dimensions taken from actual measurements from Bill's Chestnut Prospector, according to page 144. Keeping in mind the variability that can exist in any manufactured product (especially when Chestnut had at least 3 molds for the Prospector and had a habit of changing dimensions on various models of canoes during the years), comparing your canoe to the drawing in Bill's book may be your best bet.
All that being said, your picture shows a very nice looking canoe that does look a lot like Bill's Prospector, seats and all.
I hope the above is clear. If not, post any questions and I am sure someone will be able to explain it better.
Happy Paddling.