Goshin Jutsu Karate is a style of empty-handed fighting supposedly brought to the United States in the 1950s by Gerard Durant. It is unclear who Durant studied with, or what styles he was taught. In fact, the only thing known for certain is that he ended up in Erie, PA, where he started his own school teaching "Goshin-Jutsu Karate" in 1965.
The history of Goshin Jutsu before it came to the US is entirely suspect. It seems like every master of the style tells a different story, and in fact there are no known styles of karate in Japan or Okinawa called "Goshin Jutsu", so it seems that Durant must have assembled the system himself. This, in itself, is not troubling, since many legitimate masters have created their own systems after long years of study in their parent systems (see Morihei Ueshiba or Jigoro Kano). What is strange is that none of the ranks Durant claimed to hold have been verified and, in fact, some of the organizations who supposedly issued them deny having had any contact with him at all.
A few years after Durant opened his school, he renamed it the "Goshin Jutsu Kyo Jujo". In 1974, he claimed that the governing body of his organization, the Yudan-shakai, promoted him to 10th Dan after the death of his master, a supposed "Samurai prince" named Shigeru Murakami (the samurai class had been abolished in 1868). In 1983, the system split into two factions, one headed by Joe Brague, which called itself "Goshin Jutsu Karate." The same Yudan-shakai who promoted Durant to 10th dan did the same for Brague in 1993, making him Grand Master of Goshin Jutsu. The other branch is apparently led by Matthew Durant, and is called either "Goshin" or "Goshin Jutsu" (research is inconclusive on this). This branch seems to focus on the Aiki-jutsu techniques taught by Jerry Durant.
The basic tenets of this system are hard to come by. Different sources will say that the system focuses on joint locks, or pressure points, or is "traditional karate." This last claim is extremely suspect, since only one (Heiyan Yodan) of the system's 11 kata even closely resembles any traditional Okinawan kata. One other, Heian Shodan, starts just as the Shotokan kata of the same name does, but quickly turns into an arbitrary collection of moves.
Goshin Jutsu Karate appears to be a system of self-defense thrown together by an ill-trained man who wanted to promote himself to black belt instead of training under an authentic teacher. The system has likely improved over the years as people of actual skill and expertise have left their mark on it, but it is by no means authentic Karate.
Note: The phrase "goshin jutsu" is a commonly used term for "self-defense" in Japanese. Also, this system is not to be confused with the Goshin Jutsu kata of Kodokan judo.