This is a demonstration of the classical japanese martial art Shinto Muso-ryu Jodo. It is a clip from the “Nihon Kobudo“-series(google it) featuring SMR.
Shinto Muso-ryu was founded roughly 400 years ago by Muso Gonnosuke. History states that Gonnosuke was defeated in a duel with Miyamoto Musashi. After his defeat he had an insight and created techniques for use with the quarterstaff (128 cm. staff called Jo). Legend states he returned and defeated Musashi in a rematch.
The whole Nihon Kobudo SMR-video features Omote, Chudan and Okuden kata series, (about 12 kata each), though this clip features one kata (tachi otoshi) from the Omote-series.
The performers are Namitome Shigenori (staff) and Otofuji Ichizō (sword).
*Edit* (thanks for correction of shidachis name)