Estonia’s anthem shares the same melody as the anthem of Finland, with whom they share a similar culture, and was adopted in 1869, several decades before early twentieth century independence (and about 20 years after the anthem was adopted by Finland).
During the Soviet occupation period, it was illegal to sing “Mu isamaa, mu õnn ja rõõm”, however Estonians near enough to Finland to listen to broadcasts from that country were able to listen to the melody of the anthem that way, and thus the anthem stayed in the public consciousness.
There has been discussion about replacing the anthem with an original Estonian work, but generally the two nations have been content to share a melody.
See also: Finland