In 2019, the late Yunupingu, of behalf of the Gumatj clan, made an application for native title for land in the Gove Peninsula, in north-eastern Arnhem Land.
At the same time he lodged a compensation application, for the alleged effects on native title of certain executive and legislative acts from 1911-1978.
Yunupingu died in April and the ceremonies honouring his life are continuing this week, following a public memorial last Thursday.
The Commonwealth argued for a number of reasons that the compensation case was misconceived in law, but the court rejected all of those arguments, meaning the case can proceed.
Gumatj clan leader Djawa Yunupingu said the case centred around the Commonwealth's decision to allow mining on Gumatj country in 1968 without their consent.
"The case signifies the enormous contribution which my brother has made to the development of the law in this country in the service of all First Nations people," Djawa Yunupingu said.
"It is a continuance of his life's work, which began with the Bark Petition and the Gove Land Rights case to have native title properly recognised as the heart of the identity of all First Nations people."
Yunupingu launched the case in 2019, claiming compensation under section 51 of the constitution, which empowers the parliament to make laws for the acquisition of property on just terms.
That means the Commonwealth can acquire land, if they pay the landowner, for example, when building highways.
The compensation is being sought regarding the land from which bauxite has been mined since 1968, when the Australian government entered into a lease with Nabalco, on land within the Arnhem Land Reserve.
The mining lease is now held by Swiss Aluminium.
Other Yolngu clan groups, including the Rirratjingu people, have also made claims on parts of the land in question, as well the Gumatj.
Native title is yet to be determined.
Djawa Yunupingu said his brother believed that all First Nations people were entitled to receive compensation in accordance with the constitution.
"Like any other Australian when their sacred land is taken away from them without their consent," he said.
"The ramifications of these findings are significant, potentially impacting all native title in the NT acquired by the Commonwealth between 1911-1978.
"Although my brother did not live to hear today's judgment, he would have been pleased that the Federal Court's decision recognised the fundamental right of First Nations People to be treated equally by Australian law."
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