Unkovsky was born in Kolyshevo, in the Peremyshlsky Uyezd of Kaluga Governorate, where his father was an officer in the Imperial Russian Navy.

However, in spring 1841, at the request of his father, he transferred to the Black Sea Fleet at Mykolaiv(Nikolaev), serving on numerous vessels through 1843, gathering intelligence on the status of foreign navies and political environment in the Balkans and the eastern Mediterranean.

From 1846, he commanded the yacht and participated in manly sailing competitions, winning several awards, including the imperial prize in a three-month-long race from the Black Sea to the Baltic, via Gibraltar.

In 1849, he was appointed commander of the brig Aeneas, and from 1850 to 1851 was assigned to intelligence gathering missions in the Mediterranean.

As commander of the frigate Pallada in 1852, he participated in the secret diplomatic mission to Japan, headed by Vice-Admiral Yevfimy Putyatin.