The Soviet Union had GLONASS for aviation civilian use in the latter part of the requested 50s-90s period.
From 1982 to April 1991, the Soviet Union successfully launched a total of 43 GLONASS-related satellites plus five test satellites.
(...) For a long time, the USA could not find out the nature of those "objects". The Telegraph Agency of the Soviet Union (TASS) covered the launch, describing GLONASS as a system "created to determine positioning of civil aviation aircraft, navy transport and fishing-boats of the Soviet Union".
(...) the Ilyushin Design Bureau learned much from the Il-86 program and in 1988 developed the Il-96, with the 80-400-type computer integrating triple INS, Omega and GLONASS displays in the navigation HUD for Cat IIIA performance (aviationtoday.com).
VOR/DME, ADF, inertial, and Doppler navigation were all present on Soviet airliners in varying combinations based on the mission/plane. They also had computerized astro-navigation (not sure if a Western equivalent existed for the civil aviation -- the computerized part):
[C]ommercial transports (...) were able to hold the large central TsNV navigation computer complex (multiple boxes with different sub-functions), although the TsNV was too large for smaller aircraft. The complex’s main unit was the BTs-63A astro-orienter, which included an auto sextant, course indicator and computer. Inputs by the navigator to the digital navigation computer (TsNV) were through a PUISH keyboard, part of the control-indicator unit (aviationtoday.com).
Navigators were part of the crew (primarily for long-haul), but it took longer for the navigator position to become redundant compared to the West. Longer not because of a technological deficit, but because of stronger unions and job creation.
Let's look at an example, the Ilyushin Il-62 (1967—), it's long range and it matches the period.
(wikipedia.org) Part of the navigator's panel showing 1) ADF and 2) DME.
Above you see ADF and DME instruments. And much like the attitude indicators, they're the same but with a different look. A typical Soviet VOR (CDI) instrument is shown below (they also used kilometers for the DME):
(wikimedia.org) CDI instrument for VOR on the Ilyushin Il-62.
Its avionics include a
- Polyot-1 automatic flight control system -- a "super autopilot," able to be programmed with a set route which it can fly without human intervention but under constant flight crew monitoring
- ICAO Cat. 1 approaches standard, Cat. 2 optional
- Doppler navigational radar...
- replaced by triplex INSS (Inertial Navigation System Sets) on Il-62M after 1978
- and by GPS (Global Positioning System) navigation sets on many aircraft after 1991
- triple VHF and HF flightdeck radios
- automatic direction finders
- Soviet and Western instrument landing system receivers
- [VHF] omnidirectional radio range and radio beacon receivers.
(Edited to be a list for easier reading.)
I also found en route charts for the Soviet Union showing NDB and VOR stations (but I couldn't confirm the date).
The first plane to have an FMC as it is known today as default equipment, was the Boeing 767 (1981), a few years later (1988) the Ilyushin Il-96 followed in the glass cockpit trend:
It features (...) a glass cockpit, and a fly-by-wire control system.
I tried to look for specific dates, the best I got to was an American 1974 report, 'CIVIL AVIATION OF THE USSR', by the Foreign Technology Division, Wright-Patterson Air Force Base, Ohio, which noted:
More than 90 airports were reconstructed or newly built, lines were equipped with modern means of air navigation and radio equipment.
Also since the USSR joined ICAO in 1970 (nytimes.com), it's safe to assume at least since then any radio-based navigation technology that's been in use eventually met the standards of international civil aviation.