To control exoskeletons for walking gait assistance, it is of primary importance to control them to act synchronously with the gaits of users. To effectively estimate the gait cycle (or the phase within a stride) of users, we propose a new adaptive frequency oscillator (AFO). While previous AFOs successfully estimated the walking frequency from joint angles as inputs, the new AFO, called particularly-shaped adaptive oscillator (PSAO) can estimate gait cycle from the same inputs, which would have required foot contact sensors in previous approaches. To predict the effects of PSAO-based gait assistance on human walking, it has been tested with neuromuscular walking simulation. In the simulation, the gait assistance system reduced the metabolic cost of walking for some assistance patterns. The walk ratio (step length per step rate) also changed as assistance patterns shifted in phase, which is meaningful because metabolic cost of walking in general is minimal at specific walk ratio. For a prototype exoskeleton we developed, the effect of gait assistance was experimented on a human subject walking on level ground and inclining slopes to verify the predictions from the simulation: (1) physiological cost index computed from heart rate significantly decreased indicating reduction in metabolic energy expenditure; (2) walk ratio was in fact controllable to an extent.