Underwater inertial navigation is particularly difficult for the long-durance operations as many navigation systems such global satellite navigation systems are unavailable. The acoustic signal is a marvelous choice for underwater inertial error rectification due to its underwater penetration capability. However, the traditional Acoustic Positioning Systems (APS) are expensive and incapable of positioning with limited acoustic observations. Two novel underwater inertial error rectification algorithms with limited acoustic observations are proposed. The first one is the single acoustic-beacon Range-only Matching Aided Navigation (RMAN) method, which is inspired by matching navigation without reference maps and presented for the first time. The second is the improved single acoustic-beacon Virtual Long Baseline (VLBL) method, which considers the impact of indicated relative position increments on virtual beacon reconstruction. Both RMAN and improved VLBL are further developed when multi acoustic-beacons are available, named mAB-RMAN and mAB-VLBL. The comprehensive simulations and field investigations were conducted. The results demonstrated that the proposed methods achieved excellent accuracy and stability compared to the baseline, specifically, the mAB-RMAN and mAB-VLBL can reduce the inertial error by more than 90% and 98% when using single and double acoustic-beacons, respectively. These proposed techniques will provide new perspectives for underwater positioning, navigation, and timing.