Accurate relative state observation of Unmanned Underwater Vehicles (UUVs) for tracking uncooperative targets remains a significant challenge due to the absence of GPS, complex underwater dynamics, and sensor limitations. Existing localization approaches rely on either global positioning infrastructure or multi-UUV collaboration, both of which are impractical for a single UUV operating in large or unknown environments. To address this, we propose a novel persistent relative 6D state estimation framework that enables a single UUV to estimate its relative motion to a non-cooperative target using only successive noisy range measurements from two monostatic sonar sensors. Our key contribution is an observability-enhanced attitude control strategy, which optimally adjusts the UUV's orientation to improve the observability of relative state estimation using a Kalman filter, effectively mitigating the impact of sensor noise and drift accumulation. Additionally, we introduce a rigorously proven Lyapunov-based tracking control strategy that guarantees long-term stability by ensuring that the UUV maintains an optimal measurement range, preventing localization errors from diverging over time. Through theoretical analysis and simulations, we demonstrate that our method significantly improves 6D relative state estimation accuracy and robustness compared to conventional approaches. This work provides a scalable, infrastructure-free solution for UUVs tracking uncooperative targets underwater.