Route alignment design in surveying and transportation engineering frequently involves fixed waypoint constraints, where a path must precisely traverse specific coordinates. While existing literature primarily relies on geometric optimization or control-theoretic spline frameworks, there is a lack of systematic statistical modeling approaches that balance global smoothness with exact point adherence. This paper proposes an Adaptive Nadaraya-Watson (ANW) kernel regression estimator designed to address the fixed waypoint problem. By incorporating waypoint-specific weight tuning parameters, the ANW estimator decouples global smoothing from local constraint satisfaction, avoiding the "jagged" artifacts common in naive local bandwidth-shrinking strategies. To further enhance estimation accuracy, we develop an iterative data sharpening algorithm that systematically reduces bias while maintaining the stability of the kernel framework. We establish the theoretical foundation for the ANW estimator by deriving its asymptotic bias and variance and proving its convergence properties under the internal constraint model. Numerical case studies in 1D and 2D trajectory planning demonstrate that the method effectively balances root mean square error (RMSE) and curvature smoothness. Finally, we validate the practical utility of the framework through empirical applications to railway and highway route planning. In sum, this work provides a stable, theoretically grounded, and computationally efficient solution for complex, constrained alignment design problems.

翻译：在测绘与交通工程中，路径对齐设计常涉及固定航点约束，即路径必须精确经过特定坐标点。现有文献主要依赖几何优化或控制理论样条框架，缺乏能够平衡全局平滑性与精确点附着性的系统性统计建模方法。本文提出一种自适应Nadaraya-Watson（ANW）核回归估计器，旨在解决固定航点问题。通过引入航点特定的权重调节参数，ANW估计器实现了全局平滑与局部约束满足的解耦，避免了朴素局部带宽收缩策略中常见的“锯齿状”伪影。为提升估计精度，我们进一步开发了迭代数据锐化算法，在保持核框架稳定性的同时系统性地降低偏差。通过推导ANW估计器的渐近偏差与方差，并在内部约束模型下证明其收敛性，我们建立了该估计器的理论基础。在一维与二维轨迹规划中的数值案例研究表明，该方法能有效平衡均方根误差（RMSE）与曲率平滑度。最后，通过铁路与公路路径规划的实际应用验证了该框架的实用价值。综上所述，本研究为复杂约束对齐设计问题提供了稳定、理论完备且计算高效的解决方案。