A regression‐based waveform interpretation model for accurate soil moisture estimation under incomplete time domain reflectometry probe insertions

Abstract Time domain reflectometry (TDR) is widely used and provides accurate estimates of soil moisture when sensor rods are fully inserted into the soil. However, automation of sensor insertions, especially in field conditions, is hindered by inaccuracies caused by possible incomplete sensor rod insertion, which distorts waveforms and leads to inaccurate travel‐time readings. We address this challenge by introducing a depth‐aware multi‐linear regression model that incorporates sensor insertion depth to predict soil permittivity under partial insertion conditions accurately. The goal is to bridge the gap between lab‐grade or manually inserted TDR measurements and the practical constraints of autonomous, mechanized field sensing, particularly for robotic systems in heterogeneous soils. Our approach estimates permittivity in two steps. First, a depth‐based linear model was used for predicting the amplitudes corresponding to the time at which the pulse reflects from the tip of the metallic probe for each depth. Second, the linear model was intersected with a polynomial function fitted to the deformed waveform, allowing for the accurate estimation of the amplitude at which reflection occurs at the probe tip ( t 3 ). The model was trained on curated datasets of TDR waveforms and validated against lab and manual insertion depths ranging from 2.5 to 5.0 cm. The proposed method demonstrated high predictive accuracy, with an R 2 value of 0.82, mean absolute error of 71.55 ps, and a root mean square error of 98 ps. The results confirm the method's effectiveness in overcoming the TDR limitations under partition insertion, providing a low‐complexity and robust solution for automated soil moisture sensing in environmental and agricultural monitoring applications.