Single-antenna BDS/INS/OD integrated positioning system for small-scale agricultural machinery in hilly and mountainous areas

With the acceleration of agricultural modernization, the demand for intelligent and precise agricultural production has been continuously increasing. In the hilly and mountainous areas of China, due to geographical constraints and diverse planting patterns, small and micro agricultural machinery are more suitable for field operations. However, the research and development of small and micro unmanned agricultural machinery dedicated to hilly and mountainous areas started relatively late with a weak foundation. Furthermore, constrained by the limited body size of such machinery, the well-established high-precision positioning equipment designed for medium and large unmanned agricultural machinery can hardly be adapted to them. Therefore, in order to improve the operation accuracy of the navigation system for small and micro unmanned agricultural machinery in hilly and mountainous areas under complex environments and working conditions, this study proposed a variable-structure single-antenna BDS/INS/OD integrated positioning system. During the availability of BDS, the non-holonomic constraint (NHC) was incorporated into the Sage-Husa adaptive filter-based BDS/INS/OD system to construct a complete velocity constraint. This not only suppressed the velocity error that tended to diverge due to the severe vibration of agricultural machinery, but also enhanced the efficiency and accuracy of position measurement noise estimation. During BDS outages, the position measurement was disabled and the system was switched to the INS/OD system. The strong tracking filter was adopted to reduce the impact of abnormal velocity observation information, achieving high-precision seamless navigation. In addition, based on the differences in positioning noise characteristics between the two navigation modes, first-order and third-order Savitzky-Golay (S-G) low-pass filters based on a sliding window were designed respectively to smooth the navigation waypoints, which improved the accuracy of heading angle estimation using historical positioning information when the agricultural machinery operated at low speeds. The sliding window length of the smoothing filter was correlated with the traveling speed of the agricultural machinery: a short distance caused the heading angle estimation to be overly sensitive and resulted in large fluctuations, while an excessively long distance made the estimation more susceptible to historical paths and reduced real-time performance. In this paper, the distance between the latest positioning point and the farthest positioning point was set within the range of 1.5–2.0 m. Meanwhile, to avoid overshoot of the adaptive filter, the boundaries of the noise variance matrix and the posteriori estimation covariance were constrained. An integrated system was built using a self-developed small agricultural machinery as the platform, and vehicle-mounted field experiments were conducted. The experimental site was selected as an open area with low susceptibility to interference, and the traveling speed of the agricultural machinery was approximately 0.38 m/s. The results showed that: during the normal and stable operation of BDS, the mean, root mean square (RMS), and maximum value of the horizontal distance error of the standalone BDS were 0.018 m, 0.01 m, and 0.045 m, respectively; the mean, RMS, and maximum value of the horizontal distance error of the BDS/INS/OD system were 0.007 m, 0.007 m, and 0.063 m, respectively, and the maximum error occurred during the severe oscillation caused by emergency braking. During three 60-second BDS outages periods, the mean, RMS, and maximum value of the error of the INS/OD system were 0.051 m, 0.022 m, and 0.134 m, respectively. To simulate the BDS interference condition, preset random errors following a zero-mean normal distribution with an RMS of 1 m were artificially injected into the BDS positioning results along the north, east and up directions during three 60-second periods. When the BDS positioning error increased under simulated interference, the mean, RMS, and maximum value of the error of the BDS/INS/OD system were approximately 0.075 m, 0.039 m, and 0.166 m, respectively; additionally, there was no divergence trend in the velocity and attitude angle errors, and the latter could be used to compensate for positioning deviations caused by the inclination of the agricultural machinery. This study demonstrates that the single-antenna BDS/INS/OD integrated navigation system, which organically combines adaptive filtering and motion constraint principles, exhibits high stability under complex working conditions. It not only meets the operation accuracy requirements of unmanned agricultural machinery in hilly and mountainous areas, but also possesses strong adaptability and anti-interference performance. The findings also provide an important reference for the research and development of positioning systems for other outdoor vehicles operating under complex working conditions and environments.