## 2 Beidou-Binocular Cooperative Navigation Model
### Beidou Navigation Positioning Module
#### 2.1.3 Optimization Strategies for Beidou Positioning  
To address the above challenges, this paper proposes the following optimization strategies, combining existing research and engineering practices, to improve the robustness and precision of the Beidou navigation positioning module in complex environments:  
* Signal Filtering and Error Compensation: To reduce the effects of electromagnetic interference and multipath effects, a Weighted Kalman Filter (WKF) is introduced for dynamic filtering and correction of pseudorange measurements. The state update formula for the WKF is as follows: \[\left\{\begin{aligned} \hat{x}_{k|k}&=\hat{x}_{k|k-1}+K_{k}( z_{k}-H\hat{x}_{k|k-1})\\ K_{k}&=\frac{P_{k|k-1}H^{T}}{HP_{k|k-1}H^{T}+R}\end{aligned}\right.\] (2) where \(\hat{x}_{k|k}\) is the current state estimate; \(\hat{x}_{k|k-1}\) is the predicted state at the previous time step; \(K_{k}\) is the Kalman gain; \(z_{k}\) is the current measurement (pseudorange); \(H\) is the observation matrix; \(P_{k|k-1}\) is the state covariance matrix; and \(R\) is the measurement noise covariance matrix. By assigning dynamic weights to pseudorange signals (e.g., higher-confidence satellite signals have higher weights), the WKF can maintain high positioning stability even when the signal is experiencing interference.  
Figure 1: RTK schematic diagram.  
* Multi-frequency Redundancy Design: The Beidou navigation system supports multi-frequency signals (such as B1, B2, B3), each with different interference resistance and signal penetration capabilities. By receiving signals from multiple frequencies and using least-squares optimization for pseudorange measurements, ionospheric and multipath errors can be effectively reduced: \[\rho_{\min}=\min_{\rho}\sum_{i=1}^{n}w_{i}\cdot(P_{i}-\rho)^{2}\] (3) where \(P_{i}\) is the pseudorange measurement value of the \(i\)-th frequency band; \(w_{i}\) is the weight for each frequency band (determined by signal strength and confidence); and \(\rho\) is the optimized geometric distance. This strategy allows the system to still perform high-precision positioning by utilizing other frequency bands even when one band is experiencing interference.
* Satellite Signal Selection and Geometry Optimization: To minimize the impact of signal obstruction, a satellite signal geometry optimization algorithm is used to select satellites with the best geometric distribution for positioning calculations. The satellite's geometric precision factor (GDOP, Geometric Dilution of Precision) is calculated to assess signal quality: \[G=\sqrt{Q_{xx}+Q_{yy}+Q_{zz}+Q_{tt}}\] (4) where \(G\) is the geometric precision factor, and \(Q_{xx},Q_{yy},Q_{zz},Q_{tt}\) are the diagonal elements of the position and time covariance matrix. A lower \(G\) value indicates a better satellite geometric distribution and higher positioning accuracy. In positioning computation, satellites with the smallest \(G\) value are dynamically selected, improving computation quality in complex environments.
* Data Redundancy and Fusion: To enhance the reliability of Beidou navigation data, multi-source data fusion based on the Unscented Kalman Filter (UKF) is introduced. This combines Beidou positioning data with Inertial Measurement Unit (IMU) data. The state transition and observation models of UKF are as follows: \[\left\{\begin{aligned} x_{k+1}&=f(x_{k},u_{k})+w_{k} \\ z_{k}&=h(x_{k})+v_{k}\end{aligned}\right.\] (5) where \(x_{k+1}\) is the next state; \(x_{k}\) is the current state; \(u_{k}\) is the control input; \(z_{k}\) is the current observation; and \(w_{k}\) and \(v_{k}\) are process and observation noises, respectively. The UKF compensates for the short-term, high-precision characteristics of IMU data while using Beidou data to correct IMU drift errors, thus maintaining high-precision positioning even in the case of severe signal interference or short-term signal loss.