Theoretical Analysis and Experimental Evaluation of Wide-Lane Combination for Single-Epoch Positioning with BeiDou-3 Observations

Greenberg November 25, 2024 in News - 1 Minute

$D = [\begin{matrix} σ_{p}^{2} I_{k} & 0 \\ 0 & σ_{φ}^{2} ψ \end{matrix}] \otimes Q$

(14)

$T_{W L} = [\begin{matrix} \frac{i_{1} \cdot f_{1}}{f_{(i_{1}, j_{1}, k_{1}, l_{1}, m_{1})}} & \frac{j_{1} \cdot f_{2}}{f_{(i_{1}, j_{1}, k_{1}, l_{1}, m_{1})}} & \frac{k_{1} \cdot f_{3}}{f_{(i_{1}, j_{1}, k_{1}, l_{1}, m_{1})}} & \frac{l_{1} \cdot f_{4}}{f_{(i_{1}, j_{1}, k_{1}, l_{1}, m_{1})}} & \frac{m_{1} \cdot f_{5}}{f_{(i_{1}, j_{1}, k_{1}, l_{1}, m_{1})}} \\ \frac{i_{2} \cdot f_{1}}{f_{(i_{2}, j_{2}, k_{2}, l_{2}, m_{2})}} & \frac{j_{2} \cdot f_{2}}{f_{(i_{2}, j_{2}, k_{2}, l_{2}, m_{2})}} & \frac{k_{2} \cdot f_{3}}{f_{(i_{2}, j_{2}, k_{2}, l_{2}, m_{2})}} & \frac{l_{2} \cdot f_{4}}{f_{(i_{2}, j_{2}, k_{2}, l_{2}, m_{2})}} & \frac{m_{2} \cdot f_{5}}{f_{(i_{2}, j_{2}, k_{2}, l_{2}, m_{2})}} \\ \frac{i_{3} \cdot f_{1}}{f_{(i_{3}, j_{3}, k_{3}, l_{3}, m_{3})}} & \frac{j_{3} \cdot f_{2}}{f_{(i_{3}, j_{3}, k_{3}, l_{3}, m_{3})}} & \frac{k_{3} \cdot f_{3}}{f_{(i_{3}, j_{3}, k_{3}, l_{3}, m_{3})}} & \frac{l_{3} \cdot f_{4}}{f_{(i_{3}, j_{3}, k_{3}, l_{3}, m_{3})}} & \frac{m_{3} \cdot f_{5}}{f_{(i_{3}, j_{3}, k_{3}, l_{3}, m_{3})}} \\ \frac{i_{4} \cdot f_{1}}{f_{(i_{4}, j_{4}, k_{4}, l_{4}, m_{4})}} & \frac{j_{4} \cdot f_{2}}{f_{(i_{4}, j_{4}, k_{4}, l_{4}, m_{4})}} & \frac{k_{4} \cdot f_{3}}{f_{(i_{4}, j_{4}, k_{4}, l_{4}, m_{4})}} & \frac{l_{4} \cdot f_{4}}{f_{(i_{4}, j_{4}, k_{4}, l_{4}, m_{4})}} & \frac{m_{4} \cdot f_{5}}{f_{(i_{4}, j_{4}, k_{4}, l_{4}, m_{4})}} \end{matrix}]$

(16)

the correlation matrix. In this study, we assume that the pseudo-range measurements at different frequencies share identical random properties, and similarly, the carrier phase observations exhibit consistent random characteristics across frequencies. The STD of the pseudo-range observation is 100 times that of the carrier-phase, i.e.,

. Based on this assumption, combining Formulas (13) and (14), we use the LS method to calculate the variance–covariance matrix of the position parameters

.

is the number of the involved frequencies, ∑ means to sum all elements in the matrix, and

means to take the determinant of the matrix.

, and the same applies below. The matrix

reflects the stochastic characteristics of the estimated position parameters and is a key indicator for evaluating positioning precision.

Source link

Yulu Wang www.mdpi.com