Rotation method for direction finding via GPS carrier phases

Abstract

A baseline rotation method is proposed for determining the direction of the baseline vector via Global Positioning System (GPS) carrier phase measurements. The space difference technique is adopted to resolve GPS carrier phase cycle ambiguities. Possible applications include the determination of the aiming directions of artillery rockets and the line of sights of tracking radars, etc. For such armaments, the direction findings are important and the rotating mechanisms are well equipped already. A general baseline vector which can be rotated on a two-degree-of-freedom platform is considered first. The relationship among the baseline vector and the two rotation axes is not known. A sequence of rotations is used to change the configuration of the system to find the direction of the baseline. Under different circumstances such as the cases that some orthogonal conditions among the unknown vectors are given, simplified algorithms are devised. To verify our method, software simulation and hardware experiments have been conducted. The simulation outcomes are used to determine the experimental parameters, such as the length of the baseline, the rotation angles etc. The results of repeated hardware experiments show that the sample standard deviation for the azimuth angle and the elevation angle of the 1.35 m baseline vector are 0.91 deg and 1.23 deg, respectively. The GPS receivers employed are Motorola ONCOREs. The errors of the estimated direction angles induced by the inaccuracy of rotation angles, which are unavoidable due to the imperfectness of the mechanical structure, are analyzed as well. Numerical examples for the error analysis are included.

Accurate Rigid Body Localization Using DoA Measurements from a Single Base Station

“…For simultaneously determining the position and attitude of a rigid target, several techniques have been proposed in literature. An efficient approach for the RBL of outdoor, large-scale rigid bodies was developed based on the GNSS [11][12][13]. In this scheme, the absolute position was determined by pseudo-range observations, while the attitude was estimated from the measured carrier phases of the satellite signals received at multiple GNSS antennas.…”

Rate-Gyro-Integral Constraint for Ambiguity Resolution in GNSS Attitude Determination Applications

“…, the success rate and the shrinking efficiency. The simulation experiments are carried out by means of the basic steps as follows: a⃑ ( b ) = [3 0 0] T and $C_b^n\left(t_o\right)=I$ are chosen, respectively, and the updating frequency of GNSS measurements is chosen as 1 Hz;with the actual locations and GPS constellation imposed, select a reference satellite and three master satellites, then compute G i with Equation (3);set the parameters for rotation axis x⃑ ( n ) , the complete rotational angle θ , and angle velocity vector ${\stackrel{\rightharpoonup }{\omega }}_{nb}^b(\tau )={\left[00\omega (\tau )\right]}^T$, respectively, then compute a⃑ ( n ) ( t k ) from: ${\stackrel{\rightharpoonup }{a}}^{(n)}(t_k)=\left\{I-sin\theta \left[W^{{\stackrel{\rightharpoonup }{x}}^{(n)}}\right]+(1-cos\theta )\cdot {\left[W^{{\stackrel{\rightharpoonup }{x}}^{(n)}}\right]}^2\right\}{\stackrel{\rightharpoonup }{a}}^{(n)}(t_0).$with [13]: $\begin{array}{cc}{W}^{{\stackrel{\rightharpoonup }{x}}^{(n)}}=& \left[\begin{array}{ccc}0& n_3& -n_2\\ -n_3& 0& n_1\\ n_2& -n_1& 0\end{array}\right]\\ {\stackrel{\rightharpoonup }{x}}^{(n)}=& {[n_1{n}_2{n}_3]}^T,\theta =|{\int }_{t_0}^{t_k}{\stackrel{\rightharpoonup }{\omega }}_{}^{}\end{array}$…”

“…However, the model of this method is too idealistic to implement. On the basis of Tu's research, another method based on two-degree-of-freedom rotational motions was carried out by [13]. But the validity of ambiguity resolution is disturbed by the complex rotating mechanism and inaccurate rotation angle measurements in practice.…”

Direction Finding Using Rotated Long Baseline Interferometer

“…Determining the angle (such as azimuth and elevation) of a unknown radio emitter, also referred as direction finding, has been widely used in many areas such as navigation and communication [1,2] . To measure the angle precisely, spatial spectrum-based direction finding techniques such as MUSIC (MUltiple SIgnal Classification) [3] or ESPRIT (Estimation of Signal Parameter via Rotation Invariant Subspace) [4] methods, have high computation complexity due to signal covariance matrix estimation and need large number of antennas for achieving good performance [5] .…”