Prototype System for Unmanned Reference Point Determination at the Sub-Millimeter Level

Abstract

The determination of reference points for telescopes is crucial for obtaining the local-tie vector for a multi-technology co-located station. Traditional methods suffer from labor-intensive fieldwork, long execution cycles, and systematic errors due to the incident angle of the total station's laser beam on the prism. In this paper, we propose an algorithm aligning the prism pointing vector with the prism-to-total station vector and introduce a pan-tilt platform and the Tianma VGOS telescope for sub-millimeter unmanned reference point monitoring. Our results show that the prototype system based on the pan-tilt achieves a formal error of ±100 μm (1σ) in reference point positions with just 2.5 hr of automated monitoring. The consistency of reference point positions is comparable to the local control network accuracy. Single-direction observations may introduce a deviation of ±1 mm in the reference point compared to multiple direction observations. Preliminary experiments on the Tianma VGOS telescope have also shown that this system can efficiently automate the monitoring of prism scatter points (one measurement every minute) and achieve sub-millimeter horizontal precision in reference point positions within a single day.

Introduction

Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), Global Navigation Satellite System (GNSS), and other multi-technology space geodetic measurement devices play a crucial role in the construction of a combined terrestrial reference frame. The reference points of these devices, such as VLBI and SLR telescopes, are the projection points of their secondary axes onto their primary axes. As the only inertial measurement technique that connects celestial reference frames, Earth orientation parameters, and terrestrial reference frames, VLBI is essential in building a reference frame (Schuh & Behrend, 2012). Therefore, it is highly necessary to perform multi-technology determination of the reference points of VLBI telescopes.

In addition to using VLBI delay observations to compute the reference point coordinates of VLBI telescopes, their reference point coordinates can also be determined through local survey measurements, which is a necessary step to build the local-tie vector and a combined terrestrial reference frame (Glaser et al., 2019; Ray & Altamimi, 2005) and upgrade the co-located stations to fully functional geodetic reference stations capable of ”shape, orientation, and gravity” measurements (Ma et al., 2021; Zhang et al., 2021).

However, the reference point determination of VLBI telescope encounters the following challenges:

1. The reference points of VLBI telescopes are not physically visible and need to be indirectly determined through some methods, which involve fitting the reference points by observing and calculating the coordinates of the targets that move with the VLBI telescope.

2. As large structures, VLBI telescopes face difficulties in reference point determination due to their own gravitational deformation (Lösler et al., 2019; Sarti et al., 2011), thermal deformation (McGinnis, 1977; Nothnagel, 2009), wind-induced deformation, and steel track deformation (Gawrtonski et al., 2006; Zhang et al., 2019).

3. When observing reflective targets co-moving with VLBI telescopes, the line of sight between the reflective targets and the ground observation equipment (e.g., total stations) needs to be considered. To achieve high-precision target point determination, reflective prisms are used. However, the observation angles of these prisms are limited. To obtain a well-distributed set of scatter points (there should be an appropriate incident angle for the prism), repeated coordination between the antenna operator and the total station surveyor are required. This leads to longer observation cycles.

These challenges limit the accuracy of VLBI telescope reference point and directly affect the determination accuracy of the local-tie vector at multi-technology co-located stations. As a result, the local-tie technical note or specifications (Technical Note No.33, 2003) was proposed by International Earth Rotation and Reference Systems Service, with a requirement that the local-tie vector and the reference frame vector's XYZ components should be less than ±5 mm. However, due to the lack of breakthroughs in the above-mentioned challenges, only half of the 76 VLBI-GNSS connection vectors used to construct the International Terrestrial Reference Frame (ITRF) meet this requirement. Moreover, in ITRF2020 (ITRF, 2022), among the 11 co-located stations with dual or triple VLBI telescopes, only one station's local-tie vectors satisfy the above criterion.

On the other hand, to further investigate global phenomena, such as geological, hydrological (including ice layers), atmospheric, and crustal deformation and mass migration, the Global Geodetic Observing System proposed geodetic aims to an accuracy of 1 mm in 2003. This imposes high requirements for the real-time monitoring of reference points in space geodetic facilities.

Therefore, since 2009, international efforts have been made to continuously determine the reference points of VLBI telescopes using GNSS technology (Kallio & Poutanen, 2012). Successful experiments have been conducted at various VLBI stations, including Medicina (Abbondanza, Altamimi, et al., 2009; Abbondanza, Negusini, et al., 2009), Metsähovi (Kallio et al., 2016), Onsala (Ning et al., 2015), Sheshan (Ma et al., 2022) and so on. The advantage of using GNSS antennas as targets for reference point determination is that GNSS antennas can continuously observe and accumulate a large amount of data. However, compared to optical reflective prisms, the coordinate positions of GNSS antennas are affected by multi-path and phase center variations, making it difficult to achieve millimeter-level accuracy with a single-point observation. Abbondanza and Sarti (2012) demonstrated that side shots preserve a precision similar to that of redundant forward intersections, which has laid the foundation for monitoring prism positions using high-precision measuring equipment such as a total station and prisms. In the later stage, the Onsala station used a laser tracker and developed an automated continuous reference point monitoring system. During the 15-day VLBI CONT14 observation period, synchronous monitoring and model corrections were performed on the telescope targets (Lösler et al., 2013). The corrected model improved the spatial distribution accuracy of most prism points by 1 ∼3 mm (Lösler et al., 2015).

Experimental observations using reflective prisms as targets have shown that when the incident angle of the total station's laser beam on the prism surface exceeds −20° ∼20°, significant systematic errors are introduced in distance and angle measurements (Lösler et al., 2013). For ball or spherical prisms, when the incident angle exceeds −40° ∼40°, the total station cannot receive the reflected signal of the prism. This is also the main reason why high-precision reference point determinations are challenging to achieve in unattended observations, as precise coordination between the observer and the telescope operator is required.

In addition, the configuration of different observation networks also has a certain impact on reference point determination. Abbondanza and Sarti (2012) conducted simulation verification on different network configurations around a 64-m telescope and concluded that an 8-pillar strategy is comparable to a 14-pillar strategy in terms of reference point accuracy. However, for small-dish VLBI global observing system (VGOS) antennas (Petrachenko et al., 2009) or SLR telescopes, there may typically be only three or four control pillars available for reference point monitoring. The impact of different directional observations on reference point determination needs to be further evaluated through actual measurements. Apart from observation techniques and methods, various error sources, such as telescope gravity deformation errors, thermal deformation errors, system biases, and uneven distribution of target points, are coupled and further increase the difficulty of reference point determination.

To address these challenges, this study introduces an azimuth/elevation or yaw/pitch pan-tilt platform (alternatively referred to as a pan tilt, with the dimensions of 34 × 16 × 40 cm), which is immune to thermal deformation and gravity deformation. Four tripods are arranged around the pan tilt to form a local control network. The principle for realizing a ”face-to-face” status between the surface of reflector prism and the total station's lens is derived for the first time (Section 2). An unmanned reference point measurement prototype system with sub-millimeter accuracy is built indoors. By eliminating the effects of telescope gravity deformation and thermal deformation on reference point determination, strict limitations on the incident angle of the total station's laser beam on the reflective prism are imposed. Real survey and prism monitoring are conducted to evaluate the impact of different directional target points on reference point estimation, and corresponding data are obtained (Section 3). Furthermore, this method has also been applied to reference point monitoring on the Tianma VGOS telescope. The collected data are analyzed and discussed (Section 4), and conclusions are summarized (Section 5).

Principles and Algorithms

To achieve the functionality of high-precision unmanned automated monitoring for the prism and the total station, not only should the rotational and orientational relationships between the above-mentioned three objects should be properly matched, but the systematic errors of the multi-technology system also need to be accurately controlled. This requires providing precise information to the total station (referred to as the instrument) regarding the position of the target point (or the prism), enabling the maximum possible alignment between the surfaces of the total station lens and the prism lens (the incident angle of the total station laser beam on the prism lens surface needs to be within the range of ±20°). Therefore, an automatic pointing capability is necessary, achieved by changing the azimuth and elevation pointing of the telescope to align the line of sight of the prism with the lens of the total station.

To address the key technical challenges mentioned above, it is crucial to establish an accurate relationship between the moving position and pointing of the prism and the position and pointing of the total station within the local control network. This is the key to conducting high-precision unmanned automated monitoring for self-alignment. This section will provide a detailed description of the algorithm and the operational flow of the prototype system.

Coordinate Systems

Since the co-located station survey is conducted only within an area of 3 ∼8 ha, the influence of the coordinate scales between different technologies can be disregarded when defining the coordinate systems for small-scale survey areas. The coordinate systems used in this paper only involve the orientation and origin of the coordinates. For the sake of calculation and description convenience, the coordinate systems mentioned in this paper are all Cartesian coordinates (right-handed coordinate systems). Additionally, to obtain the geocentric coordinates of the telescope reference point, other measurement technologies such as GNSS need to be introduced separately. Since this experiment is an indoor prototype experiment, this paper is limited to discussing the coordinates of the reference points within the local control network.

Figure 1 shows the experimental site and three coordinate systems: the local control coordinate system L_xyz, the telescope coordinate system T_xyz, and the prism coordinate system J_xyz. The local control coordinate system is defined by the user, with two known points in the local control network used for orientation. The local control point P₁ is set as the origin of the local coordinate system, and the vector P₁P₂ is taken as the L_y axis of the local control coordinate system. The L_z axis points in the opposite direction of the vertical line passing through P₁, and the L_x axis, along with the L_y − L_z plane, forms a right-handed coordinate system.

Figure 1. Schematic diagram of the local control coordinate system, telescope coordinate system, and prism coordinate system.

The telescope coordinate system, also known as the antenna coordinate system, has the T_y axis aligned with the zero directions of the telescope's azimuth and elevation. The T_z axis points toward the zenith, and the T_x axis is perpendicular to the T_y − T_z plane, forming a right-handed coordinate system. The origin of the telescope coordinate system is located at the reference point of the telescope.

The prism coordinate system is defined as follows: the J_y axis is the normal vector that passes vertically through the prism lens surface from the prism center. The J_x axis is aligned with the T_x axis of the telescope coordinate system, and the J_z axis is perpendicular to the J_x − J_y plane, forming a right-handed coordinate system. The origin of the prism coordinate system is located at the center of the prism.

Alignment of Prism Pointing Vector and Prism-To-Total Station Vector in the Local Control Coordinate System

In the telescope coordinate system, the orientation of the prism can be described in two components: the fixed position of the prism relative to the telescope reference point and the direction of the prism pointing vector in the telescope coordinate system. As shown in Figure 2, in this prototype system, an azimuth-elevation mount pan tilt is used instead of a large azimuth-elevation telescope for experimentation. Such a pan tilt is commonly used in optical telescope systems, and its azimuth and elevation slewing rates are both no less than 30°/s.

Figure 2. Position of the prism and the orientation of the prism in the telescope coordinate system.

The fixed position of an individual prism relative to the telescope reference point P_prism can be described by three quantities: a, b, and O_E. a represents the projection of the distance between the prism center and the telescope reference point in the T_y − T_z plane. b represents the projection of the distance between the prism center and the telescope reference point in the T_x − T_y plane. O_E represents the dihedral angle between the plane containing the prism center and the telescope reference point and the T_y − T_z plane. Note that in Figure 2, the pan tilt in the telescope coordinate system has an elevation pointing of 90°. The thicker coordinate axes show how to rotate along the T_x axis, from the initial state to the state in Figure 2.

The expression for P_prism is given by Equation 1: [Image Omitted. See PDF]

The constraint for the above equation is that the azimuth and elevation of the telescope are both zero. In Figure 2, to facilitate visualization, the origins of each coordinate system is offset. The prism undergoes a rotation of −t_z and t_x around the J_z and J_x axes, respectively. t_z and t_x can also be understood as the azimuth and elevation changes of the prism, respectively.

The initial pointing vector of the prism relative to its center can be represented by the prism direction, which is a point at a unit distance (or any non zero positive length) in the J_y direction, given by $${\left(\begin{array}{@{}ccc@{}}\hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \end{array}\right)}^{\mathrm{T}}$$. In the telescope coordinate system, it can be described as: [Image Omitted. See PDF]

Here, R_z and R_x represent the rotation matrices for rotations around the third and first axes, respectively. t_z and t_x denote the rotation angles around the third and first axes, respectively.

When the prism and the pan tilt change their azimuth and elevation to A and E, respectively, the positions of the prism center and the point on the unit distance in the prism pointing direction in the telescope coordinate system are given by: [Image Omitted. See PDF]

In the local control system, the prism position $${\mathbf{P}}_{\text{prism}}^{\mathrm{L}}$$ and the point on its unit distance in the pointing direction $${\mathbf{D}}_{\text{prism}}^{\mathrm{L}}$$ can be described as: [Image Omitted. See PDF]

Here, O_A represents the north orientation angle of the local control coordinate system relative to the telescope coordinate system. The pointing vector u of the prism in the local control system is given by: [Image Omitted. See PDF]

Let S^L be the position of the total station in the local control coordinates. The prism-total station vector v in the local control coordinates is: [Image Omitted. See PDF]

The condition for collinearity between vectors u and v is that the angle θ between them is zero, which can be expressed as: [Image Omitted. See PDF]

Taking the partial derivatives of cos θ with respect to A and E and setting them to zero, we have: [Image Omitted. See PDF]

By solving the above equations, we can find the azimuth and elevation angles that allow the prism and total station to have a ”face-to-face” orientation. In practice, there may be multiple solutions or extreme values to the above equations. Therefore, it is necessary to substitute the solved azimuth and elevation angles into Equations 2–5 and check if the calculated prism pointing vector u is collinear and in the same direction as the prism to total station vector v. If no solution satisfies these conditions, the initial pointing angles t_z and t_x relative to the telescope need to be adjusted.

For a multi-prism observation system, when calculating the θ angle, a limitation on the azimuth and elevation angles within −20° ∼20° can be applied. If the actual pointing of the telescope falls within this range, the total station can be automatically driven to point to the prism and obtain the prism coordinates.

Indirect Method

Compared to the method (Dawson et al., 2007) used for the classical restricted telescope pointing mode, other indirect methods (Li et al., 2014; Lösler, 2008, 2009) based on the unrestricted pointing mode are more suitable for unattended reference point monitoring. In this paper, we adopt the indirect model proposed by Lösler et al. (2016) (Lösler & Hennes, 2008) to establish the relationship between the prism, the pan tilt orientations, and its axis parameters.

Several parameters are used to model the axis errors of the pan tilt or other rotating bodies with primary and secondary axes. These parameters include the azimuth axis tilt angles α and β, the elevation axis tilt angle γ, and the axis offset e. O_A represents the angle between the north direction of the pan tilt and the zero orientation of the local control network.

When the pan tilt is pointing in a certain direction (azimuth A and elevation E), the relationship between the calculated target position $${\mathbf{P}}_{\text{calc.}}^{\mathrm{L}}$$ and the pan tilt reference point $${\mathbf{P}}_{\text{RP}}^{\mathrm{L}}$$ can be expressed as in Equation 9. [Image Omitted. See PDF]where R represents a rotation matrix and axis offset $$\mathbf{e}={\left(\begin{array}{@{}ccc@{}}\hfill 0\hfill & \hfill e\hfill & \hfill 0\hfill \end{array}\right)}^{\mathrm{T}}$$. By applying Gauss-Helmert adjustment (Koch, 2014) to Equation 9 and performing re-weighting, we can obtain the reference point coordinates, axis-related parameters, and their corresponding formal errors.

Operational Flow

The operation process of the prototype system can be divided into three main parts, consisting of 13 steps, as shown in Figure 3. The three main parts are local datum and priori values determination, unmanned target point monitoring, and reference point estimation. The specific execution process is as follows:

1. Conduct a local control network survey, including horizontal and leveling measurements. Perform a least squares adjustment of the local control network to determine the coordinates of the control points.

2. Based on the coordinates of the control points, set up a total station on the control points. Manually drive the pan tilt to change the azimuth and elevation angles, which will move the prism. Align the prism with the total station by manual adjustment. Use a 3D circle fitting method to determine the initial values of the pan tilt reference point, axis-related parameters, prism position parameters, and initial pointing angles.

3. Using the initial values from the previous step combined with the equations in Section 2.2, solve for the pan tilt azimuth and elevation angles that align the prism surface with the total station lens surface. Set the azimuth and elevation angle tolerance limits to ±20° and define parameters such as the start time and interval for azimuth and elevation step increments. Prepare observation schedules for the pan tilt and the total station.

4. Send the observation schedules to the pan tilt and the total station control computers. Before loading the schedules, the pan tilt and computer need to synchronize their clocks over the internet then execute the schedules. After each orientation of the pan tilt is complete, the total station will observe prism target points by means of forward and backward observation and then record the prism scatter data.

5. After the schedules are executed, perform a reference point computation using the observations from different prisms and control points, along with the pan tilt azimuth and elevation information. Finally, output the coordinates of the reference points, axis-related parameters, and their measurement errors.

Figure 3. Flowchart of sub-millimeter level unmanned reference point determination prototype system.

Data and Methods Local Datum and Initial Values Determination Indoor Local Control Network Survey

We used a Leica DS03 level to measure the elevation of four control points (P1 ∼P4) indoors. For the horizontal survey of the local control network, we used a Leica TS16A-1R500 total station with a nominal distance accuracy of 1 mm, along with a Leica prism set (GPR1+GZT4+GPH1). During single-point setup, the total station performed face left and face right observation cycles on each control point for 20 measurements.

Table 1 provides the adjusted coordinates and corresponding 1σ accuracies of the control points in the local control network. It is important to note that the prototype system does not use control pillars or forced centering devices. Especially when determining the height difference relative to the ground points using the tape or the laser for height measurement from the total station. This can introduce an elevation error of approximately ±1 mm, which will affect the observed points of the total station in conjunction with the control point errors in the local control network. Therefore, the elevation errors of the total station in the local control network are approximately ±1 mm.

Table 1 Coordinates and 1σ Standard Deviations (STD) of Control Points in the Local Control Network

Points	x(m)	y(m)	z(m)
P1	0.0000(0.0000)	0.0000(0.0000)	0.0000(0.0000)
P2	0.0000(0.0000)	4.5157(0.0006)	−0.0013(0.0001)
P3	4.2122(0.0006)	4.3385(0.0006)	−0.0044(0.0001)
P4	4.4481(0.0006)	−0.1597(0.0001)	0.0000(0.0001)

Determination of Prior Values for Parameters

The prior values of the parameters include the prior values of the reference point and the prism position parameters a and b. The prior values of the reference point coordinates P_rp0 can be determined by conducting a 3D circle fitting (Pan & Li, 2010) on the observed target scatters. It should be noted that the reference point obtained using the fitting method may include the influence of telescope axis errors. In this study, this reference point is used only as a prior value for adjustment.

In the indirect method, the prism position relative to the telescope reference point and the orientation of the telescope are described using three quantities: a, b, and O_E. To determine the initial values of a, b, and O_E, the initial azimuth of the telescope is set to 0 and the elevation is set to E. The prism position measured by the total station at this time is denoted as P_(0,E), and the difference between this prism position and the initial reference point can be described by a, b, and O_E as follows: [Image Omitted. See PDF]

The initial values of a, b, and O_E can be expressed as: [Image Omitted. See PDF]

Other parameters such as the axis offset e, two azimuth axis tilt angles α and β, and the elevation axis tilt angle γ can be set to 0 as prior values. In this study, the local control coordinate system's azimuth angle relative to the telescope coordinate system, O_A, is also initially set to 0.

Unmanned Automatic Reference Point Monitoring

For the manual drive interface of the pan tilt, an automatic drive program for the pan tilt was developed using the Au3 language. The program automatically reads the observing schedule sent by the central control computer to the pan tilt driven computer, which includes the start time, pan tilt azimuth angle, pan tilt elevation angle, control point name and the observed prism name.

Solving Configuration

Two ball prisms named J1 and J2 are symmetrically fixed above the pan tilt in the prototype system. A total station is set up for each of the four control points in the indoor local control network, and automatic monitoring is performed for the J1 and J2. This forms a set of four observed points for each prism's direction measurement.

For the J1 and J2, each set of position parameters (a, b, O_E) is estimated, and a set of reference points, axis-related errors, and orientation parameter for the pan tilt are also estimated. In order to analyze the influence of different direction observations and prism incident angles on the reference point coordinates, subsequent analysis and comparison of the adjustment will be carried out for different combinations of observed points for the prisms.

The indirect method utilizes observations of positions and azimuth and elevation angles of the pan tilt. When assigning weights to the observations, the nominal errors of 0.1° are used for the azimuth and elevation angles of the pan tilt. The prism position errors are weighted using the strategy of reweighting (Gipson, 1997). In each adjustment, a reweighting strategy is initially applied, followed by the removal of outliers. To further constrain the systematic errors introduced by the prism incident angles, outlier removal is performed using a 2.5σ strategy. This process is repeated until no outliers are removed, and the value of χ²/(degree of freedom, dof) is equal to unity. The indirect method and error adjustment strategy described above is applied to each data set.

Results and Discussion Results

Figure 4 shows the residuals after iterative process of the indirect method using all direction measurements as described in Section 3.3. The process is iterated 4 times, gradually eliminating outliers, as shown in Figure 4a ∼(d). The red, green, and blue colors represent the xyz coordinate components of the post-fit residuals for prism positions, respectively. The blue and red lines are the limitations of the 2σ and 3σ of the maximum of the post-fitted xyz residuals, respectively. Each subplot represents the results based on the χ²/dof = 1. The first 96 points in Figure 4a correspond to the observations for prism J1, while the observations for prism J2 start from point 97. Due to the relative biased (∼10°) pointing direction (deliberately introduced) of prism J2 with respect to its given direction in the schedule, significant systematic errors are introduced in the residuals. These outliers tend to occur in regions with larger angles of θ, particularly near the start-points and endpoints of the intervals depicted in Figure 4, since the face to face conditions are arranged at the midpoint of each schedule for each target in the directional measurements, represented by the intervals in Figure 4. By iteratively eliminating outliers, post-fit residuals with a similar dispersion level as prism J1 can be obtained, as shown in Figure 4d. If a more stringent outlier removal strategy, such as 2σ, is applied, all scatters will be iteratively removed, indicating the measurement capability for prism positions in this experiment is approximately within 2.5σ, or in ±0.4 mm.

Figure 4. Prism point residuals change in the iterative process using all direction prism coordinate observations.

Table 2 presents the information of the reference point position and pan tilt axis parameters obtained from the solution using a total of 173 valid data points from all observing directions (from the reference points of the total station above the P1, P2, P3, and P4). It shows that the coordinate error of the reference point coordinates is approximately 100 μm.

Table 2 The Reference Point Coordinates, Axis-Related Parameters, and Their Respective Standard Deviations Obtained Using the Entire Data Set of Multiple Direction Observations

Parameters	x	y	z	e	α	β	γ	OA
Units	mm	mm	mm	mm	″	″	″	′
Estimates	2,594.799	2,082.334	929.477	0.039	865.216	−5,096.144	−50.106	−269.409
1σ STD	0.024	0.024	0.101	0.067	31.859	32.606	164.464	1.402

To investigate the influence of different direction measurements on the reference point position, the process described in Section 3.3 was applied to each individual direction measurement and their combinations. The reference point coordinates were then compared with the information in Table 2, and the results are shown in rows 1 ∼14 of Table 3.

Table 3 The Differences and Their Respective Standard Deviations Between the Reference Points Obtained From Different Combinations of the Directional Observations and the Observations From the Entire Data Set

No.	Comb.	Numb. of points	dx(μm)	dy(μm)	dz(μm)
1	P1	40	−564(70)	−741(141)	410(172)
2	P2	40	−40(138)	104(81)	−692(176)
3	P3	43	−332(144)	−199(65)	−161(176)
4	P4	44	−349(96)	314(141)	−314(187)
5	P1 P2	75	−166(37)	53(52)	−66(140)
6	P1 P3	81	5(26)	−118(35)	−191(125)
7	P1 P4	82	−117(45)	−27(31)	−208(129)
8	P2 P3	76	−172(40)	−296(34)	106(126)
9	P2 P4	77	−217(34)	6(26)	325(121)
10	P3 P4	81	23(32)	36(38)	217(127)
11	P1 P2 P3	128	9(36)	69(46)	−143(155)
12	P1 P2 P4	112	−70(36)	4(31)	−138(147)
13	P1 P3 P4	120	28(26)	7(28)	−145(122)
14	P2 P3 P4	103	26(28)	−95(26)	173(125)
15	J1	94	0(42)	2(46)	−172(768)
16	J2	79	−13(41)	−20(44)	−967(735)

Overall, the maximum differences in the reference point components obtained from different direction measurements are 592, 1055, and 1,377 μm, respectively. These differences are comparable to the measurement precision of the local control network, which indicates that significant offsets, that is, >3 mm, in the reference point position due to different lateral direction measurements were not observed within the precision range of the local control network (approximately ±1 mm). In a study by Lösler et al. (2013) on the reference point results of the Onsala 20-m radio telescope using different direction measurements, the differences in the results were 3.9 and 6.2 mm in the horizontal and vertical directions, respectively. These differences were much higher than the measurement precision of their local control network (approximately 0.3 mm for local monument point measurements), suggesting that they were likely caused by the telescope deformation.

From rows 1 ∼4 of Table 3, it can be observed that single-direction measurements lead to non-uniformal errors in the horizontal components of the reference point and relatively poorer solutions compared to multi-direction measurements, with differences of up to 0.9 mm in the horizontal direction. Overall, as the number of valid observations increases (rows 1 ∼14), the formal errors decrease, which is consistent with measurement experience. Rows 11 ∼14 show that the consistency of the reference point position obtained from three-direction measurements is better than that from two-direction and single-direction measurements. The horizontal components (x and y coordinates) exhibit more uniform formal errors, which is necessary for obtaining an error ellipsoid with evenly distributed error components when transforming the telescope reference point coordinates from the local control coordinate system to the geocentric system.

Furthermore, the reference points obtained from three-direction measurements do not exhibit significant deviations compared to those from four-direction measurements (deviation values are smaller than or equal to the formal errors).

In addition, we also performed reference point solutions separately for the two prisms and calculated the reference point differences between their respective coordinates and the result in Table 2. These differences are shown in rows 15 and 16 of Table 3. It can be observed that the differences in the horizontal components of the reference point coordinates obtained from the two prisms's observations are within the range of their formal errors. The differences in the vertical direction are consistent with the height accuracy of the total station measurements.

When fixing prism J2, we set a significant deviation between its actual pointing direction and the prior specified pointing direction provided in the description. This deviation is represented by the two angles t_z and t_x in Equation 2, which indicate the pointing direction of the prism relative to the fixed position on the pan tilt. As shown in Figure 4, this deviation results in more outliers in the measurements for prism J2 compared to those for prism J1. The effective data rate for prism J2 is lower than that for prism J1, and it may introduce certain systematic errors in determining the reference point elevation.

On 6 September 2023, we applied the aforementioned automated monitoring method to the reference point determination of the Tianma VGOS telescope in Shanghai, as shown in Figure 5. Point O2 serves as the origin of the local control network, and the direction from O2 to point O3 is designated as the local control network's y-axis (or the zero orientation in a right-hand coordinate system). Since the Tianma VGOS telescope is not located at the central area of the Tianma park, Actually, It is located in the southeast corner of the park. The two additional control points, B1 and B2, were established for target point monitoring. B1 is situated in the village on the east side of the Tianma park, and B2 is located on the south bank of the river. Considering the difficulties of establishing control points in these two locations and in order to minimize systematic errors, the strategy adopted for these two control points involved performing surveying measurements (including control survey and unmanned target survey) only once as the tripod set up over these control points. We divide the telescope's azimuth and elevation into 6° increments, namely −18°, −12°, −6°, 0, 6°, 12°, 18°. For each individual direction and each prism, there are (6 + 1)(6 + 1) = 49 scatter points, resulting in a theoretical total of 294 target points. In practice, we obtained a total of 258 target points, with 64 from O2 point, 98 from B1 point, and 96 from B2 point. The reason for the fewer observed prism points from the O2 point is due to obstruction caused by the Tianma park's fences affecting the line of sight between the total station at O2 and the prisms. The prisms located on the counterweights on both sides of the Tianma VGOS telescope. The observation time for each prism point is 1 min, including 30 s for telescope slewing and stabilization, and 30 s for the total station to perform positive and negative mirror monitoring on the prism.

Figure 5. Local control pillars and the Tianma VGOS telescope.

Table 4 provides the results of a single-day solution for the reference points of the Tianma VGOS telescope in the local control coordinate system. Using a 3σ criterion, and after iterative adjustment and excluding target points that exceeded this limit, a total of 193 target points were ultimately utilized. Since no telescope pointing correction model was applied during the determination of reference point coordinates, the pre-fitting empirically determined accuracy of the azimuth and elevation angles used in constructing the a priori weight matrix for the telescope pointing information was set to 1.5°. The 1σ standard deviations in other telescope axis-related parameters, which were determined to be greater than the solved values, have not been included in Table 4.

Table 4 The Reference Point Coordinates and Their Respective Standard Deviations of the Tianma VGOS Telescope in the Local Control Network

Parameters	x	y	z
Units	mm	mm	mm
Estimates	−70901.187	69,695.500	10,798.521
1σ STD	0.262	0.209	1.385

In Figure 6, the residuals of the target points after the reference point determination of the Tianma VGOS telescope are presented. Starting with the number of 151 points, there is an increase in target point residuals, which is due to the fact that this batch of data was obtained from observing the prism J2 at point B2. These observations not only took place after dark (prism's automatic observations can survey during both day and night), but it is also likely that there is initial deviation in the prism's pointing direction manually adjusted at night.

Figure 6. Residuals of the target points following the calculation of the Tianma VGOS reference point.

Discussion Target Observations and Product Timeliness

In our two test runs, the total station had a delay of 10 and 30 s compared to the startup times of the pan tilt and the Tianma VGOS telescope, respectively. Consequently, it took a total of 40 and 60 s to determine the positional coordinates of the reflecting prisms on the pan tilt and telescope, respectively. In the future, we can reduce the proportion of time taken for telescope rotations in the observation schedule by fixing more prisms. This means leveraging the advantage of the total station's faster slewing rate compared to the telescope's. In a single telescope pointing, multiple reflecting prisms can be sequentially observed, which can also enhance the spatial coverage of prism scatter points.

Considering the parameter settings for the solution, for a single reference point determination session, we typically solve for a total of 8 global parameters, which include the reference point coordinates and axis errors. When dealing with a single prism fixed at a specific location, we estimate three position parameters. As prism pointing adjustments occur, we add 3 more prism position parameters to the design matrix for estimation. Based on experiments with the Tianma VGOS telescope, if we observe 2 targets, there will be a total of 8 + 2 × 3 = 14 parameters. This requires the monitoring of at least 5 target point coordinates to obtain observational data covering these parameters. From the experiments conducted, it is evident that observing 5 target points can be completed within 5 min. In the future, we will carry out reference point position monitoring experiments with higher time resolution (e.g., 0.5 hr to 5 min) for the VGOS telescope.

The automatic target recognition (ATR) time of the total station for the prisms depends on the accuracy of the prisms' prior positions and the parameters of the pan tilt or telescope axes. If the difference between the theoretical positions and the measured positions of the prisms in the local control coordinate system is only a few millimeters, the ATR function of the total station can be completed within 1 s. The high-precision prior positions of the prisms are the basis for the fast prism recognition and data measurement by the total station. The γ values in Table 2 relative to their formal errors are not significant. From the values of α and β, it can be seen that the influence of the azimuth axis inclination on the positions of J1 and J2 is about 5 mm. If a higher-precision model is considered to solve the azimuth and elevation angles of the telescope for unmanned observations, Equation 4 can be extended to Equation 12 to further shorten the recognition time. [Image Omitted. See PDF]

Observing Capability

The formal error of the reference point of the pan tilt can reach 0.1 mm, and the reference point evaluation accuracy of the observations in multi-direction is comparable to that of the local control network. In the case of the application of this method on the Tianma VGOS telescope, achieving sub-millimeter precision in horizontal coordinates for the reference points is relatively straightforward. The reason for the lower precision in z-component or elevation measurements is due to the poor precision of the local leveling control network. This is because, outside the park, the elevation values for B1 and B2 are determined using temporary station setups and triangulation-based elevation measurements. Our method enables the system to achieve the following for geodetic telescopes:

1. Improve the efficiency of obtaining prism or target observations, providing a theoretical basis for high-precision real-time monitoring of reference points for radio telescopes.

2. Minimize the usage of telescope's own observation time, supporting concomitant reference point monitoring with VLBI and SLR telescopes, as well as fast reference point monitoring with the pre-provided telescope azimuth and elevation information.

3. Reduce systematic errors caused by prism incident angle issues and scatters based on the forward and backward observations of the total station, thereby improving reference point accuracy.

4. Reduce the operational risks and time and effort involved in repeatedly adjusting the prism's pointing for telescope measurements. In the future, a full-range measurement can be achieved by deploying multiple prisms on the telescope.

The VGOS and the next-generation SLR telescopes proposed by the International VLBI Service for Geodesy and Astrometry (IVS) and the International Laser Ranging Service (ILRS), respectively, need to operate continuously in a 7 × 24-hr mode. To achieve unmanned reference point monitoring synchronized with VLBI and SLR observation scenarios (concurrent observations), the value of θ in Equation 7 in Section 2.2 should be set to ± 20°, and the corresponding limits on the telescope's azimuth and elevation angles should be determined. When the telescope drives the prism and ensures that the angle between the prism's pointing and the prism-to-total station vector is within the range of ±20°, the total station is driven to observe the prism.

In addition, we also discuss the impact of telescope axis errors on automated monitoring and the issues to be aware of when monitoring multiple prisms with a total station. If the inclination angle of the telescope's azimuth axis with respect to the tangential plane of the total station observation direction is 50″, and the prism is located 8 m away from the reference point, the influence of the azimuth axis inclination on the prism position can reach approximately 0.2 m. Considering that the total station is 20 m away from the prism, the total station needs to search for the target within a field of view azimuth of 0.6°. On the other hand, it also indicates that when using the total station's ATR function to recognize the prisms, only one prism within the 0.6° field of view can be visible. If more prisms are deployed as targets, the pointing direction of these prisms or the above model with axis errors needs to be considered.

Conclusion Remarks and Future Outlook

The algorithm proposed in this paper and the sub-millimeter unmanned prototype system constructed have significant implications for high-precision reference point determination and identifying systematic errors in local-tie vectors.

By introducing the pan tilt in the prototype system, thermal deformation and gravitational deformation can be neglected in the reference point determination. The differences in reference point coordinates obtained from scatter point observations in different directions are consistent with the measurement accuracy of the local control network. Single-direction measurements may introduce a systematic error of approximately ±1 mm in the reference point coordinate. Observations from multiple directions yield a relatively uniform distribution of formal errors in the horizontal component, which is meaningful for the subsequent transformation of local-tie vectors. The system has also undergone initial experiments on the Tianma VGOS telescope and has achieved sub-millimeter precision in horizontal coordinate components.

In the future, we will further optimize the elevation measurement accuracy of the local control network, including constructing control pillars, conducting leveling measurements, and optimizing the prism pointing fixed on the telescope. It is highly likely to obtain sub-millimeter precision reference point within a few hours. It is also possible to consider deploying multiple prisms with different orientations and optimize the total station observing strategy. This will enable fast and efficient unmanned monitoring of telescopes, either in a following-up (non-restricted) or a restrict pointing mode, with high precision.

Acknowledgments

Thanks for the comments provided by the anonymous reviewer. Thanks to our field survey team. The research was supported by the National Key Research and Development Program of China (Grant 2022YFE0133700), the National Natural Science Foundation of China (Grants 11963003 and 12273007), the funding project of the State Key Laboratory of Geographical Information Engineering, with project number SKLGIE2021-M-1-1, the ”Technology Innovation Action Plan” of Shanghai Municipality for the year 2022 (project number 22DZ2201800), and the key cultivation project of the Shanghai Astronomical Observatory.

Data Availability Statement

Software and data for this research is available and can refer to Zhibin Zhang (2023, November 9). Unmannded high-precision reference point monitoring scheduling and solving software (Version 1.0) [Software]. Zenodo. https://doi.org/10.5281/zenodo.10089100.