An Observation Scheduling System for Radio Telescope Array

Abstract

The 4 × 4.5 m radio telescope array at Guizhou Normal University is an astronomical observation facility in operation, mainly aiming at the scientific detection of pulsars and fast radio bursts. To adequately address the observational requirements of this telescope array, we developed an observation scheduling system. This system is able to predict and plot the elevation change curves of the observed targets in relation to the telescope array during the whole day. In addition, for multiple targets, it provides intelligent scheduling and processing according to the observable time. The system also offers a comprehensive database of calibrators for the flux calibration of the targets. Moreover, it can generate pre-configured array $uv$ coverage maps, which assist in determining the optimal configuration of the array. This system has been operating during the daily observations of the $4\times 4.5$ m radio telescope array and has successfully detected two typical pulsars. It has also been tested for applicability in target-observation prediction in other radio telescope arrays.

1. Introduction

The Five-hundred-meter Aperture Spherical radio Telescope (FAST) [1], located at Pingtang, Guizhou, China, is currently the largest single-dish radio telescope in the world and almost approaches the sensitivity limits of single-dish radio telescopes [2,3]. In the future, as we look ahead, developments in telescope array technology will significantly improve both sensitivity and spatial resolution, two crucial factors in astronomical observations. Presently, many radio telescope arrays are under construction or have already been completed and put into use internationally, such as the Canadian Hydrogen Intensity Mapping Experiment (CHIME) [4], the American Deep Synoptic Array (DSA) [5], and the Square Kilometer Array (SKA) radio telescope [6]. To ensure the smooth progress of radio astronomical observations, it is essential to accurately predict the visible time and relative position of the target at the telescope array that is required for an observation project. However, most existing software for predicting sources with different radio telescope arrays is either not publicly available or lacks completeness. Moreover, the problem of prioritizing multiple targets for observation remains unresolved. Additionally, given the varying samples (commonly referred to as $uv$ coverage in radio astronomy) of the target in different array configurations, obtaining a radio telescope array layout with maximum coverage through numerical simulations is crucial. The $uv$ coverage represents the coordinate points of u and v on the $uv$ plane, which are determined by transforming the coordinates of the baselines of the telescope array. Here, the line connecting each pair of telescopes in the array is called a baseline. Therefore, developing a highly adaptable antenna array observation simulation system is of significant importance for radio astronomy observations.

In astronomical observations, planning the observation of targets traditionally involves manually scheduling based on factors such as their rise and set times and the significance of the sources. This process can be time-consuming and resource-intensive. Currently, there is not a universally accepted software for simulating radio sources behavior, when people perform observations. Most of the existing software has successfully used sky coordinates as input to perform observations. However, they were independently developed, are not publicly available, and are tailored only to the specific array for which they were developed, requiring significant manual effort to create observation plans. The publicly available software is the source position predictor on the Parkes Observatory website (https://www.parkes.atnf.csiro.au/observing/utilities/coord.php/, accessed on 11 October 2024) and SCHED (https://pypi.org/project/pythonSCHED/, accessed on 11 October 2024) developed by the National Radio Astronomy Observatory (NRAO) in the United States. The Parkes software can only predict the elevation of a single target and cannot handle multiple sources simultaneously, while the SCHED software only provides trajectory prediction and lacks intelligent scheduling capabilities. Additionally, there are some non-public simulation software, such as the observation summary page for the 100-meter Effelsberg telescope (https://eff100mwiki.mpifr-bonn.mpg.de/doku.php/, accessed on 11 October 2024) in Germany and the Dynamic Scheduling System (DSS) [7] for the Green Bank Telescope (GBT) in the United States. However, the Effelsberg software does not offer a detailed predictor for target source observation or similar functionality, only providing an observation scheduling interface, while DSS is not publicly available. Furthermore, both systems lack a visual interface and can only fit one target at a time.

The 4 × 4.5 m radio telescope array at Guizhou Normal University is primarily intended for preliminary research on the search and localization of transient sources, such as fast radio bursts (FRBs) and giant pulses from pulsars. This array is responsible for the observation tasks of multiple distinct targets daily. Given the large number of such tasks, it is required to arrange them rationally and guarantee the validity of the data collected during each observation. Moreover, the scale of the array will be upgraded in the future as well. Based on the observational and upgrade needs of the array, this paper focuses on the design and development of an observation scheduling system for the telescope array at Guizhou Normal University, aiming to create a fully functional and highly adaptable target prediction system. This paper adopts a modular design approach using Python and PyQt5 (PyQt5-5.15.2), proposing features such as simulating and visualizing the positional changes in targets over the upcoming 24 h, intelligent scheduling for multiple target observations, calibration source observations, and array layout simulation based on maximizing $uv$ coverage.

2. The 4 × 4.5 m Telescope Array at Guizhou Normal University

To investigate the SKA beamforming and aperture synthesis imaging technologies, the Department of Astronomy at Guizhou Normal University proposed to build a small-scale of 4 × 4.5 m radio telescope array (see Figure 1) for preliminary research. Depending on the Guizhou Frontier Science Center of Astrophysics project and the resources of the Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing, Guizhou Normal University independently constructed the entire telescope array in January 2020. The radio telescopes (antennas) in the array are assembled from 16 high-precision panels and 16 radiation beams, and the latitudes and longitudes of the antennas are presented in

Table 1. The locations of the antennas in the 4 × 4.5 m telescope array.

Telescope Name	Longitude	Latitude	Altitude
	(deg)	(deg)	(m)
Telescope 1	106.388	26.2249	1168
Telescope 2	106.387	26.2249	1168
Telescope 3	106.387	26.2251	1174
Telescope 4	106.388	26.2251	1174

.

This telescope array has completed the verification of key core technologies, including antenna, feed, low noise, acoustic amplifier, receiver, and multi-scientific terminals to realize base-band data recording, spectral lines, pulsars, beamforming, and other modes. The relevant parameters of the antenna in the telescope array are shown in

Table 2. The antenna parameters.

Name	Parameters
Diameter	4.5 m
Frequency range	1.0–1.5 GHz
Focal ratio	0.38
Pointing accuracy	<$0.2^{\circ }$ RMS
Source switching time	≤10 min
Azimuth rotation range	0–${360}^{\circ }$
Elevation rotation range	0–${360}^{\circ }$
Source switching speed	$0.5^{\circ }$${\mathrm{s}}^{-1}$

.

3. The Overall Architecture of the System

Based on the Linux operating platform and Python language programming, our radio sources observation prediction system is designed with four modules: the target trajectory prediction module, the intelligent scheduling module, the calibrator prediction module, and the $uv$ coverage module. Figure 2 shows the overall architecture and interface of the system. The system interface was developed using Qt Designer in the Python module of PyQt. Users can obtain observation schedules via trajectory prediction and intelligent scheduling results and determine the optimal antenna array configuration through $uv$ coverage maps. Multiple user experiences have shown that the system interface is well-designed, highly integrated, and user-friendly.

The target trajectory prediction module is located at the top left side of Figure 2. The information display status bar shows the current sidereal time and world time information. The right side displays the simulation time for the current prediction, the antenna number in use, and the azimuth and elevation information of the leading target source. In the “Load Observation Source File” section, click “Browse” to select the target source file for observation. After clicking the “Submit” button, a trajectory plot showing the variation of the target source’s azimuth and elevation over time will be generated. The red dot in the trajectory map is the elevation value corresponding to the target at the current observation time. For different telescopes, ones just manually input the longitude and latitude of the telescope in the address input field, then click the “Track” button to fit the azimuth and elevation trajectory of the target source using the new location of the telescope. The right side will display the longitude and latitude information of the currently used antenna.

Intelligent scheduling module: In the middle left of the information display status bar, enter the observation time and click the “Import Time” button to set the duration for which the observation will be applied. On the right side of the interface, input the minimum elevation limit to filter out target sources with elevation values below this threshold. In the address input section, enter the geographical coordinates of the antenna, click “Import Address” to update the system with the antenna’s location, and then click the “Sort” button to initiate the scheduling and processing of all target sources in the selected file. On the right side of the status bar, sort and process the data using the respective antennas according to your specific needs. The number of antennas displayed in this section can be expanded based on the number of antennas in different arrays, allowing for customization to match various array configurations.

Calibrator prediction module: To ensure the accuracy of the observed target source’s flux, calibration sources commonly used in astronomical observations must be included during the observation with the telescope array. Click “Browse” in the calibration source canvas to select and submit the calibration source file. The corresponding calibration sources visible during the specified time period will appear. When creating the observation plan, include calibration sources in the target source’s surrounding area to calibrate the flux of the target source.

Located at the bottom right corner of Figure 2 is the $uv$ coverage module. To operate this module, an initial setup of observation parameters is required, including details about the telescope array, target information, and the range of observation times. Once the parameters are set, users can click the “Mapping” button within the $uv$ coverage module to generate the $uv$ coverage map for the target over the specified time period as observed by the telescope array. Concurrently, the system will produce $uv$ data, which is then exported in a TXT file format. These data are essential for calculating the coverage ratio of the observation. By comparing the coverage ratios across various telescope array configurations, the optimal setup can be determined.

Details of the implementation of each module are shown below.

3.1. Target Trajectory Prediction Module

The target trajectory prediction module is designed to compute the relative elevation (${\theta }_{\mathrm{el}}$) and azimuth (${\theta }_{\mathrm{az}}$) angles of a celestial target with respect to the radio telescope array over a specified duration. This calculation is based on the array’s geographical coordinates and the target’s celestial coordinates, including right ascension ($RA$) and declination ($DEC$). Therefore, for effective tracking and observation within a given time interval, the radio telescope array must adjust its observational pointing continuously, which requires predicting the target’s trajectory relative to the telescope. The module then visualizes these calculated angles on the system interface, facilitating the accurate alignment of the array with the celestial target. This module operates through a three-step process, as depicted in Figure 3. Initially, the module retrieves essential data: the target information, which includes the right ascension ($RA$) and declination ($DEC$) coordinates, along with the observation time range, from a target list file. Concurrently, it gathers the geographical latitude ($\phi$) and longitude (${\lambda }_{\mathrm{long}}$) of the telescope array. Subsequently, the module employs these data to compute the target’s ${\theta }_{\mathrm{el}}$ and ${\theta }_{\mathrm{az}}$ values throughout the observation period. Ultimately, it projects the target’s trajectory onto the horizontal coordinate system for the subsequent 24 h, commencing from a specific observation time, and presents this trajectory on the system interface, enabling users to visualize and track the target’s movement in relation to the telescope array.

In this module, the ${\theta }_{\mathrm{el}}$ and ${\theta }_{\mathrm{az}}$ were calculated by [8]:

$$\left\{\begin{array}{c}{\theta }_{\mathrm{el}}=arcsin\left(sin\left(DEC\right)sin\left(\phi \right)+cos\left(DEC\right)cos\left(\phi \right)cos\left(H\right)\right)\hfill \\ {\theta }_{\mathrm{az}}=\left\{\begin{array}{c}arccos\left(\left(sin\left(DEC\right)-sin\left({\theta }_{\mathrm{el}}\right)sin\left(\phi \right)\right)/\left(cos\left({\theta }_{\mathrm{el}}\right)cos\left(\phi \right)\right)\right),\mathrm{if}sin\left(H\right)<0\hfill \\ 360-arccos\left(\left(sin\left(DEC\right)-sin\left({\theta }_{\mathrm{el}}\right)sin\left(\phi \right)\right)/\left(cos\left({\theta }_{\mathrm{el}}\right)cos\left(\phi \right)\right)\right),\mathrm{otherwise}\hfill \end{array}\right.\hfill \end{array}\right.$$

(1)

where $H=LST-DEC$ is the hour angle. $LST$ represents the Local Sideral Time, which is calculated by the $\phi$ and ${\lambda }_{\mathrm{long}}$ of the telescope array and the international standard time, which is given as [8]

$$LST=100.46+0.985647D+{\lambda }_{\mathrm{long}}+15UT,$$

(2)

where $UT$ is the Universal Time, and D is the number of days since J2000.0. For instance, the $LST$ for the telescope array (${\lambda }_{\mathrm{long}}$ = ${106.67}^{\circ }$, $\phi$ = ${26.44}^{\circ }$) at 16:50 on 10 October 2023, is calculated using Equation (2) to be 17 h 11 m 30.932 s.

Utilizing Equation (1), we can calculate and predict the elevation (${\theta }_{\mathrm{el}}$) and azimuth (${\theta }_{\mathrm{az}}$) angles of a celestial target for the 24-h period following a given moment, and plot the target’s trajectory change curve within this timeframe. It is common for targets with lower ${\theta }_{\mathrm{az}}$ angles to have larger calibration errors and poorer signal quality in the telescope array. As a result, data from these targets is typically discarded. This function enables observers to identify the observable time range within the following 24 h for a target, based on a minimum threshold of ${\theta }_{\mathrm{el}}$, known as the visible time range. With this information, managers can optimize the observation sequence according to the visible time ranges of different targets. For further details on this process, refer to the section on the intelligent scheduling module.

3.2. Intelligent Scheduling Module

Generally, when observing multiple targets, manual scheduling becomes necessary if the cumulative observation time for all targets exceeds 24 h or if there is an overlap in the sky areas where the targets are located. To make observations more convenient, this module in question calculates the observable duration of each target within the visible sky of the radio telescope array and prioritizes them based on the inverse of their observation durations as weights. The scheduling process begins by allocating the time slot for the target with the highest weight from the preset total observation time, marking this slot as used. Subsequently, the process is repeated for the target with the next highest weight. This continues until all targets are sorted or the available time slots are exhausted. The final step is to visualize the sorted targets. Figure 4 depicts the intelligent scheduling process flow, providing a clear overview of how targets are sequenced efficiently within the constraints of observation time and sky coverage.

The specific methodology involves extracting all target information from the source file and then utilizing Equation (1) to calculate the elevation variations of all targets across a 24-h period. Given that the antenna at Guizhou Normal University has an elevation restriction, with a minimum limit of ${15}^{\circ }$, any elevation values falling below this threshold are omitted from the analysis. The target sources are subsequently sorted in ascending order based on the range of their elevation variations, and their observation priority is assigned according to the inverse of their respective observation durations. The observation time for the highest-priority target is set first, followed by the secondary target, and so on until all targets are scheduled or the allocated observation time is completely used. The sorted schedule is then displayed on the software interface, with time plotted on the horizontal axis and elevation on the vertical axis.

3.3. Calibrator Prediction Module

The intensity, or flux density, of a target received by a radio telescope array can be affected by various factors, such as the system noise of the telescope, the elevation of radio sources, and atmospheric and ionospheric interferences. These factors introduce a discrepancy between the received intensity and the target’s true intensity. In radio astronomy, it is common practice to use one or more stable and bright radio sources, known as calibrators, to calibrate the flux density of the observed target. At present, the performance and receiving capacity of the telescope array are limited, so it is unable to detect the calibrator signal. Consequently, this module mainly serves the telescope array that will be upgraded subsequently. In radio astronomical observations, one or more calibrators are usually observed before and after the target, and they can be used to calibrate the flux of the target. Sources listed in the Third Cambridge Catalogue (3C) [9] are often employed for this purpose. Calibrator observations are typically scheduled immediately before or after the target observations. Consequently, during the observation planning for targets, it is necessary to include observational predictions for calibrators to ensure a more rational and efficient observation plan.

This paper identifies commonly utilized calibrators for radio astronomy within the observable sky area, drawing from sources such as [10,11]: 3C286, 3C196, 3C295, 3C123, 3C48, 3C138, 3C147, 3C380, 3C353, 3C444, Taurus A, Cygnus A, Fornax A, Pictoris A, and Cassiopeia A, as potential calibration candidates. The suitability of each calibrator is determined based on the specific observational requirements. Figure 5 delineates the workflow of the calibrator module within the antenna array target source simulation software. In the system interface, a secondary canvas is established for importing the selected calibrator source file. The elevation and azimuth values of the calibrator for the ensuing 24 h are computed and subsequently visualized on this secondary canvas.

3.4. $uv$ Coverage Module

$uv$ coverage is one of the basic functions of the radio astronomical observation scheduling system. Radio astronomical observation schedules are generally created through the optimization of uv coverage. The SCHED software, for instance, can plot the uv coverage in a schedule and supports moving stations around to explore uv coverages in array configuration design projects. Therefore, we also include this basic function in the system. This function in our system has two main goals: one is to make the astronomical schedule plans for the current telescope array; the other is to determine the optimal layout of the upgraded telescope array. The theory of uv coverage is introduced in detail below.

Synthetic aperture is an important radio astronomy observation technique that provides high angular resolution images of radio sources by measuring the phase differences between radio telescopes, a method that has been widely used in the field of radio astronomy [12]. During synthetic aperture measurements, radio telescopes interfere in pairs (i.e., interferometers), leveraging Earth’s rotation to form multiple distinct interference baselines. These baselines sample the area of the sky where the radio source is located [13]. Following the standard processing steps in radio astronomy, the sampling data of radio sources yield sky images of the radio sources. To facilitate the transformation from the sampling domain to the sky image domain, the foremost task is to establish the sampling coordinate system and the imaging coordinate system [14]. The sampling coordinate system is referred to as the (u, v, w) coordinate system. Generally, the projection of the radio telescopes’ baselines (the distance between two telescopes) in the (u, v, w) coordinate system is referred to as $uv$ coverage. $uv$ coverage reflects the degree of sampling of the target source by the telescope array and indirectly indicates the quality of the telescope array layout.

The following introduces the (u, v, w) coordinate system, which is derived from the transformation of the coordinate system of radio telescope antennas. As shown in Figure 6, this diagram illustrates the transformation relationship between the telescope antenna coordinate system and the sampling coordinate system. In the diagram, the (X, Y, Z) coordinates represent the equatorial coordinate system, where the X and Y planes are parallel to the celestial equator. The X-axis is aligned along the meridian of the reference station of the radio telescope array, the Y-axis points East, and the Z-axis points towards the North Pole. In the (u, v, w) coordinate system, the w-axis is directed towards the target. The angle between the w-axis and the XOY plane denotes the declination ($\delta$) of the target S, while the angle between the meridian plane of the w-axis and the local meridian plane signifies the hour angle (H). The u-axis lies in the XOY plane, and the angle between the u-axis and the Y-axis represents the hour angle (H). The zenith angle of the meridian plane containing the v-axis represents the declination ($\delta$) of the radio source. Given the components of a baseline vector ($D_{\lambda }$) in the (X, Y, Z) coordinate system: $X_{\lambda }$, $Y_{\lambda }$, $Z_{\lambda }$, and in accordance with the coordinate transformation relationships illustrated in Figure 6, the components in the (u, v, w) coordinate system are calculated as follows [12]:

$$\left[\begin{array}{c}u\\ \nu \\ w\end{array}\right]=\left[\begin{array}{ccc}sin\left(H\right)& cos\left(H\right)& 0\\ -sin\left(\delta \right)cos\left(H\right)& sin\left(\delta \right)sin\left(H\right)& cos\left(\delta \right)\\ cos\left(\delta \right)cos\left(H\right)& -cos\left(\delta \right)sin\left(H\right)& sin\left(\delta \right)\end{array}\right]\left[\begin{array}{c}{X}_{\lambda }\\ Y_{\lambda }\\ Z_{\lambda }\end{array}\right]$$

(3)

Through matrix operations, Equation (3) can be simplified as [12]:

$$u^2+{\left({\displaystyle \frac{\nu -Z_{\lambda }cos\delta }{sin\delta }}\right)}^2=X_{\lambda }^2+Y_{\lambda }^2.$$

(4)

From Equation (4), it can be observed that, theoretically, the sampling points of u and v (i.e., the $uv$ coverage) will form an ellipse or a segment of an elliptical arc over continuous time, without considering other influencing factors, such as the occlusion of the Sun. The major semi-axis of the ellipse is given by $\sqrt{X_{\lambda }^2+Y_{\lambda }^2}$, while the ellipse itself has a minor semi-axis of $sin\delta \sqrt{X_{\lambda }^2+Y_{\lambda }^2}$. The center of this ellipse is located at the coordinates $\left(\begin{array}{c}0,Z_{\lambda }cos\delta \end{array}\right)$. Simultaneously, it is evident that the distribution of $uv$ coverage is influenced by both the telescope antenna layout and the visible time of the target within the same observation time [15,16]. Conversely, when observing the same target, the coverage rate of $uv$ coverage serves as an indicator of the telescope array layout’s efficiency.

Based on the fundamental principle of $uv$ coverage, the functionality of this module has been devised. The module encompasses various parameters, including the observation time range (scanning H), target position (RA, DEC), and telescope station position (X, Y, and Z) [17,18,19]. Specifically, a Python class (FuncUV) is defined in this module, which is used to calculate the $uv$ coordinates in the synthetic aperture using the input parameters. Simultaneously, within this module, numerous constraints encountered in actual observations have been incorporated into the $uv$ coverage, including terrain effects on elevation angles and solar occlusion of targets, aiming to simulate the actual observation process as closely as possible. The $uv$ coverage map is plotted using a QT interface. In the imaging of targets, the sufficiency of $uv$ coverage sampling plays a pivotal role in determining the imaging quality of the target. A denser sampling of $uv$ coverage correlates with enhanced imaging quality, whereas a less dense sampling results in diminished quality [20,21,22].

4. Main Function Testing

4.1. Trajectory Prediction Module

In this section, we assess the accuracy of our trajectory prediction model on a set of well-known targets using Equation (1). The six targets selected for this evaluation are PSR B0329+54, B0531+21, J1846-0258, FRB190523, SGR1935, and FRB20220912A. The predicted trajectories for these targets are detailed in

Table 3. Targets’ trajectory prediction results.

Target	RA	DEC	Rise Time	Set Time	Visible Time Range
	(h:m:s)	(d:m:s)	(h:m)	(h:m)	(h:m–h:m)
PSR B0329+54	03:32:59.4096	+54:34:43.329	00:50	14:30	00:50–14:30
PSR B0531+21	05:34:31.973	+22:00:52.06	04:10	15:20	04:10–15:20
PSR J1846-0258	18:46:24.94	−02:58:30.1	18:10	03:50	00:00–03:50, 18:10–24:00
FRB190523	13:48:15.60	+72:28:11	09:20	02:40	00:00–02:40, 09:20–24:00
SGR1935	19:34:55.68	+21:53:48.2	18:50	05:10	00:00–05:10, 18:50–24:00
FRB20220912A	23:09:04.90	+48:42:25.4	20:50	09:50	00:00–09:20, 20:50–24:00

. Columns 1 to 3 show the target name as well as the RA and DEC positions of the target. Columns 4 to 6 present the UT time with the observation date set for 1 April 2024. Specifically, columns 4 and 5 indicate the rise and set times of the targets, respectively. The rise time refers to the time when the target rises to the observable elevation (${15}^{\circ }$), and the set time is the time when it drops to the unobservable elevation (${15}^{\circ }$). Column 6 lists the final visible time range of the targets within a 24-h period for the telescope array. These visibility time ranges were determined using a threshold elevation (${\theta }_{\mathrm{el}}$) of 15 degrees. The distribution of ${\theta }_{\mathrm{el}}$ across UT time is visualized on the system interface, as depicted in Figure 7.

To assess the precision and practicality of the trajectory predictions generated by this module, it was utilized in target-observation tasks involving the radio telescope array from August 2022 to March 2024. The module was employed to generate a 24-h ${\theta }_{\mathrm{el}}$ curve for each target. Subsequently, the telescope was directed to track the corresponding target at the designated times in conjunction with the telescope array control software [23]. The findings revealed that the actual observational outcomes were highly consistent with the computed predictions, which underscores the high computational accuracy and reliability of this method.

4.2. Intelligent Scheduling Module

In the intelligent scheduling module, target sources are prioritized according to the inverse of their observable duration in the visible sky, which serves as their weight. On 1 April 2024, at 11:00:00 local time, the observation station, located at longitude ${106.67}^{\circ }$ and latitude ${26.44}^{\circ }$, sorted six target sources: PSR B0329+54, SGR B1935+21, PSR B0531+21, FRB190523, PSR J1846-0258, and FRB20220912A. The details are presented in

Table 4. Intelligent scheduling result.

Target	RA	DEC	${\mathit{\theta }}_{\mathbf{el}}$ Difference	Observation Priority	Visible Time Range
	(h:m:s)	(d:m:s)	(deg)		(h)
FRB190523	13:48:15.6	+72:28:11	29.08	1	15.53–20.49
PSR J1846-0258	18:46:24.94	−02:58:30.1	45.43	2	20.52–24, 0–2.47
PSR B0329+54	03:32:59.4096	+54:34:43.329	46.73	3	6.74–10.7
FRB20220912A	23:09:04.9	+48:42:25.4	52.50	4	4.13–7.1
SGR1935	19:34:55.68	+21:53:48.2	70.47	5	2.5–4.1
PSR B0531+21	05:34:31.973	+22:00:52.06	70.49	6	10.73–15.0

. Columns 4 and 5 present the difference between the maximum and minimum elevation of the target within 24 h and the observation priority of the target. Column 6 lists the visible time range within 24-h observations for each target. Based on the information provided in the table, these sources are visualized in the system interface sequentially and then sorted accordingly. Figure 8 shows the trajectory prediction of the six targets after scheduling. As shown in Figure 7, FRB190523 has the smallest elevation difference and thus ranks first in priority. Its visible time is from 15.53 h to 20.49 h. Next is PSR J1846-0258. Since its elevation difference is the second smallest, it ranks second in priority, and its observation time is from 20.52 to 24 h and 0 to 2.47 h. By the same reasoning, the priorities and corresponding observation times of all six sources are obtained.

4.3. Calibrator Prediction Module

For calibrating target sources positioned at various locations, we utilize a calibration source library consisting of radio sources with stable flux densities spread across different right ascensions and declinations. The selection of calibration sources is tailored to each observation. Figure 9 depicts the 24-h elevation tracking for these calibration sources. It presents the tracking curves for four calibration sources with strong flux: 3C48, 3C196, 3C286, and Cygnus A. This visual representation facilitates the identification of calibration sources that correspond to the sky region of the target source at any given time.

For instance, when tracking the fast radio burst FRB190523 (represented by the blue line at the top of Figure 8), 3C286 (the blue line at the lower left corner of Figure 9) can be observed both before and after to serve as a flux calibration source for FRB190523. Similarly, when tracking the target source J1846-0258 (the orange line at the top of Figure 8), Cygnus A (the red line at the lower left corner of Figure 9) can be observed before and after to act as a flux calibration source for J1846-0258. The calibration source signal is weak. At present, the number of our array antennas is small, so we use the Sun as the calibration source, and the receiving time is 4 s.

4.4. $uv$ Coverage Test and Analysis

Given the limited number of antennas in the telescope array at Guizhou Normal University, there is little significance in testing and evaluating the quality of $uv$ coverage for different array configurations within this array. Consequently, this paper mainly focuses on testing the quality of $uv$ coverage of the telescope array to be upgraded in the future and other commonly used array configurations, aiming to prove that $uv$ coverage has the function of optimizing array configurations. To evaluate the quality of $uv$ coverage and identify the optimal configuration for the telescope array, we calculate both the total and effective areas of the $uv$ plot using $uv$ coordinates. The coverage ratio is determined by dividing the effective area by the total area. The configuration that yields the highest coverage ratio is deemed the optimal telescope array layout.

Figure 10 illustrates the upgraded telescope array configuration we intend to build in Liupanshui City, whose center position is located at longitude ${104.70}^{\circ }$ and latitude of +${26.45}^{\circ }$ [24,25,26]. The transformation of this center position to the position in the equatorial coordinate system is (X = −1449.91, Y = 5528.14, Z = 2825.79) in km. Here, the equatorial coordinate system can be observed in Figure 6, and its introduction can be found in Section 3.4. In this coordinate system, the signs of the transformed points’ values on the X and Y axes depend on the longitude. For $0^{\circ }<\mathrm{longitude}\le {90}^{\circ }$, both X and Y are positive; for ${90}^{\circ }<\mathrm{longitude}\le {180}^{\circ }$, $X<0$ and $Y>0$; for ${180}^{\circ }<\mathrm{longitude}\le {270}^{\circ }$, both X and Y are negative; for ${270}^{\circ }<\mathrm{longitude}\le {360}^{\circ }$, $X>0$ and $Y<0$. The sign of the transformed point’s value on the Z-axis depends solely on the latitude. When $\mathrm{latitude}>0$, $Z>0$; otherwise, $Z<0$. The longitude (${104.70}^{\circ }$) of the upgraded telescope array’s center is greater than ${90}^{\circ }$ and less than ${180}^{\circ }$, and its latitude (+${26.45}^{\circ }$) is greater than $0^{\circ }$. Consequently, for points centered on this, the transformed X values are all negative, while the Y values are all positive; see Figure 10. This upgraded telescope array contains 49 antennas and the diameter of each antenna is 4.5 m. Taking into account the local traffic and network construction conditions, we follow the sightseeing road in the Yeyuhai Scenic Area of Liupanshui and keep away from the relevant construction land. There are 49 point positions that have been selected as candidate locations for the antennas of the upgraded array. With this array, we perform a series of observation simulations for the celestial target 0316 + 413 (RA = 03 h 19 m 48.16 s, DEC = 41 d 30 m 42.1 s), beginning at 00 h:00 m:00 s on 1 May 2023, and lasting for durations of 1, 2, 4, 8, 12, and 24 h, respectively. The integration time of each duration of observation was set at 5 min.

Our simulations produced six sets of $uv$ coverage data. For each dataset, we first determine the minimum baseline using the formula $\sqrt{{(u_1-u_2)}^2+{(v_1-v_2)}^2}$, where $(u_1,v_1)$ and $(u_2,v_2)$ are coordinates of two distinct points within the dataset’s $uv$ plane. The square of this minimum baseline is then taken as the unit area. Next, the effective area is calculated by multiplying the unit area by the number of $uv$ points. The total area ($A_{\mathrm{total}}$) is derived by finding the difference between the maximum and minimum $uv$ values in each dimension and multiplying these differences: $A_{\mathrm{total}}=(u_{max}-u_{min})\times (v_{max}-v_{min})$. The coverage ratio is finally calculated as the ratio of the effective area to the total area [17]. The resulting $uv$ coverage ratios for the six datasets are 0.3%, 0.5%, 0.8%, 1.0%, 1.3%, and 1.5%, respectively. These findings suggest that as the observation time increases, both the $uv$ coverage area and the coverage ratio also increase. Figure 11 displays the $uv$ coverage maps for these six datasets, showing that the density of the $uv$ coverage increases as the observation duration increases. This is consistent with their $uv$ coverage ratios.

To determine the telescope array layout that offers the best $uv$ coverage, we also tested circular and Y-shaped configurations. Figure 12 illustrates the layout configuration of the circular array. The $uv$ coverage maps corresponding to observation durations of 1, 2, 4, 8, 12, and 24 h are presented in Figure 13. The coverage ratios for these durations are calculated as 0.5%, 1.0%, 1.9%, 3.9%, 5.8%, and 6.5%, respectively. Figure 14 shows the layout configuration of the Y-shaped array. The $uv$ coverage maps for the Y-shaped array, for observation durations of 1, 2, 4, 8, 12, and 24 h, are presented in Figure 15. The corresponding coverage ratios are 0.2%, 0.4%, 0.6%, 1.0%, 1.6%, and 1.7%, respectively. The integration time for each observation duration of these two arrays was set at 5 min.

Finally, a comparison of the coverage ratios for the three telescope array configurations is depicted in Figure 16. The analysis reveals that the circular array exhibits the greatest variation and the highest peak in coverage ratio compared to the other configurations, making it the optimal layout for this station in terms of coverage. The coverage ratios for both the upgraded and Y-shaped configurations are nearly identical across the six observation durations. The Y-shaped layout, a common configuration in radio astronomy such as the NRAO Very Large Array [27], is noted for its widespread use. Given the primary scientific objective of the radio telescope array under construction—to detect transient sources like fast radio bursts (FRBs)—the observation duration at any single position is significantly less than one hour, typically on the order of minutes. Under these circumstances, the coverage rates of the three layout configurations are essentially equivalent based on the current computational results. Therefore, after a comprehensive evaluation, we have decided to adopt the upgraded layout configuration.

5. Discussion and Conclusions

This paper discusses the observational requirements for the 4 × 4.5 m radio telescope array at Guizhou Normal University and outlines the development of an observation scheduling system. The code of this system software is publicly available on Github (https://github.com/MC-git37/astronomical-observation, accessed on 11 October 2024). Designed for any antenna array and any geographical location, the system is built using Python and Qt Designer and offers the following capabilities: predicting the azimuth and elevation changes in target sources over the upcoming 24 h based on the current antenna position, with visualization; scheduling and processing target source collections; visualizing calibration sources across all sky regions; and $uv$ mapping for any antenna array. The system is compatible with both Windows and Linux operating systems and boasts a user-friendly, intuitive interface, along with strong versatility, portability, and expandability.

Since its deployment in June 2022 for daily observations of the 4 × 4.5 m array at Guizhou Normal University, by combining this system and the telescope control system to predict the trajectory of pulsars, two typical pulsars have been successfully detected: PSR B0329+54 (J0332+5434) and PSR B0833-45 (J0835-4510), as shown in Figure 17 and Figure 18, respectively. Note that since there is no calibration in our system, we use the pdv package in PSRCHIVE [28] to give the relative flux density, which is the “intensity” axis shown in the tow figures. Looking ahead, the system will be integrated with upgraded arrays or other arrays to identify and address any deficiencies and areas for improvement. Currently, the system may face challenges in scheduling when observation periods have extremely low or high ${\theta }_{\mathrm{el}}$ values, requiring manual insertion of calibrators post-scheduling. Future development will focus on optimizing ${\theta }_{\mathrm{el}}$ value selection to enhance the efficiency of target observations and automating the insertion of calibrators after scheduling.