Mountain Top-Based Atmospheric Radio Occultation Observations with Open/Closed Loop Tracking: Experiment and Validation

Article Mountain Top-Based Atmospheric Radio Occultation Observations with Open/Closed Loop Tracking: Experiment and Validation

Fenghui Li 1,2, Chunping Hou 1, Liang Kan 1,*, Naifeng Fu 1 , Meng Wang 3 and Zhipeng Wang 1

1 School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China; [email protected] (F.L.); [email protected] (C.H.); nﬀ[email protected] (N.F.); [email protected] (Z.W.) 2 Tianjin Yunyao Aerospace Technology Co., Ltd, Tianjin 300300, China 3 Aerospace Star Technology Co., Ltd, Beijing 100089, China; [email protected] * Correspondence: [email protected]; Tel.: +86-022-6095-6530

Received: 23 October 2020; Accepted: 8 December 2020; Published: 13 December 2020

Abstract: Through Global Navigation Satellite System (GNSS) occultation measurement, the global ionosphere and atmosphere can be observed. When the navigation satellites’ signal passes through the lower atmosphere, the rapid change of the atmospheric refractive index gradient will cause serious multipath phenomena in radio wave propagation. Atmospheric doppler frequency shift and amplitude signal fluctuations increase drastically. Due to the attenuation of signal amplitude and the rapid change of the Doppler frequency, the general phase locked loop (PLL) cannot work properly. Hence, a more stable tracking technology is needed to track the occultation signal passing through the lower atmosphere. In this paper, a mountain-top based radio occultation experiment is performed, where we employ an open-loop receiver and remove the navigation bits by the internal demodulation. In the process of the experiment, we adopt the open-loop tracking technique and there is no feedback between the observed signal and the control model. Specifically, taking the pseudo-range and doppler information from models as input, three key parameters, i.e., accurate code phase, carrier doppler and code doppler, can be obtained, and furthermore, the accurate accumulation is determined by them. For the full open-loop occultation data, a closed-loop observation assisted strategy is presented to compare the tracking results between open-loop and closed-loop occultation data. Through the compared results, we can determine whether the initial phase has been reversed or not, and obtain the high consistency corrected open-loop data that can be directly used for subsequent atmospheric parameters inversion. To verify the effect of open-loop tracking and open-loop inversion, we used the company’s self-developed occult receiver system for verification. The company’s self-developed occult receiver system supports Global Position System (GPS)/Beidou satellites constellation (BD, the 2nd and 3rd generations) dual systems. We have verified GPS and BD open-loop tracking and inversion, carried out in a three-week mountain-based experiment. We used closed-loop and open-loop strategies to track and capture the same navigation star to detect its acquisition effect. Finally, we counted the results of a week (we only listed the GPS data; BD’s effect is similar). The experimental results show that the open-loop has expanded the signal-cut-off angle by nearly 20% under the condition of counting all angles, while the open-loop has increased the signal-cut-off angle value by nearly 89% when only calculating the negative angle. Finally, the atmosphere profiles retrieved from observations in open-loop tracking mode are evaluated with the local observations of temperature, humidity and pressure provided by the Beijing Meteorological Bureau, and it is concluded that the error of open-loop tracking method is within ~4% in MSER (mean square error of relative error), which meets the accuracy of its applications (<5%, in MSER).

Remote Sens. 2020, 12, 4078; doi:10.3390/rs12244078 www.mdpi.com/journal/remotesensing Remote Sens. 2020, 12, 4078 2 of 16

Keywords: atmospheric occultation; open-loop tracking; mountain base test; BD3; internal processing

1. Introduction Global Navigation Satellite System (GNSS) occultation measurement is a meteorological remote sensing technology, which utilizes occultation phenomenon between GNSS navigation constellation and low earth orbit (LEO) satellites in its orbit to measure the earth’s ionosphere and atmosphere [1–3]. By installing GNSS occultation antennas on the LEO satellites, it is possible to obtain the atmospheric refractive index, temperature, pressure from the earth’s surface to 40 km and the ionospheric electronic distortion rate from ~60 km to the orbital height of the occultation LEO satellite [4,5]. Atmospheric detection is of great significance for the weather forecast, scientific research and military application [6–8]. The occultation signal from GNSS satellites has low and negative elevation angles [9–11]. Many approaches to data processing in the presence of multipath propagation (methods based on Fourier Integral Operators, like Canonical Transform, Full Spectrum Inversion and Phase Matching) can be found in references [12–18]. When the occultation signal passes through the lower atmosphere, especially the equatorial low latitude area, serious multipath phenomena appear in radio waves due to the rapid change of atmospheric refractive index gradient [19–21]. The fluctuation of atmospheric doppler frequency shifts and amplitude signal increases sharply, and the spectrum of occultation signal expands [6–8]. Due to the attenuation of signal amplitude and the rapid change of doppler frequency, the general phase locked loop (PLL) cannot work normally. Until recently, two very important challenges remained outstanding: (1) the ability to record and retrieve rising occultations; and (2) the ability to penetrate the lowest 2 km in the tropical troposphere routinely (for rising or setting occultations) without introducing tracking errors. These challenges have largely been overcome by the use of open-loop (OL) tracking implemented in the GPS receivers onboard the SAC-C satellite, and later Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) [22]. Closed-loop tracking is a method of tracking the carrier frequency and code frequency of satellite launches in real time, through the adjustment of the software’s own loop route. The OL tracking technique is different from the traditional closed-loop tracking, in that there is no feedback between the observation signal and the control model. Meanwhile, signal tracking in the OL mode uses the predicted Doppler model and pseudo-range model to track the full signal, and has the ability to track stably [22–24]. A mountain-based occultation experiment for three weeks in Wuling Mountain of Hebei Province is planned and implemented, with the following works to be carried out: 1. A hardware and software system supporting Global Position System (GPS)/Beidou satellites constellation (BD, the 2nd and 3rd generations) dual-mode occultation being developed for full OL tracking technology’s verification; 2. An open-loop data processing method assisted with closed-loop observations, which is proposed to solve the problem to determine the initial sign of the recovered phase; 3. In the mountain-based occultation experiment, the robustness of the hardware and software systems using OL technology to track L1C/GPS and B1/BD signals being verified; and 4. The atmosphere profiles retrieved from observations in open-loop tracking mode being evaluated with the local observations of temperature, humidity and pressure provided by the Beijing Meteorological Bureau.

2. Open-Loop Tracking and Inversion Algorithm

2.1. Open-Loop Tracking Algorithm OL tracking uses the predicted Doppler and pseudo-range models to track the signal [25,26]. The difference between the OL and the traditional PLL is that there is no feedback between the observation signal and the control model, but only the model control signal is used, so it will not be Remote Sens. 2020, 12, 4078 3 of 16 affected by the change of the signal [27,28]. It can track full information of phases (the effects of motion, atmospheric multipath, etc.), and can detect rising occultation events more conveniently [29,30]. The mountain-based OL tracking algorithm is different from the spaceborne OL tracking algorithm in terms of the model Doppler and pseudo range. In the satellite OL tracking module, we employ the international reference atmospheric model CIRA86-Q for pseudo-range/Doppler prediction. The mountain-based OL tracking algorithm is mainly used to verify the correctness of OL tracking, not to verify the correctness of the Doppler and pseudo range model. In the verification process of the mountain-based OL tracking algorithm, we assume that the Doppler and pseudo-range are mainly changed by the movement of GNSS satellites, while the effects of the atmosphere and the ionosphere are small. In the mountain-based test, the position and speed of the navigation satellite can be obtained through the ephemeris. The geometric distance of between the station and the satellite at an occultation and the Doppler of motion obtained based on the velocity of that satellite are used as the output of the pseudo-range/Doppler model to narrow the phase search range in full OL tracking. The chip array of the mountain-based occultation receiver is expanded to ensure that the phase delay caused by the atmosphere is within the chips’ range.

2.2. Open Open-Loop Data Processing In the OL mode, the phase used to retrieve for atmosphere profiles can be expressed as sum of the modeled phase (MP) and the recovered phase (RP). The MP is obtained from the occultation geometry and climate models. The RP is restored from observations of the In-Phase(I)/Quadra-Phase(Q) components through three steps: frequency reduction conversion; NDM removal; and adjacent phase connection [28,31–34]. The ways to eliminate the influence of NDM in the OL mode are the internal and external methods, and the biggest difference between them is that the external mode requires GPS bit data. Due to geographical restrictions, however, only about 70% of the COSMIC occultation data has corresponding GPS bit data [31–34]. Due to a lack of information in determining the initial sign of RP, there may be a different sign between the initial I/Q components and the real phase, which will negatively correct the MP. We adopt the strategy of the full OL data recovery process, assisted with closed-loop observations to avoid the above-mentioned problems. Through MPs adding or subtracting RPs, we can obtain two series phases, named corrected phases A/B(CPA/CPB). We use the correlation between the mountain-based closed-loop observation data of an elevation angle above 3 degrees and CPA/CPB to determine the initial sign of RP, and obtain a high-consistency corrected OL phase for subsequent atmospheric parameter inversion.

2.3. Mountain-Based Atmospheric Retrieval Algorithm The GNSS signal can generally be expressed as follows:

s,r( ) = s,r( ) + ( s( ) + r( )) + ( ) + s,r( ) + s,r( ) + s,r( ) Li t ρ t c σ t σ t exLi t m t n t N t (1) s,r( ) = s,r( ) + s,r( ) exLi t Ioni t Atmi t (2) s,r( ) where c is the speed of light, and Li t is the observed phase of the transmitter (s) and receiver (r) of the i-th frequency at time (t). ρs,r(t) is the geometric distance between transmitter (s) and receiver (r) at time t. σs(t), σr(t) are the clock difference of the transmitter (s) and receiver (r) at time (t), respectively. s,r( ) s,r( ) s,r( ) mi t is the local multipath error [35,36]; ni t is the residual phase. Ni t is the ambiguity of s,r( ) the whole cycle. The excess phase exLi t of transmitter s and receiver (r) of the i-th frequency at s,r( ) time (t) is generally defined as the sum of neutral atmospheric delay Atmi t and ionospheric delay s,r( ) Ioni t [36–40]. Based on Internet GNSS Servers (IGS) products and low-orbit satellite precision orbit determination products, it is possible to obtain a sufficiently accurate distance ρs,r(t) from the navigation satellite transmitter to the low-orbit satellite receiver and its clock difference σs(t). The local multipath error can be ignored in mountain-based occultation. The receiver clock error σr(t) can generally be eliminated Remote Sens. 2020, 12, x FOR PEER REVIEW 4 of 17 Remote Sens. 2020, 12, 4078 4 of 16 can generally be eliminated by selecting a higher altitude navigation star as a reference and applying the satellites’ phase difference. As a result, high-precision excess phase observations of the occultation by selecting a higher altitude navigation star as a reference and applying the satellites’ phase difference. can be obtained, which only include the influence of the ionosphere and atmosphere through the As a result, high-precision excess phase observations of the occultation can be obtained, which only path. In the process of spaceborne neutral atmosphere inversion, the combination of different include the influence of the ionosphere and atmosphere through the path. In the process of spaceborne frequency point bending angle sequences can better eliminate the ionospheric influence. In extracting neutral atmosphere inversion, the combination of different frequency point bending angle sequences the excess phase, only the ionospheric influence of the reference star can be eliminated. In the can better eliminate the ionospheric influence. In extracting the excess phase, only the ionospheric mountain-based atmospheric occultation inversion, the atmospheric state information from the influence of the reference star can be eliminated. In the mountain-based atmospheric occultation ground to the top of the mountain can be obtained through the relationship between the impact inversion,height observed the atmospheric by the positive state information and negative from altitude the ground angle. to theAs topshown of the in mountainFigure 1, canobservation be obtained of through the relationship between the impact height observed by the positive and negative altitude negative elevation angle (light and dark green thick line, bending angle is  ) can be regarded as angle. As shown in Figure1, observation of negative elevation angle (light and- dark green thick line, the Abel integral (light green thick line) and positive elevation angle (light blue thick line, bending bending angle is α ) can be regarded as the Abel integral (light green thick line) and positive elevation angle is  ) from− the top to the impact height, namely [39–42]: angle (light blue thick line, bending angle is α+) from the top to the impact height, namely [39–42]: dInn Z n1r1 dInn nr dx α (a) = α+ 2a 11 dx dx (3)(3) − a − −  2 a2 2 dx a a √x 22a xa−

Figure 1. Figure 1. SchematicSchematic diagram diagram of ofmountain mountain base base inversion inversion.. M stands M stands for the for top the of topthe mountain, of the mountain, where where the antenna and receiver are installed, and Global Navigation Satellite System (GNSS) stands the antenna and receiver are installed, and Global Navigation Satellite System (GNSS) stands for the for the navigation satellite we want to receive, that is, the navigation satellite that generates the navigation satellite we want to receive, that is, the navigation satellite that generates the occultation occultation event. event. Let Z n1r1 dInn dx eα(a) = α (a) α+(a) = 2a dx, (4) − − − a √x2 a2 −

Remote Sens. 2020, 12, x FOR PEER REVIEW 5 of 17

Let dInn nr11 dx (4) a   a    a  2 a dx ,  a 22 Remote Sens. 2020, 12, 4078 xa 5 of 16 then the refractive index n of the impact height  ( n1 is the peak refractive index, 휉 is the maximumthen the refractive impact height index ofn ofthe the occultation impact height) is: α (n1 is the peak refractive index, ξ is the maximum impact height of the occultation) is: 1 푛1푟1 훼̃(푥) 푛(푎) = 푛1 푒푥푝( Z∫n r  푑푥) (5)  1휋 1 1 eα(x2) 2 n(a) = n exp 푎 √휉 −dx푎 1  p  (5) π a ξ2 a2 Thus, the refractive index profile from the ground to the− top of the mountain can be obtained from Thus,the mountain the refractive-based indexoccultation profile data from [42 the,43] ground. to the top of the mountain can be obtained fromIn the the mountain-based above process, occultation the influence data of [ 42the,43 atmosphere]. or ionosphere on the observation data aboveIn the the top above of process,the mountain the influence can be ofeliminated the atmosphere in the orprocess ionosphere of searching on the observation for the symmetrical data above impactthe top height of the mountain and its combination. can be eliminated Therefore, in the when process the of clock searching error for of the the symmetrical mountaintop impact receiver height is eliminatedand its combination. by the reference Therefore, star, when only the the clock ionospheric error of the influence mountaintop of the receiver reference is eliminated star needs by to the be eliminated,reference star, while only the the mountain ionospheric-based influence occultation of the observation reference star data needs does to not be eliminated, need to consider while the its influencemountain-based on the excess occultation phase. observation Even with only data single does frequency not need to observation consider its data, influence the refractive on the excessindex inversionphase. Even results with from only the single ground frequency to the observationtop of the mountain data, the can refractive be obtained. index inversion results from the groundAs shown to thein F topigure of 2 the, according mountain to can the begeometric obtained. relationship of the mountain-based occultation, As shown in Figuresr, 2, according to the geometricsr, relationship of the mountain-based occultation, Excess phase exLi () t and Doppler dopi () t of transmitter (s) and receiver (r) at frequency (i) at Excess phase exLs,r(t) and Doppler dops,r(t) of transmitter (s) and receiver (r) at frequency (i) at time time (t), The impacti height a (the superscripti and subscripts and the time label are omitted here) (t), The impact height a (the superscript and subscripts and the time label are omitted here) and the and the bending angle  have the following relationship [44]: bending angle α have the following relationship [44]: s,, r s r dopii()() t1  exL t s,r( )  s,r( ) (6) dopi t 1 ∆exLi t fi = c t (6) fi c ∆t 푠,푟 푓 푣 푖 2 (7) 푑표푝푖 (푡) = −fiv2 푐표푠( 훾 − 휙2) dops,r(t) = 푐 cos(γ φ ) (7) i − c − 2 푛2푟2 푠푖푛(휙2) 푎(푡) = 푛2푟2 푠푖푛( 휙2) = 푛1푟1 푠푖푛( 휙1) → 휙1 = 푎푟푐푠푖푛n2r2sin((φ2) ) (8) a(t) = n2r2sin(φ2) = n1r1sin(φ1) φ1 = arcsin( 푛)1푟1 (8) → n1r1

훼α = θ휃 −φ휙++φ2휙 ((9)9) − 1 1 2

Figure 2. Geometry diagram of mountain base occultation. Coordinate point 1 represents the site of the mountain base test, at the top of Wuling Mountain. Coordinate point 2 represents the navigation satellite at an occultation event.

Among these, fi is the frequency of frequency point i, and φ1, φ2, r1, r2 are the signal incident angle and the center distance of the receiver and transmitter, respectively. θ is the angle between the Remote Sens. 2020, 12, x FOR PEER REVIEW 6 of 17

Among these, fi is the frequency of frequency point i , and 휙1, 휙2, 푟1, 푟2 are the signal Remoteincident Sens. angle2020, 12and, 4078 the center distance of the receiver and transmitter, respectively.  is the angle6 of 16 between the vector from the Earth’s center to the receiver and the transmitter. v2 is the occultation vectorvelocity, from and the  Earth’s is the angle center between to the receiver the occultation and the transmitter. velocity andv2 theis the vector occultation from the velocity, Earth’s and centerγ is theto the angle transmitter between. the occultation velocity and the vector from the Earth’s center to the transmitter.

3. Mountain Mountain-Based-Based Test Results The mountain-basedmountain-based occultation experiment is from 25 August to 8 SeptemberSeptember 2020. The site of thethe observation is the top of Wuling Mountain, the main peak of the Yanshan Mountains (located in Chengde, Hebei Province, 117.48 degrees east longitude, 40.60 degrees north latitude, and 2118 m above sea level) level),, and and the the occultation occultation antenna antenna is is deployed deployed on on the the roof roof of of Dingfeng Dingfeng Hotel. Hotel. As As shown shown in inFigure Figuress 3 3and and 44, ,the the south south side side of of the the mountain mountain is is empty. empty. Our Our occultation occultation antenna antenna (right (right side) side) is isinstalled installed on onthe the top top of ofthe the building building and and placed placed facing facing south, south, and and the thereceiver receiver is installed is installed inside inside the theroom. room.

Figure 3. Mountain-based location, behind our experiment team is the bottom of the mountain. Our Figure 3. Mountain-based location, behind our experiment team is the bottom of the mountain. Ouroccultation occultation antenna antenna (the part (the marked part marked in red in in red the inpicture) the picture) is mounted is mounted on a tripod on a tripodand placed and placedfacing facingsouth, south,and our and positioning our positioning antenna antenna (the part (the marked part marked in green in in green the picture) in the picture) is also isinstalled also installed on the ontripod. the tripod.On the tripod, On the place tripod, it placetowards ittowards the zenith. the The zenith. south The side south of the side mountain of the mountain is empty, iswhich empty, is whichconducive is conducive to our experiments. to our experiments.

3.1. AnalysisThe GNSS of GPS occultation and BD Open-Loop receiver Tracking system Resultsused for testing is developed by Tianjin Yunyao Aerospace Technology Co., Ltd, which is compatible with GPS/BD systems. The I and Q components of the signal have different characteristics in OL and closed-loop tracking. In the tracking process, the phases of the OL flipped by NDM and error from the OL predict model in the form of a trigonometric function on the I/Q components, which can be seen from Figure5. The phases of the closed-loop are of huge value, with signal flipped in the I component, and the Q component is signal noise. The closed-loop tracking can detect the phase or frequency difference between the locally reproduced carrier and the received carrier through the phase detector or frequency discriminator in the carrier loop. Then, the phase alignment of the local PN code and the received code can be continuously adjusted through the code loop discriminator, so as to obtain the highest self-phase correlation peak value. Remote Sens. 2020, 12, x FOR PEER REVIEW 7 of 17

Remote Sens. 2020, 12, 4078 7 of 16 Remote Sens. 2020, 12, x FOR PEER REVIEW 7 of 17

Figure 4. Installation drawing of equipment room, our equipment is installed indoors, as shown in the figure (red marking part) and verified by the company’s self-researched occultation detector. It has the characteristics of small volume and low power consumption. It is also the equipment we will use in satellite networking in the future. It is placed on the anti-static pad, and ground treatment is also carried out to prevent the occurrence of static electricity and lightning strike events on the mountain.

3.1. Analysis of GPS and BD Open-Loop Tracking Results The I and Q components of the signal have different characteristics in OL and closed-loop tracking. In the tracking process, the phases of the OL flipped by NDM and error from the OL predict modelFigure in the 4.4 .form Installation of a trigonometric drawingdrawing ofof equipment equipment function room, onroom, the our our I/Q equipment equipment components, is installedis installed which indoors, canindoors, be as seen shownas shown from in the Figurein 5. Thetheﬁgure phases figure (red of(red marking the marking closed part) -part)loop and andare veriﬁed ofverified huge by the byvalue company’sthe , companywith signal self-researched’s self flipped-researched in occultation the occultation I component, detector. detector. and It has Itthe Q componenthasthe characteristicsthe characteristicsis signal noise. of small of smallThe volume closedvolume and- loopand low low powertracking power consumption. canconsumption. detect It the is It also isphase also the equipmentthe or equipmentfrequency we willwe difference will use betweenusein satellite in the satellite locally networking networking reproduced in the in future.the carrier future. It is andIt placed is placed the on received the on anti-staticthe anti carrier-static pad, throughpad and, and ground ground the treatment phase treatment detector is also is or frequencyalsocarried carried discriminator out to out prevent to prevent in the th occurrencee thecarrier occurr loop. ofence static Then, of electricity static the electricityphase and lightning alignment and lightning strike of eventsthe strike local on theeventsPN mountain. code on and the the receivedmountain. code can be continuously adjusted through the code loop discriminator, so as to obtain the highestThe self GNSS-phase occultation correlation receiver peak value. system used for testing is developed by Tianjin Yunyao Aerospace 3.1.Technology Analysis Co.,of GPS Ltd, and which BD Open is compatible-Loop Tracking with Results GPS/BD systems.

6 The x I10 and Q components of the signalOpen Loop have Tracking differentAccumulation Data characteristics in OL and closed-loop 1.5 tracking. In the tracking process, the phases of the OL flipped by NDM and errorIn-Phase Accumulationfrom the Data OL predict Quadra-Phase Accumulation Data model in1 the form of a trigonometric function on the I/Q components, which can be seen from Figure 5. The phases of the closed-loop are of huge value, with signal flipped in the I component, and the Q component0.5 is signal noise. The closed-loop tracking can detect the phase or frequency difference

between0 the locally reproduced carrier and the received carrier through the phase detector or frequencyUnit:1 discriminator in the carrier loop. Then, the phase alignment of the local PN code and the received-0.5 code can be continuously adjusted through the code loop discriminator, so as to obtain the

highest -1self-phase correlation peak value.

Remote Sens. 2020, 12, x FOR PEER REVIEW 8 of 17 -1.5 0 100 200 300 400 500 600 6 x 10 Open LoopRelativeGpsTimes(s) Tracking Accumulation Data 1.5 5 x 10 Close Loop Tracking Accumulation Data In-Phase Accumulation Data 3 Quadra-Phase Accumulation Data 1 In-Phase Accumulation Data Quadra-Phase Accumulation Data 2 0.5

1 0

Unit:1

Unit:1 -0.5

-1 -1

-2 -1.5 0 100 200 300 400 500 600 RelativeGpsTimes(s) -3 0 100 200 300 400 500 600 700 RelativeGpsTimes(s)

Figure 5. Real-time results of open-loop (OL)/closed-loop signal components of In-Phase (I, in blue line) andFigure Quadra-Phase 5. Real-time (Q, results in red of line). open The-loop abscissa (OL)/closed is relative-loop time signal in second, components and the of ordinateIn-Phase represents (I, in blue theline) components’ and Quadra value.-Phase The (Q, top in redplane line). shows The the abscissa characteristics is relative of time OL tracking in second, mode andthat the extreme ordinate valuesrepresents alternately the components appear in’ Ivalue. and Q The components; top plane shows the bottom the characteristicsplane shows of the OL characteristics tracking mode of thethat closed-loopextreme values tracking alternately mode thatappear extreme in I and values Q components; appeared in the the bottom I component. plane shows the characteristics of the closed-loop tracking mode that extreme values appeared in the I component.

This paper analyzes the mountain-based occultation observations from full OL tracking mode in the following ways. First, using the excess phase obtained from the observation data in the closed- loop tracking mode as the reference, the continuity and duration of the excess phases obtained in the OL tracking verifies that the full OL tracking mode of GPS and BD are more robust than the closed- loop tracking mode. Second, the refractivity profiles retrieved from observations in the OL and closed-loop tracking modes are compared to verify their consistency. We selected (part of) the data on September 7 for analysis. The data include rising and falling occultations. As shown in Figures 6 and 7, excess phases retrieved from observations of L1C/GPS in OL/closed-loop tracking mode are compared, as well as that of B1/BD. Figure 8 shows the difference of the excess phase retrieved from observations of L1C/GPS and B1/BD in OL/closed-loop tracking mode, which are within 0.2 m. From Figures 6–8, the following can be concluded: (1) OL tracking time is longer than closed-loop, that is, for low-angle occultation events, OL has a better tracking effect. (2) The mountain-based occultation data can only detect the peak height and below. It can be seen from Figures 6 and 7 that compared to closed-loop tracking, the OL tracking can capture a lower height, and has the same result as the closed-loop tracking. Hence, the continuity of the OL is relatively robust. From the curve, we can see that the excess phase changes obtained by GPS and BD are relatively robust, and there is no deterioration in signal capture quality due to drastic changes in the signal. (3) The OL tracking effect of GPS and BD are similar, and both have a greater improvement compared to closed-loop tracking.

Remote Sens. 2020, 12, 4078 8 of 16

(1) OL tracking time is longer than closed-loop, that is, for low-angle occultation events, OL has a better tracking eﬀect. (2) The mountain-based occultation data can only detect the peak height and below. It can be seen from Figures6 and7 that compared to closed-loop tracking, the OL tracking can capture a lower height, and has the same result as the closed-loop tracking. Hence, the continuity of the OL is relatively robust. From the curve, we can see that the excess phase changes obtained by GPS and BD are relatively robust, and there is no deterioration in signal capture quality due to drastic changes in the signal. (3) The OL tracking eﬀect of GPS and BD are similar, and both have a greater improvement compared Remoteto Sens. closed-loop 2020, 12, x tracking.FOR PEER REVIEW 9 of 17

Figure 6. Excess phases retrieved from observations of B1/BD in OL/closed-loop tracking mode. RedFigure/green 6. linesExcess represent phases retrievedthe phases from in closed-loop observations/OL of tracking B1/BD in mode, OL/closed respectively.-loop tracking (a) C24 mode./BD occultation;Red/green ( linesb) C28 represent/BD occultation; the phases and ( inc) C20 closed/BD-loop/ occultation.OL tracking mode, respectively. (a) C24/BD occultation; (b) C28/BD occultation; and (c) C20/BD occultation.

Figure 7. Excess phase retrieved from observations of L1C/GPS in OL/closed-loop tracking mode. Red/green lines represent the phases in closed-loop/OL tracking mode, respectively. (a) G19/GPS occultation; (b) G24/GPS occultation; and (c) G12/GPS occultation.

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Figure 6. Excess phases retrieved from observations of B1/BD in OL/closed-loop tracking mode. Red/green lines represent the phases in closed-loop/OL tracking mode, respectively. (a) C24/BD occultation; (b) C28/BD occultation; and (c) C20/BD occultation. Remote Sens. 2020, 12, 4078 9 of 16

Figure 7. Excess phase retrieved from observations of L1C/GPS in OL/closed-loop tracking mode. RemoteFigureRed Sens./green 20207. Excess, lines 12, x FOR representphase PEER retrieved REVIEW the phases from inobservations closed-loop of/OL L1C/GPS tracking in mode, OL/closed respectively.-loop tracking (a) G19 mode./GPS10 of 17 Red/greenoccultation; lines (b) G24 represent/GPS occultation; the phases and in closed(c) G12-loop//GPSOL occultation. tracking mode, respectively. (a) G19/GPS occultation; (b) G24/GPS occultation; and (c) G12/GPS occultation.

FigureFigure 8.8. DifferenceDiﬀerence of excess of excess phase phase retrieved retrieved from observations from observations of B1/BD of and B1 /L1C/GPSBD and in L1C OL/GPS/closed in- OLloop/closed-loop tracking mode. tracking Left mode. panel, Left B1/BD; panel, Right B1/ BD;panel, Right L1C/GPS. panel, L1C/GPS.

FiguresFigures9 9and and 10 1 0show show the the refractivity refractivity profiles profiles obtained obtained from from the the observations observations of of L1C L1C/GPS/GPS and and B1B1/BD/BD inin thethe OL OL/closed-loop/closed-loop tracking trackingmode, mode,respectively. respectively. InIn thesethese figures,figures, thetherefractivity refractivity profilesprofiles obtainedobtained fromfrom the observations observations in in the the OL OL/closed/closed-loop-loop mode mode in the in the overlap overlap heigh heightt have have the same the same trend trendalong along altitude altitude.. The minimum The minimum height height of refractiv of refractivityity profile profiless obtained obtained from L1C/GPS from L1C signal/GPS signalin OL inmode OL modeare about are about0.4 km, 0.4 and km, that and of thatthe closed of the- closed-looploop mode are mode about are 1. about6 km. 1.6The km. minimum The minimum height of heightrefractivity of refractivity profiles profilesfrom B1/BD from signal B1/BD in signal OL mode in OL are mode about are 1. about2 km, 1.2 and km, that and of that closed of closed-loop-loop mode modeare between are between 1.3–1.5 1.3–1.5 km. Figure km. Figure 11 visualizes 11 visualizes the difference the difference of refractivity of refractivity profiles profiles retrieved retrieved from fromobservations observations of B1/BD of B1 and/BD L and1C/GPS L1C/ GPSin OL in/closed OL/closed-loop-loop mode mode,, from fromwhich which it is concluded it is concluded that: 1. that: the 1.bias the of bias the of refractiv the refractivityity retrieved retrieved from fromobservations observations of L1C/GPS of L1C /andGPS B1/BD and B1 in/BD OL in/closed OL/closed-loop-loop mode modeis within is within 1N; and 1N; 2. and The 2. trend The trend of the of refractivity the refractivity profiles profiles retrieved retrieved from from observations observations of ofL1C/GPS L1C/GPS in inOL OL/closed/closed-loop-loop mode mode is isslightly slightly better better than than the the result result of of B1/BD B1/BD..

Figure 9. Refractivity profiles retrieved from observations of B1/BD in OL/closed-loop tracking mode, respectively. Red/green lines represent results in closed-/OL mode tracking, respectively. (a) C24/BD Occultation; (b) G28/BD Occultation; and (c) C12/BD Occultation.

Remote Sens. 2020, 12, x FOR PEER REVIEW 10 of 17

Figure 8. Difference of excess phase retrieved from observations of B1/BD and L1C/GPS in OL/closed- loop tracking mode. Left panel, B1/BD; Right panel, L1C/GPS.

Figures 9 and 10 show the refractivity profiles obtained from the observations of L1C/GPS and B1/BD in the OL/closed-loop tracking mode, respectively. In these figures, the refractivity profiles obtained from the observations in the OL/closed-loop mode in the overlap height have the same trend along altitude. The minimum height of refractivity profiles obtained from L1C/GPS signal in OL mode are about 0.4 km, and that of the closed-loop mode are about 1.6 km. The minimum height of refractivity profiles from B1/BD signal in OL mode are about 1.2 km, and that of closed-loop mode are between 1.3–1.5 km. Figure 11 visualizes the difference of refractivity profiles retrieved from observations of B1/BD and L1C/GPS in OL/closed-loop mode, from which it is concluded that: 1. the bias of the refractivity retrieved from observations of L1C/GPS and B1/BD in OL/closed-loop mode is within 1N; and 2. The trend of the refractivity profiles retrieved from observations of L1C/GPS in Remote Sens. 2020, 12, 4078 10 of 16 OL/closed-loop mode is slightly better than the result of B1/BD.

Figure 9. Refractivity proﬁles retrieved from observations of B1/BD in OL/closed-loop tracking mode, Figure 9. Refractivity profiles retrieved from observations of B1/BD in OL/closed-loop tracking mode, respectively. Red/green lines represent results in closed-/OL mode tracking, respectively. (a) C24/BD Remoterespectively. Sens. 2020, 12 ,R xed/green FOR PEER lines REVIEW represent results in closed-/OL mode tracking, respectively. (a) C24/BD11 of 17 Occultation; (b) G28/BD Occultation; and (c) C12/BD Occultation. Occultation; (b) G28/BD Occultation; and (c) C12/BD Occultation.

Figure 10. Refractivity proﬁles retrieved from observations of L1C/GPS in OL/closed-loop tracking Figure 10. Refractivity profiles retrieved from observations of L1C/GPS in OL/closed-loop tracking mode. Red/green lines represent results in closed-/OL mode tracking, respectively. (a) G19/GPS mode. Red/green lines represent results in closed-/OL mode tracking, respectively. (a) G19/GPS Occultation; (b) G24/GPS Occultation; and (c) G12/GPS Occultation. Occultation; (b) G24/GPS Occultation; and (c) G12/GPS Occultation.

Figure 11. Difference of refractivity profiles retrieved from observations of B1/BD and L1C/GPS in OL/closed-loop tracking mode. Left panel, B1/BD; Right panel, L1C/GPS.

3.2. Comparison of Closed-Loop Tracking and Open-Loop Tracking In order to verify the effectiveness of the OL tracking algorithm, the comparison of the OL and closed-loop methods is used for verification, and the OL and closed-loop channels are used to capture and track the same satellite. Compare the start capture angle and end capture angle of the two to verify the capture effect. We selected 7 days of observation data for statistics, and the selected data are shown in Table 1:

Remote Sens. 2020, 12, x FOR PEER REVIEW 11 of 17

Figure 10. Refractivity profiles retrieved from observations of L1C/GPS in OL/closed-loop tracking mode. Red/green lines represent results in closed-/OL mode tracking, respectively. (a) G19/GPS Remote Sens. 2020 12 Occultation, ;, ( 4078b) G24/GPS Occultation; and (c) G12/GPS Occultation. 11 of 16

FigureFigure 11. 11. DiDifferenceﬀerence ofof refractivityrefractivity proﬁlesprofiles retrievedretrieved fromfrom observationsobservations ofof B1B1/BD/BD andand L1CL1C/GPS/GPS inin OLOL/closed-loop/closed-loop tracking tracking mode. mode. Left Left panel, panel, B1 B1/BD;/BD; Right Right panel, panel, L1C L1C/GPS./GPS.

3.2. Comparison of Closed-Loop Tracking and Open-Loop Tracking 3.2. Comparison of Closed-Loop Tracking and Open-Loop Tracking In order to verify the e ectiveness of the OL tracking algorithm, the comparison of the OL and In order to verify the effectivenessff of the OL tracking algorithm, the comparison of the OL and closed-loopclosed-loop methods methods is is used used for for verification, verification, and and the the OL OL and and closed-loop closed-loop channels channels are are used used to to capture capture andand track track the the same same satellite. satellite Compare. Compare the the start start capture capture angle angle and endand captureend capture angle angle of the of two the to two verify to theverify capture the capture effect. We effect. selected We 7selected days of 7 observation days of observation data for statistics, data for andstatistics, the selected and the data selected are shown data inare Table shown1: in Table 1: Table 1. List of the closed-loop initial pitch angle (CLIPA), closed-loop end pitch angle (CLEPA), open-loop initial pitch angle (OLIPA), open-loop end pitch angle (OLEPA) and start/end azimuth (SA, EA) from selected occultation events.

GPS NO Data/UTC CLIPA/ CLEPA/ OLIPA/ OLEPA/ SA/ EA/ PRN ◦ ◦ ◦ ◦ ◦ ◦ 1. 30 2020-9-1 0:10:43.20 4.98 0.99 4.98 1.87 201.34 195.87 − − 2. 5 2020-9-1 1:46:43.5 0.91 4.99 2.54 5.02 212.47 175.49 − − 3. 28 2020-9-1 2:37:45.60 4.97 1.23 4.98 2.13 175.49 173.51 − − 4. 13 2020-9-1 3:46:13.2 1.11 4.98 2.87 5.02 184.44 151.35 − − 5. 17 2020-9-1 4:27:38.30 4.97 0.97 4.98 1.96 151.35 152.57 − − 6. 19 2020-9-1 5:7:12.70 4.97 2.18 4.98 3.08 156.96 157.57 − − 7. 24 2020-9-1 6:43:14.70 1.93 4.99 2.63 5.02 183.66 149.86 − − 8. 2 2020-9-1 7:53:44.20 4.98 1.35 4.98 2.34 149.86 151.07 − − 9. 17 2020-9-2 4:23:38.40 4.97 1.51 4.98 2.45 151.37 152.65 − − 10. 19 2020-9-2 5:3:9.70 4.97 1.91 4.98 3.07 159.96 157.57 − − ...... 57. 1 2020-9-7 18:39:1.50 1.53 4.99 2.6 5.03 181.63 177.46 − − 58. 4 2020-9-7 19:36:49.00 4.96 1.37 4.96 2.52 200.61 195.33 − − 59. 22 2020-9-7 20:12:19.00 1.67 4.99 2.84 4.99 151.94 144.3 − − 60. 3 2020-9-7 20:54:48.60 1.51 4.99 2.68 5.03 156.9 146.99 − −

From Table1, it can be seen that the full OL tracking method can e ffectively capture occultation events at lower angles. As shown in Table1, observations from an occultation of GPS (PRN 30) at 1 September 2020 0:10:43 UT showed that its OL end pitch angle reached 1.87 deg, which is 0.88 deg − smaller than its closed-loop end pitch angle. At low elevation angles, it is difficult to track in the closed-loop strategy stably, and problems such as drastic changes in the signal-to-noise ratio and loss of signal lock will occur. The fully OL tracking method effectively solves the above problems. We have made statistics on all the data to evaluate the effect of OL tracking. One calculation method is to calculate the angles of the whole occultation tracking, and mark it as strategy A; the other is to calculate the negative angles of the occultation tracking, and mark it as strategy B. For strategy A Remote Sens. 2020, 12, 4078 12 of 16

or B, the way to evaluate the capture capability of the OL/closed loop tracking, and the effect of OL tracking are: X X A E = (αe α ) + (α αe) (10) o,c − i i − j occ. rising events j occ. setting events ∈ ∈ X X Remote Sens. 2020, 12, x FOR PEERB REVIEW 13 of 17 E = (0 α ) + (0 αe) (11) o,c − i − j occ. rising events j occ. setting events ∈ ∈ 퐴 퐴 퐵 퐵 퐸표 E−A 퐸푐EA 퐸E표B −E퐸B푐 퐴 =A = o − c, 퐵, B== o − c (12(12)) 퐴 A B퐵 퐸푐Ec E퐸c푐 훼 훼 E퐴 A E퐵 B inin which which 푖α,i, 푒α eareare the the initial initial pitch pitch angl anglee and and end end pitch pitch angle, angle, respectively; respectively; 표E,푐o,,c,표E,푐o ,careare values values to to evaluevaluateate the the capture capture capability capability of ofthe the OL OL/closed/closed-loop-loop tracking tracking with with strategy strategy A orA Bor; andB; and 퐴, A퐵, Bareare the the effectseffects of of OL OL tracking tracking evalu evaluatedated withwith strategystrategyA Aor orB .B According. According to observationsto observations from from Table Table1 , the 1, resultthe resultof accumulating of accumulating the seven-day the seven- dataday dat are:a are: (13) AA == 1919.35%,.35%, BB= =88.54%.88.54%. (13) The results show that in the case of counting all angles, the OL improves the capture angle range of dataThe volume results by show nearly that 20%, in theand case when of countingonly the negative all angles, angle the OL is calculated, improves the the capture OL improves angle range the captureof data angle volume value by nearlyby nearly 20%, 89%. and The when mountain only the-based negative situation angle is is different calculated, from the the OL onboard improves situation.the capture We anglewill continue value by to nearlyverify 89%.the actual The mountain-basedcapture effect in the situation future. isHowever, different there from is the no onboard doubt thatsituation. the fully We OL will capture continue method to verify greatly the actual improves capture the effect capture in the future. effect. However,We make there the difference is no doubt betweenthat the the fully OL OL angle capture and methodthe closed greatly-loop improves angle (only the the capture negative effect. angle We makeis counted), the diff anderence the between result isthe shown OL angle in Figure and the12. closed-loopThere is no angle specific (only coupling the negative relationship angle is between counted), OL and tracking the result and is shownclosed- in loopFigure tracking, 12. There but is the no overall specific effect coupling is better relationship than closed between-loop. OL The tracking reason and why closed-loop there is tracking,no specific but couplingthe overall relationship effect is better is due than to the closed-loop. difference The between reason the why two there capture is no methods. specific coupling The angle relationship difference is isdue mainly to the concentrated difference betweenbetween the1° and two 1.2 capture°. methods. The angle difference is mainly concentrated between 1◦ and 1.2◦.

FigureFigure 12 12.. HistogramHistogram of ofthe the difference diﬀerence of ofthe the start/end start/end elevation elevation angle angle from from a rising/setting a rising/setting occultation occultation eventevent between between close closed-loopd-loop and and OL.OL Because. Because the the top top height height of the of mountain the mountain is about is 2 about km, the 2 minimumkm, the melevationinimum elevation angle value angle is generally value is generallyabout 3 aboutin OL − mode,3° in OL and mode the di, ﬀanderence the is difference mainly concentrated is mainly − ◦ concentratedbetween 0.8 between◦ and 1.2 ◦0.8. ° and 1.2°.

3.3.3.3. Comparison Comparison of ofOpen Open-Loop-Loop Tracking Tracking Inversion Inversion Results Results and and Meteorological Meteorological Observations Observations TheThe atmosphere atmosphere profiles proﬁles retrieved retrieved from from observations observations in OL in tracking OL tracking mode modeare evaluated are evaluated with thewith local the observations local observations of temperature, of temperature, humidity and humidity pressure andprovided pressure by the provided Beijing Meteorological by the Beijing Bureau.Meteorological Bureau. The atmospheric refractive index of the observation point can be calculated by temperature, relative humidity and pressure data, which is used to verify the accuracy of the inversion of the mountain-based experimental data. The calculation method is as follows [45–48]: Using the temperature data of the analysis field to calculate the corresponding saturated vapor pressure: 7.5t 237.3t (14) E( t ) E0 10

Remote Sens. 2020, 12, 4078 13 of 16

The atmospheric refractive index of the observation point can be calculated by temperature, relative humidity and pressure data, which is used to verify the accuracy of the inversion of the mountain-based experimental data. The calculation method is as follows [45–48]: Using the temperature data of the analysis ﬁeld to calculate the corresponding saturated vapor pressure: 7.5t E(t) = E 10 237.3+t (14) 0 × In the above formula, E(t) is the saturated vapor pressure at the corresponding temperature, and t is the temperature in Celsius. The constant E0 = 6.1078hpa. There is the following relationship between actual vapor pressure Pw, saturated vapor pressure and relative humidity:

Pw(t) = E(t) j (15) × Finally, the approximate relationship between refractive index and atmospheric parameters can be used to obtain the atmospheric refractive index:

p P N = 77.6 + 3.73256 105 W (16) T × T2 In the above formula, N is the refractive index of the atmosphere, p is the total atmospheric pressure (hpa), Pw is the water vapor pressure (hpa) and T is the atmospheric temperature (K). For each sounding profile data, find the matching occultation profile (one or more), and interpolate them to the altitude points with a distance of 0.05 km. Calculate the standard deviation of the average refractive index deviation and the absolute refractive index deviation within the height range covered by both the occultation and the sounding profile as the evaluation standard. The results are shown in the following Table2 (partially):

Table 2. The relative refractive index deviation standard deviation statics of each atmosphere proﬁle.

No GPS PRN Time Ascending/Descending Occultation BIAS (%) MSER (%) 1. 30 2020/9/01 Down 0.10 0.19 2. 5 2020/9/01 Up 0.29 2.36 3. 17 2020/9/02 Down 0.24 1.92 4. 5 2020/9/02 Up 0.22 1.32 5. 28 2020/9/03 Down 0.23 2.14 6. 13 2020/9/03 Up 0.30 4.01 7. 13 2020/9/04 Up 0.23 3.06 8. 17 2020/9/04 Down 0.21 1.22 9. 24 2020/9/06 Up 0.25 2.35 10. 29 2020/9/06 Down 0.10 0.10 11. 18 2020/9/06 Down 0.20 1.37 12. 17 2020/9/07 Down 0.11 1.02 13. 19 2020/9/07 Down 0.27 2.94 14. 24 2020/9/07 Up 0.21 1.82

It can be seen from the results that the BIAS/MSER of the OL tracking method is within 0.5% and 4%, respectively, which meet the accuracy of its applications (<0.5%, in BIAS; <5%, in MSER).

4. Conclusions 1. We designed and developed the occultation equipment that supports the GPS/BD systems, and tested its performance based on mountain-based experiments. It is concluded that B1/BD observation data can obtain atmospheric retrieval accuracy similar to L1C/GPS observation. Since the 2nd and 3rd generations of the BD constellations have more than 50 satellites in orbit, the equipment will be deployed on low-orbit satellites in the future to obtain more occultation observations. Remote Sens. 2020, 12, 4078 14 of 16

2. Traditional OL processing relies on external data (GPS bit) to determine the initial sign of the RP. We use internal processing to recover the phase of the full OL tracking observation data for mountain-based occultation inversion. Due to the lack of external data, it is difficult to determine the initial RP sign. We use the correlation between the mountain-based closed-loop observation data of elevation angle above 3 degrees and the RP data to determine the initial sign of RP, and accomplish the full OL data recovery process based on closed-loop observations automatically. 3. To determine the full OL tracking and capturing effect, we have performed statistics on the data for 7 consecutive days. The statistical results showed that in the case of counting all angles, the OL improves the capture angle value by nearly 20%, and when only the negative angle is calculated, the OL improves the capture angle value by nearly 89%. The full-open-loop capture mode greatly improves the capture effect, and there is no specific coupling relationship between OL tracking and closed-loop tracking, but the overall effect is better than closed-loop. The reason why there is no specific coupling relationship is due to the difference between the two capture methods. 4. The atmosphere profiles retrieved from observations in OL tracking mode are evaluated with the local observations of temperature, humidity and pressure provided by the Beijing Meteorological Bureau. It can be concluded that the error of the OL tracking method is within ~4% in the mean square error of relative error (MSER), which meets the accuracy of its applications (<5%, in MSER).

Author Contributions: Conceptualization, F.L., L.K., N.F., M.W., C.H. and Z.W.; methodology, F.L., L.K. and N.F.; formal analysis, L.K.; investigation, L.K.; data curation, F.L.; writing—original draft preparation, F.L.; writing—review and editing, F.L. and L.K.; data analysis and discrimination, F.L., N.F. and L.K.; supervision, F.L.; project administration, L.K.; and funding acquisition, F.L. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61520106002 and 61731003. Acknowledgments: The validation data was provided by Beijing Meteorological Administration, and the experiments team of Tianjin Yunyao Aerospace Technology Co., Ltd. We also thank reviewers for their suggestions on improvement in the article. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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