Multi-Constellation Software-Defined Receiver for Doppler Positioning

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Article Multi-Constellation Software-Deﬁned Receiver for Doppler Positioning with LEO Satellites

Farzan Farhangian * and René Landry, Jr. LASSENA Laboratory, Department of Electrical Engineering, Ecole de Technologie Superieure, Montreal, QC H3C-1K3, Canada; [email protected] * Correspondence: [email protected]

Received: 13 September 2020; Accepted: 15 October 2020; Published: 16 October 2020

Abstract: A Multi-Constellation Software-Deﬁned Receiver (MC-SDR) is designed and implemented to extract the Doppler measurements of Low Earth Orbit (LEO) satellite’s downlink signals, such as Orbcomm, Iridium-Next, Globalstar, Starlink, OneWeb, SpaceX, etc. The Doppler positioning methods, as one of the main localization algorithms, need a highly accurate receiver design to track the Doppler as a measurement for Extended Kalman Filter (EKF)-based positioning. In this paper, the designed receiver has been used to acquire and track the Doppler shifts of two diﬀerent kinds of LEO constellations. The extracted Doppler shifts of one Iridium-Next satellite as a burst-based simplex downlink signal and two Orbcomm satellites as continuous signals are considered. Also, with having the Two-Line Element (TLE) for each satellite, the position, and orbital elements of each satellite are known. Finally, the accuracy of the designed receiver is validated using an EKF-based stationary positioning algorithm with an adaptive measurement matrix. Satellite detection and Doppler tracking results are analyzed for each satellite. The positioning results for a stationary receiver showed an accuracy of about 132 m, which means 72% accuracy advancements compared to single constellation positioning.

Keywords: software-deﬁned radio; LEO satellite; Doppler positioning; navigation; Orbcomm; Iridium; Globalstar; signals of opportunity

1. Introduction Navigation using Signals of Opportunity (Nav-SOP) has shown enormous potential as an alternative positioning method in Global Navigation Satellite System (GNSS)-challengeable situations. Integration of Inertial Navigation System (INS) and Global Positioning System (GPS) has been one of the most reliable navigation methods in recent decades. This method utilizes the short-term accuracy of INS and long-term robustness of GPS at the same time. However, some substantial drawbacks of GPS/INS integration methods lead the researchers to focus on the Nav-SOP method, alternatively. Some of the main problems of GPS/INS integration are the possibility of signal interferences, being sensitive to jamming, and inaccessibility in some dense urban and indoor environments. Also, GPS can be blocked or banned in military situations. There are several kinds of SOPs in diﬀerent frequency ranges between 3 kHz and 300 GHz in categories of Very High Frequency (VHF), L-band, S-band, Ka-band, etc. These signals freely exist in the environment, also, their accessibility and wide-band frequency range make them the best choices for non-GPS navigation methods. FM, TV, Wi-Fi, DAB-radio, Long-term Evolution (LTE) signals, cellular, and LEO satellite signals are considered as SOPs. Compared to Geosynchronous Equatorial Orbit (GEO) and Medium Earth Orbit (MEO) satellites, LEO satellites are closer to the earth with a more powerful signal and diﬀerent constellations. Positioning using LEO satellite signals depends on the signal coverage and duration of visibility. Each LEO satellite can be visible to a receiver for a

Sensors 2020, 20, 5866; doi:10.3390/s20205866 www.mdpi.com/journal/sensors Sensors 2020, 20, 5866 2 of 17 Sensors 2020, 20, 5866 2 of 17 special duration, therefore, afterafter thisthis visiblevisible time, the receiver needsneeds toto waitwait untiluntil the next satellites is observable. Accordingly, for some constellations,constellations, there are times when no satellites are visible to the receiver. Designing a multi-constellation LEO satellitesatellite receiver can solve the satellite’ssatellite’s observability problem. Also,Also, it it can can detect detect the the best best Doppler Doppler measurement measurement for EKF-based for EKF-based Doppler Doppler positioning positioning methods bymethods selecting by the selecting suitable the measurement suitable measurement model. Figure mo1 demonstratesdel. Figure the1 demonstrates di ﬀerence of coveragethe difference between of acoverage single constellation between a single (Orbcomm) constellation and multi-constellation (Orbcomm) and multi-constellation (Orbcomm/Iridium-Next). (Orbcomm/Iridium-Next). It can be seen that It bycan increasing be seen that the numberby increasing of constellations the number and of theconstellations observability and time, the providingobservability continuous time, providing Doppler measurementscontinuous Doppler for EKF-based measurements positioning for EKF-ba systemssed canpositioning be guaranteed. systems can be guaranteed.

(a) (b)

Figure 1.1.( a(a)) Coverage Coverage of theof the Orbcomm Orbcomm constellation constellation in global in global world map;world (b )map; coverage (b) coverage of the Orbcomm of the andOrbcomm Iridium-Next and Iridium-Next constellations constellations on a global on world a global map. world map.

This paper presents an adaptive design for a software-definedsoftware-defined multi-constellation receiver with the ability to detect the visible satellites and inje injectingcting the suitable Doppler measurement to EKF-based positioning systems. Firstly, Firstly, the the method will dete detectct the overhead satellites by performing Welch Power Spectral Density (PSD) analysis, which is calledcalled thethe acquisitionacquisition part.part. In the second part, thethe Doppler frequencyfrequency of of each each detected detected satellite satellite will bewi trackedll be tracked with a Phasewith a Locked Phase LoopLocked (PLL) Loop algorithm. (PLL) Finally,algorithm. a measurement Finally, a measurement switching filter switching is designed filter foris designed selecting for the selecting right measurement the right measurement for Doppler positioningfor Doppler architecture.positioning architecture. The results showed The results that sh theowed receiver that couldthe receiver track the could Doppler track andthe Doppler rateand ofDoppler 2 satellites rate atof the2 satellites same time, at the also, same the time, results also for, the positioning results for of positioning stationary receiver of stationary demonstrated receiver thedemonstrated accuracy improvement the accuracy comparedimprovement to the co singlempared receiver to the single design. receiver design. In Section 22 wewe present a literature literature review review of of prev previousious methods methods and and studies studies in indetail. detail. In Section In Section 3 we3 wedescribe describe the the EKF-based EKF-based multi-constellation multi-constellation Doppler Doppler positioning positioning method. method. In In Section Section 4 we definedefine thethe LEO signal model and receiver design. Experimental Experimental results are presented in the the Section Section 55 and finally,finally, the conclusionconclusion andand potentialpotential ofof futurefuture studiesstudies areare discusseddiscussed inin SectionSection6 6..

2. Related Works There areare several several eff ortsefforts on addressingon addressing the Nav-SOP the Nav-SOP problems problems for receiver for designreceiver and design positioning and algorithms.positioning algorithms. In [1,2], theIn [1,2], Doppler the Doppler measurements measurements were were obtained obtained from from Quadrature Quadrature Phase-ShiftPhase-Shift Keying (QPSK) signals of LEO satellitessatellites byby usingusing carriercarrier synchronizationsynchronization and signalsignal processingprocessing design. An An opportunistic opportunistic positioning positioning method method us usinging LTE LTE downlink downlink signals signals was was designed, designed, also, also, a aSoftware-Defined Software-Defined Receiver Receiver (SDR) (SDR) was was implemented implemented for for extracting extracting and and tracking tracking the pseudorange rate measurement fromfrom LTE LTE signals signals in [3 ].in Likewise, [3]. Likewise the integration, the integration of LTE signals of LTE and Inertialsignals Measurementand Inertial UnitMeasurement (IMU) was Unit considered (IMU) inwas a navigation considered framework in a navigation for ground framework autonomous for vehicles ground [4 ].autonomous SOP-aided Inertialvehicles Navigation[4]. SOP-aided Systems Inertial (INS) Navigation have experimented Systems (INS) in various have GNSS-challengeableexperimented in various positioning GNSS- applications.challengeable positioning Estimating theapplications. location ofEstimating unknown the terrestrial locationSOPs of unknown was performed terrestrial by SOPs adaptive was maximumperformed likelihoodby adaptive filter maximum [5], and likelihood extended Kalmanfilter [5], filterand extended [6]. Observation Kalman of filter SOP’s [6]. pseudorange Observation measurementsof SOP’s pseudorange with Time-of-Arrival measurements (TOA) with and Time-of-Arrival Time-Difference-of-Arrival (TOA) and Time-Difference-of-Arrival (TDOA) was presented for navigation(TDOA) was of presented collaborative for flightnavigation vehicles of collaborative [7–9]. flight vehicles [7–9]. The SDR designs were studiedstudied deeply in [[10],10], however;however; it completelycompletely depended on the GNSSGNSS signal observations.observations. In In [11], [11], the LEO movement imaging was described by designingdesigning aa low-earthlow-earth orbiting radar, which could improve the investigating potential of scientists for studying LEO satellites. Furthermore, the augmentation of GNSS and LEO satellites was analyzed in [12], as a source

Sensors 2020, 20, 5866 3 of 17 orbiting radar, which could improve the investigating potential of scientists for studying LEO satellites. Furthermore, the augmentation of GNSS and LEO satellites was analyzed in [12], as a source of space-based monitoring and useful information for Nav-SOP applications. Many positioning methods were studied with some kind of LEO satellite, namely, Doppler positioning with Orbcomm satellites [13], Iridium satellites [14], and Iridium positioning in weak signal environments [15]. These methods could improve the positioning precision in the short-term, however; due to the short visibility time duration of each satellite, the long-term robustness is still under serious investigation. The instant positioning using the single Globalstar LEO satellite presents the importance of communication between a user terminal and an LEO satellite [16]. Positioning methods based on Doppler measurements are studied with two different estimation algorithms. First, using a nonlinear least-square filter, and second, EKF estimation systems, which are studied in [17,18], respectively. A novel K-band receiver front-end is designed and investigated in [19]. The receiver was presented for inter-satellite communication between LEO and GEO. Their design has had a significant impact on reducing power leakage, hardware cost, and automatic gain calibration. In [20], a method is studied for navigation using carrier phase measurements of LEO satellite constellations. In this paper, the Integer Least-Squared (ILS) problem is defined as a major challenge to be reduced in size and finally, the authors succeeded to decrease it, outstandingly. The fast convergence of an LEO satellite clock was studied in [21], which showed the method for the estimation of the satellite clock in real-time mode. There were also some efforts to design a Software-Defined Receiver (SDR) for obtaining the Doppler shift measurements of LEO satellites. In [22], an SDR receiver is presented for satellite communication, also, the Satellite’s Doppler, code rate, and code phase search were studied. The authors in [23] have shown a new algorithm for estimating the downlink Doppler frequency of LEO satellites as the main measurements of Doppler positioning systems in Nav-SOP applications. Moreover, the analysis of using Doppler and Doppler rate of LEO satellites for Radio Frequency (RF) geolocation and enhancement of Doppler positioning algorithms for stand-off trajectories are studied in [24,25], respectively. A Precise Point Positioning (PPP) system was also designed and validated in [26,27]. Finally, in [28], a receiver was designed for Orbcomm LEO satellites, which can track the Doppler shift and perform the positioning using a single LEO satellite. Although these designs could improve the accuracy for state estimation of the receiver and LEO satellite, all their experiments are extremely dependent on the time in which the receiver can extract the Doppler measurement from acquired signals. Consequently, designing the multi-constellation receiver will not only expand the measurement’s tracking time but can also enhance the accuracy of Doppler positioning in more functional time.

3. Doppler Positioning EKF Model and Parameters The pseudorange rate measurements were obtained from the LEO receiver in each time-step k for ˆ each n visible satellites. This measurement is related to the Doppler frequency with Equation (1). fdn (k) is the Doppler frequency of the n th LEO satellite in time-step k. fc is the downlink center frequency − n of n th satellite, and c is the speed of light. Subsequently, the pseudorange rate measurement of each − satellite is deﬁned as in Equation (2), ˆ fdn (k) zn(k) = c , (1) fcn . T pt,n (k)[pr pt,n(k)] . . zn(k) = − + c δtr δtt,n + εt,n(k), (2) pr pt,n(k) − k − k where pr is the 3D position vector of the receiver, and pt,n(k) is the position vector of the n th satellite. . . − Also, δtr and δtt,n are the clock drifts of the receiver and satellite, respectively. It should be mentioned that the ionospheric and tropospheric delays were omitted because of their negligible amounts in each measurement step [29]. As the receiver is assumed stationary, we can suppose that the clock drifts of Sensors 2020, 20, 5866 4 of 17 the LEO satellites and the receiver do not change with time. Therefore, the state and measurement vectors are deﬁned in Equations (3) and (4).

. . . T h T i x(k) = pr δtr δtt,1 ... δtt,n , (3)

h iT z(k) = z1(k) ... zn(k) , (4) As the transition matrix is obtained as an (n + 4) dimension identity matrix, the time-update equations of EKF for states vector and error covariance matrix follow xk(k + 1) = xk(k) and Pk(K + 1) = Pk(k) + Q, respectively. The EKF equations are presented in Equations (5) and (7) where Q is the process noise covariance, R is the observation noise covariance, and K is the standard Kalman gain.

h i 1 T T − K(k + 1) = Pk(k + 1)H (k + 1) H(k + 1)Pk(k + 1)H (k + 1) + R(k + 1) , (5)

x + (k + 1) = x (k + 1) + K(k + 1)[z(k + 1) H(k + 1)x (k + 1)], (6) k 1 k − k h i H(k + 1) = h(k + 1) c.In 1 c.In n , (7) × − × Herein, H is the measurement matrix and I is the identity matrices, defined by its indices. For a better understanding of the measurement Jacobian matrix, its expanded form is defined in Equations (8) and (9). h iT ( + ) = T( + ) T( + ) h k 1 h1 k 1 ... hn k 1 , (8)  h (k + 1) c c 0 0   1   − ···   h2(k + 1) c 0 c 0  H(k + ) =  − ···  1  . . .  , (9)  . . 0 0 .. 0     h (k + ) c c  n 1 0 0 n (n+4) · · · − × Where hn(k + 1) vector is defined as Equations (10) and (11). It should be mentioned that the velocity of the stationary receiver was zero vector.

T T T T h (k + 1) = h (k + 1) + h (k + 1).hv (k + 1).h (k + 1), (10) n − vt,n pt,n t,n pt,n . p p (k + 1) p (k + 1) r t,n − t,n hpt,n (k + 1) = − , hvt,n (k + 1) = , (11) pr pt,n(k + 1) pr pt,n(k + 1) k − k k − k T Finally, after combining Equations (10) and (11), the complete form of hn (k + 1) is obtained as Equation (12).

. . T pt,n(k + 1) pt,n (k + 1)[pr pt,n(k + 1)] hT(k + 1) = (p p (k + 1)). − (12) n ( + ) r t,n 3 pr pt,n k 1 − − pr pt,n(k + 1) k − k k − k By considering the velocity of the receiver, the mentioned EKF equations can be expanded for a dynamic receiver in mobile ground or ﬂight vehicles. The measurement noise was modeled as zero-mean random white Gaussian with variance σ2. Also, the initial value of the covariance matrix P(0) was selected with the noise variance on its diagonals. A small positive value was selected for covariance of process and measurement noise matrix. Figure2 illustrates the switching mode for EKF-based Doppler positioning. In the proposed system, the type and dimension of the measurement matrix is determined by an EKF mode switching block. After obtaining all the Doppler frequencies from the receiver, the mentioned switching block selects the adapted EKF system by sending the 0 or 1 binary values to the determined EKF system. As each satellite is invisible after a while, the number of measurements may vary with time. As a result Sensors 2020, 20, 5866 5 of 17 of this, the system completely depends on the satellite visibility and the number of measurements. TheSensors EKF 2020 mode, 20, 5866 switching block tracks the measurements and modiﬁes the EKF system. 5 of 17

Figure 2. Architecture of proposed multi-constellation LEO satellite receiver.

4. Multi-Constellation Receiver Design 4.1. Characteristics of LEO Downlink Signals 4.1. Characteristics of LEO Downlink Signals The main concentration of this paper is on two constellations modulated by the QPSK method, The main concentration of this paper is on two constellations modulated by the QPSK method, namely, Iridium-Next and Orbcomm LEO satellites. These satellites are from different organizations namely, Iridium-Next and Orbcomm LEO satellites. These satellites are from different organizations and they were made for communication applications, like voice, fax, data, personal massaging, military, and they were made for communication applications, like voice, fax, data, personal massaging, etc. Table1 consists of several details about each satellite including the number of working satellites military, etc. Table 1 consists of several details about each satellite including the number of working in the constellation, number of orbital planes, inclination, height, orbital time period, and downlink satellites in the constellation, number of orbital planes, inclination, height, orbital time period, and frequency range. Also, the Globalstar satellite is added for more comparison. Orbital data of each downlink frequency range. Also, the Globalstar satellite is added for more comparison. Orbital data satellite in all three constellations is updated every day in a TLE file, and it is publicly downloadable of each satellite in all three constellations is updated every day in a TLE file, and it is publicly from the North American Aerospace Defense Command (NORAD) site, and data is represented with downloadable from the North American Aerospace Defense Command (NORAD) site, and data is simplified perturbations models (SGP, SGP4, and SGP8). represented with simplified perturbations models (SGP, SGP4, and SGP8). Table 1. Specifications of Orbcomm, Globalstar, and Iridium LEO satellites. Table 1. Specifications of Orbcomm, Globalstar, and Iridium LEO satellites. Working Orbital Orbital Working Orbital Inclination Height Orbital Frequency Range Satellites Planes Inclination Height Period Frequency Range Satellites Planes Period Globalstar 48 8 52◦ 1414 km ~113 min 2483.5~2500 MHz GlobalstarIridium 48 66 8 6 52° 86.4 ◦ 1414781 km ~ ~100113 min min 1616~1626.5 2483.5~2500 MHz MHz IridiumOrbcomm 66 30 6 6 86.4 45°◦ , 70◦ 781825 km km ~ ~99100 min min 1616 137~138~1626.5 MHz MHz Orbcomm 30 6 45°, 70° 825 km ~99 min 137~138 MHz The Orbcomm satellites transmit the continuous packed data at a VHF bandwidth frequency The Orbcomm satellites transmit the continuous packed data at a VHF bandwidth frequency between 137 and 138 MHz. The Orbcomm downlink data is transmitted with a Bit rate of 4800 bps. between 137 and 138 MHz. The Orbcomm downlink data is transmitted with a Bit rate of 4800 bps. The downlink signal consists of 600 words and each word is 8 bits of data. Each minor frame is The downlink signal consists of 600 words and each word is 8 bits of data. Each minor frame is 4800 4800 bits and is transmitted in 1 s, also 16 minor frames are defined as one major frame, as depicted bits and is transmitted in 1 s, also 16 minor frames are defined as one major frame, as depicted in in Figure3. Our last experiments in signal acquisition showed that not all the Orbcomm satellites Figure 3. Our last experiments in signal acquisition showed that not all the Orbcomm satellites were were functional. Eleven channels transmitted downlink signals and each satellite transmitted in two functional. Eleven channels transmitted downlink signals and each satellite transmitted in two downlink frequencies. The main difference between Orbcomm and Iridium is that, unlike the Orbcomm downlink frequencies. The main difference between Orbcomm and Iridium is that, unlike the which transmits the continuous downlink signals, the Iridium is based on the bursts. This signal’s Orbcomm which transmits the continuous downlink signals, the Iridium is based on the bursts. This variety can assess the adaptivity of the designed multi-constellation receiver [30,31]. signal’s variety can assess the adaptivity of the designed multi-constellation receiver [30,31].

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(a) (b)

FigureFigure 3. (3.a )( Structurea) Structure of Orbcommof Orbcomm downlink downlink signals signals and and (b) architecture (b) architecture of Iridium-Next of Iridium-Next downlink downlink signals. signals. The Iridium worked at an L-band downlink frequency of 1616 to 1626.5 MHz in both duplex and simplexThe Iridium channels. worked The at Iridium an L-band signals downlink were functionalfrequency of in 1616 30 duplex to 1626.5 sub-bands MHz in both between duplex 1616 andand 1626 simplex MHz, channels. and 12simplex The Iridium channels signals between were functional 1626 and in 1626.530 duplex MHz, sub-bands whichconsisted between 1616 of a and 90 ms time1626 division MHz, and multiples 12 simplex access channels (TDMA) between frame. 1626 Both and simplex 1626.5 MHz, and duplexwhich consisted signals wereof a 90 bursts. ms time It is division multiples access (TDMA) frame. Both simplex and duplex signals were bursts. It is more more common to use the simplex bursts for Nav-SOP applications due to the fact that they are always common to use the simplex bursts for Nav-SOP applications due to the fact that they are always transmitting from Iridium satellites. As it is demonstrated in Figure3, simplex bursts were transmitting transmitting from Iridium satellites. As it is demonstrated in Figure 3, simplex bursts were at diﬀerent frequencies, which were allocated for Ring alerts and messaging channels. In each simplex transmitting at different frequencies, which were allocated for Ring alerts and messaging channels. timeslot, there were four messaging channels (Primary, Secondary, Tertiary, and Quaternary), one Ring In each simplex timeslot, there were four messaging channels (Primary, Secondary, Tertiary, and alert,Quaternary), and seven one guard Ring channels. alert, and The seven center guard frequency channels. of The the center Iridium frequency and Iridium-Next of the Iridium Ring and alert wasIridium-Next 1626.27833 Ring MHz alert and was center 1626.27833 frequencies MHz of and messaging center frequencies channels were of me 1626.437500,ssaging channels 1626.395833, were 1626.145833,1626.437500, and 1626.395833, 1626.104167 1626.145833, MHz, respectively and 1626.104167 [30,31]. The MHz, receiver respectively sampled the[30,31]. obtained The discretizedreceiver f T = f 1 signalsampled with the a special obtained sampling discretized frequency signal cwith, and a specialc− samplingis the sampling frequency time. 𝑓 , Due and to 𝑇=𝑓 the fact is that the the LEOsampling satellite’s time. downlink Due to the signals fact that were the transmitted LEO satellit withe’s downlink a QPSK signals modulator, were thetransmitted receiver with signal a QPSK from all L channelsmodulator, of mthe receiverth constellation signal from can beall formulated𝐿 channels asof Equations 𝑚−𝑡ℎ constellation (13) and (14), can be formulated as − Equations (13) and (14), XL XL j(k π + π ) j(ω n+ϕ ) [ ] 2 4 m.l m.l [ ] Rm n = Am,l e ( e) = rm,l n , k 0, 1, 2, 3 , (13) 𝑅 [𝑛] = 𝐴 𝑒 𝑒(..) = 𝑟 [𝑛] , ∈𝑘{ ∈ 0,1,2,3}, (13) l=1 , l=1 , π π h i [ ] = 𝜋+ 𝜋 [ ] + + [ ] + [ ] rm,l n Am,l . exp j k . exp j2πnT fdm,l n fIFm,l jϕm.l n b n , (14) 𝑟,[𝑛] = 𝐴, . exp 𝑗 𝑘2 +4 . 𝑒𝑥𝑝 𝑗2𝜋𝑛𝑇𝑓 [𝑛] + 𝑓 +𝑗𝜑.[𝑛] + 𝑏[𝑛], (14) 2 4 , , where k is the transmitted QPSK signal’s samples, n is the number of samples and t = t(0) + nT is the where 𝑘 is the transmitted QPSK signal’s samples, 𝑛 is the number of samples and 𝑡=𝑡(0) +𝑛𝑇 is time of the received signal. fIFm,l and fdm,l are intermediate and Doppler frequencies for l th channel the time of the received signal. 𝑓, and 𝑓, are intermediate and Doppler frequencies− for 𝑙−𝑡ℎ of m th constellation, respectively. Am,l is the totall power magnitude of the received signal. Also, channel− of 𝑚−𝑡ℎ constellation, respectively. 𝐴, is the totall power magnitude of the received b[n] is a complex model of zero-mean white Gaussian noise. The ϕm.l and ωm.l are acquired phase and signal. Also, 𝑏[𝑛]is a complex model of zero-mean white Gaussian noise. The 𝜑. and 𝜔. are angularacquired frequency phase and of theangular transmitted frequency signal, of the respectively. transmitted signal, respectively. 4.2. Receiver’s Architecture 4.2. Receiver’s Architecture TheThe main main concentration concentration ofof thisthis paperpaper isis onon three constellations, which which are are modulated modulated by bythe the QPSKQPSK method, method, namely, namely, Globalstar, Globalstar, Iridium, Iridium, and and Orbcomm Orbcomm LEO LEO satellites. satellites. InIn thisthis part,part, thethe structurestructure of theof multi-constellation the multi-constellation receiver receiver is presented is presented in twoin two sections. sections. At At ﬁrst, first, the the LEO LEO signal signal is acquiredis acquired and detectedand detected and in and the in second the second part, part, the Dopplerthe Doppler measurement measurement is extractedis extracted and and tracked tracked to to be be injectedinjected in thein EKF-based the EKF-based Doppler Doppler positioning positioning system. system. Figure Figure4 demonstrates 4 demonstrates the proposedthe proposed architecture architecture for for both partsboth of parts the receiver. of the receiver.

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Figure 4. Architecture of proposed multi-constellation LEO satellite receiver. Figure 4. Architecture of proposed multi-constellation LEO satellite receiver. 4.2.1. Signal Acquisition 4.2.1. Signal Acquisition After receiving the signal from the antenna, it goes through the Low Noise Amplifier (LNA) After receiving the signal from the antenna, it goes through the Low Noise Amplifier (LNA) electronic device. This device magnifies the signal with the least change in the signal-to-noise ratio electronic device. This device magnifies the signal with the least change in the signal-to-noise ratio (SNR), also, in the situation that the signal has low-power, it has a significant impact on the accuracy (SNR), also, in the situation that the signal has low-power, it has a significant impact on the accuracy ofof signal signal acquisition. acquisition. The Welch Welch method method is isa kind a kind of periodogram of periodogram averaging averaging technique technique to analyze to analyze the the Power Spectral Density (PSD) of the received signal [29]. The signal, Rm[n], is divided into K Power Spectral Density (PSD) of the received signal [29]. The signal, 𝑅[𝑛], is divided into K batches batchesand each and batch each batchhas M hasnumber M number of points. of points. Also, the Also, S is the the S isnumber the number of points of pointsfor overlapping for overlapping the FR [v] thesegments. segments. In InEquation Equation (15), (15), a Discrete a Discrete Fourier Fourier Transform Transform (DFT) (DFT) window, window, 𝐹𝑅,[m𝑣,k], is, calculated is calculated in in eacheach segment segment at at the the determined determined frequencies,frequencies,

() M+(k 1)S 1 X− − 𝐹𝑅,[𝑣] = 𝑅[𝑛]𝑤[𝑛]𝑒 j2πvn , 𝑘 = 1 𝑡𝑜 𝐾 (15) FRm,k[v] = Rm[n]w[n]e− , k = 1 to K (15) () n=(k 1)S − where, 𝑣 is the window frequency, and 𝑤[𝑛] is defined as the Hamming window function. Finally, where,the periodogramv is the window value frequency, was calculated and w[ nfor] is each defined segment. as the HammingSubsequently, window the mean function. value Finally, of the the periodogramperiodogram value was wasobtained. calculated Equations for each (16) segment. and (17) show Subsequently, the estimation the mean of PSD value analysis. of the periodogram was obtained. Equations (16) and (17) show the estimation of PSD analysis. 1 𝑃𝑃,[𝑣] = |𝐹𝑅[𝑣]| , 𝐺 = 𝑤 [𝑛] (16) 𝐺 XM 1 2 2 PP [v] = FRm[v] , G = w [n] (16) m,k G n=0 1 𝑃𝑆𝐷,[𝑣] = 𝑃𝑃,[𝑣] (17) 𝐾 K 1 X PSDm,k[v] = PPm,k[v] (17) [ ] K Herein, 𝑃𝑆𝐷, 𝑣 is the PSD value for each segmentk=1 of 𝑚−𝑡ℎ constellation [20]. Afterward, the satellite detection block finds the peaks of PSD values with a searching window of ±1 kHz Herein, PSD [v] is the PSD value for each segment of m th constellation [20]. Afterward, around the carrierm,k center frequency. The center frequency of −the searching window for each the satellite detection block finds the peaks of PSD values with a searching window of 1 kHz around constellation is the middle of its frequency range. The satellite detection block finds the peaks± of PSD thevalues carrier and center determines frequency. the related The center Doppler frequency frequency. of In the another searching view, window for burst-based for each constellations, constellation is thethe middle satellite of detection its frequency block range. will be The transferred satellite detectionto the burst block detection finds theblock peaks in which, of PSD the values center and determinesfrequencythe of each related burst Doppler in one frequency.timeslot is Inconsider anothered. view, The detected for burst-based frequencies constellations, of peak points the satellitewere detectioncompared block to the will specific be transferred threshold, to thewhich burst was detection assigned block −40 dB. in which, Equation the (18) center presents frequency the peak of each burstfinder in onefunction timeslot for the is satellite considered. detection The block. detected frequencies of peak points were compared to the specific threshold, which was assigned 40 dB. Equation (18) presents the peak finder function for the − 𝐼𝐹 = Max𝑃𝑆𝐷 [𝑣] (18) satellite detection block. , IF = Max PSDm,k[v] (18) Sensors 2020, 20, 5866 8 of 17

 =  exp 2jπ f nT , O 40 dB U(x) =  − IF ≥ − (19)  = 0, O < 40 dB − The signal U(x) is the output of the satellite detection block, which by multiplying to the main received signal, removes the detected carrier frequency of the signal at the l th channel. The given − signal goes through the Low-Pass Filter (LPF) with a bandwidth of between 0.5 and 1.5 kHz. The LPF’s bandwidth should be determined as a way that the Doppler shift could pass it.

4.2.2. Doppler Tracking System To extract the Doppler shift in all sampling times, it needs to be tracked by a tracking loop ﬁlter. The Doppler shift can be obtained from QPSK signals by using the classical Costas loop. The received signal is multiplied by U(x). The obtained signal followed by an LPF is deﬁned as input of the tracking loop. Equation (20) presents the acquired S [n] for l th channel of the m th constellation. m,l − − π π h i S [n] = A . exp j k + . exp j2πnT f [n] + jϕ [n] + b[n], (20) m,l m,l 2 4 dm,l m.l

Figure5 shows the structure of the tracking loop for each channel of one constellation. It consists of a phase detector, loop ﬁlter, Numerically Controlled Oscillator (NCO), and integration functions. The estimated Doppler shift was tracked by a loop ﬁlter and NCO accounts for maintaining the detected phase. To obtain the phase residual, the input signal, Sm,l[n], was multiplied by cosine and sine functions of the estimated Doppler and phase. Subsequently, I and Q signals were calculated by the sum of the Mcoh samples of S1 and S2, which is the integration in continuous mode between time Sensorssteps n2020and, 20n, 5866+ 1. 9 of 17

FigureFigure 5. ArchitectureArchitecture of of proposed proposed multi-constellation LEO satellite receiver.

Equations (21) and (22) present the𝑎𝑠 obtained +1 I and𝐾 Q signals as In-phase and Quadrature 𝐹(𝑠) = , 𝐺(𝑠) = , (24) components of the signal. bQ[n] and bI[n]𝑏𝑠are the zero-mean𝑠 white Gaussian noise related to each component. Therefore, the phase discriminator computes the residual phase in each time step with Equation (23). 𝐹(𝑠)𝐺(𝑠) 2𝜉𝜔𝑠+𝜔 2𝐵𝜉 𝐻(𝑠) = = , 𝜔 = , (25) 1+𝐹(𝑠)𝐺(𝑠) 𝑠 +2𝜉𝜔𝑠+𝜔 𝜉 + 0.25 M Xcoh Where, 𝜔 and 𝜉 are obtained from NCO’s gain (𝐾 ) and parameters of loop filter (a, b), Q = S [n]. sin 2πnT fˆ [n] + ϕˆ [n] AQ sin(δϕˆ [n]) + bQ[n], (21) m,l dm,l m.l ≈ m.l known as loop natural0 frequency and damping ratio, respectively. The value of 𝜉 = 0.707 is selected to have a flat response, also, the 𝜔 can be selected with the noise bandwidth 𝐵 [32]. The NCO M block updates the phaseXcoh using the estimated phase and Doppler shift of the previous time step. The I = S [n]. cos 2πnT fˆ [n] + ϕˆ [n] AI cos(δϕˆ [n]) + bI[n], (22) phase is updated due to Equationm,l (26). dm,l m.l ≈ | | m.l 0 𝜑.[𝑛] = 𝜑.[𝑛−1] + 2𝜋(𝑛−1)𝑀𝑓,[𝑛−1], 𝜑.[0] =0, (26)

Signal-to-Noise Ratio (SNR) for 𝑙−𝑡ℎ channel of 𝑚−𝑡ℎ constellation is defined as 𝑆𝑁𝑅, = ,. , where 𝑇 is the sampling time of Q and I signals for the phase detector block. Also, 𝑁 is the PSD value of the transmitted signal’s noise. The noise variance of tracking loop block for 𝑙−𝑡ℎ channel of the 𝑚−𝑡ℎ constellation can be estimated as 𝜎,, =2𝜎,,.𝐵.𝑇 , where noise variance of the phase detector, 𝜎,,, is defined in Equation (27) [33]. Finally, the noise variance of the receiver’s Doppler measurements are obtained as 𝜎,, = ( .𝜎,,) , where c is the speed of light. 8 20 10 8 𝜎 = 𝑆𝑁𝑅 𝑆𝑁𝑅 + 𝑆𝑁𝑅 + 𝑆𝑁𝑅 − 𝑆𝑁𝑅 +2 𝑆𝑁𝑅 (27) ,, , 9 , 3 , 3 , 3 , ,

5. Experimental Results The designed multi-constellation receiver was tested by recording the samples of two visible constellations, Iridium-Next and Orbcomm with a sampling frequency of 2 MHz. The experiment was performed on the roof of the ETS university in downtown Montreal City with BladeRF Multi- Input Multi-Output (MIMO) Software Defined Radio (SDR), which used for recording the data from visible satellites. One channel of SDR was allocated for Orbcomm with center frequency of 137.5 MHz, and the other channel was determined for Iridium simplex bursts with center frequency of 1626.25 MHz. A dual-band VHF/UHF mobile antenna was utilized for Orbcomm signals, in parallel, an Iridium antenna was selected for the second channel. During the experiment, one Orbcomm satellite (ORBCOMM FM110), and two Iridium-Next satellites (IRIDIUM 104, IRIDIUM 144) were detected overhead. TLE files of all three satellites were downloaded, and their positions were tracked and simulated by an open-source SGP4 simulator, as depicted in Figure 6. It was completely necessary to use an RF bandpass filter for the Orbcomm channel, and an ultra-Low-Noise Amplifier (LNA) for the Iridium channel. Figure 7 shows all the utilized equipment in this experiment.

Sensors 2020, 20, 5866 9 of 17

AI Q δϕˆ [n] = | | .atan , (23) m.l AQ I The ﬁrst-order loop ﬁlter tracks the Doppler shift with continuous transfer function F(s). Also, the phase is tracked by the NCO with the transfer function of G(s). Equations (24) and (25) show the transfer functions and H(s) is the transfer function of the closed-loop system.

as + 1 K F(s) = , G(s) = NCO , (24) bs s

F(s)G(s) 2ξω s + ω 2 2B ξ H(s) = = n n , ω = l , (25) 2 2 n 2 1 + F(s)G(s) s + 2ξωns + ωn ξ + 0.25

Where, ωn and ξ are obtained from NCO’s gain (KNCO) and parameters of loop ﬁlter (a, b), known as loop natural frequency and damping ratio, respectively. The value of ξ = 0.707 is selected to have a ﬂat response, also, the ωn can be selected with the noise bandwidth Bl [32]. The NCO block updates the phase using the estimated phase and Doppler shift of the previous time step. The phase is updated due to Equation (26).

ϕˆ [n] = ϕˆ [n 1] + 2π(n 1)M fˆ [n 1], ϕˆ [0] = 0, (26) m.l m.l − − coh dm,l − m.l

Am,l.Tcoh Signal-to-Noise Ratio (SNR) for l th channel of m th constellation is deﬁned as SNRm,l = , − − N0 where Tcoh is the sampling time of Q and I signals for the phase detector block. Also, N0 is the PSD value of the transmitted signal’s noise. The noise variance of tracking loop block for l th channel of − the m th constellation can be estimated as σ2 = 2σ2 .B .T , where noise variance of the phase − PLL,m,l ϕ,m,l l coh 2 detector, σϕ,m,l, is deﬁned in Equation (27) [33]. Finally, the noise variance of the receiver’s Doppler 2 measurements are obtained as σ2 = c .σ , where c is the speed of light. LEO,m,l fc PLL,m,l 2 1 8 6 20 5 10 4 8 3 2 σ = SNR− SNR− + SNR− + SNR− SNR− + 2 SNR− (27) ϕ,m,l m,l 9 m,l 3 m,l 3 m,l − 3 m,l m,l

5. Experimental Results The designed multi-constellation receiver was tested by recording the samples of two visible constellations, Iridium-Next and Orbcomm with a sampling frequency of 2 MHz. The experiment was performed on the roof of the ETS university in downtown Montreal City with BladeRF Multi-Input Multi-Output (MIMO) Software Defined Radio (SDR), which used for recording the data from visible satellites. One channel of SDR was allocated for Orbcomm with center frequency of 137.5 MHz, and the other channel was determined for Iridium simplex bursts with center frequency of 1626.25 MHz. A dual-band VHF/UHF mobile antenna was utilized for Orbcomm signals, in parallel, an Iridium antenna was selected for the second channel. During the experiment, one Orbcomm satellite (ORBCOMM FM110), and two Iridium-Next satellites (IRIDIUM 104, IRIDIUM 144) were detected overhead. TLE files of all three satellites were downloaded, and their positions were tracked and simulated by an open-source SGP4 simulator, as depicted in Figure6. It was completely necessary to use an RF bandpass filter for the Orbcomm channel, and an ultra-Low-Noise Amplifier (LNA) for the Iridium channel. Figure7 shows all the utilized equipment in this experiment. Sensors 2020, 20, 5866 10 of 17 Sensors 2020, 20, 5866 10 of 17 Sensors 2020, 20, 5866 10 of 17

(a) (b)( b)

FigureFigureFigure 6. 6.6. ( (a(aa))) Position PositionPosition ofofof satellitessatellitessatellites duringduring one oneone orbital orbitalorbital period periodperiod and andand (b ()b( bthe)) thethe locationlocation location of ofsatellitesof satellites satellites over over over Montreal’sMontreal’sMontreal’s region. region.region.

FigureFigure 7. 7.( 1()1) Dual Dual VHF VHF/UHF/UHF antennaantenna for Orbcomm Orbcomm constellation; constellation; (2 ()2 Iridium) Iridium antenna; antenna; (3)( BladeRF3) BladeRF V2 V2 Figure 7. (1) Dual VHF/UHF antenna for Orbcomm constellation; (2) Iridium antenna; (3) BladeRF V2 SDR;SDR; (4 ()4 RF) RF bandpass bandpass filter; filter; ( (55)) Low-NoiseLow-Noise Amplifier Amplifier (LNA) (LNA) for for Iridium Iridium frequency frequency range; range; (6) ( 6PC.) PC. SDR; (4) RF bandpass filter; (5) Low-Noise Amplifier (LNA) for Iridium frequency range; (6) PC. TheThe BladeRF BladeRF hashas its own embedded embedded RF RF front-end, front-end, so the so theprovided provided LNA LNA can be can sufficient be suffi forcient the for The BladeRF has its own embedded RF front-end, so the provided LNA can be sufficient for the thesignal signal acquisition acquisition of ofIridium-Next Iridium-Next bursts. bursts. Using Using one one multi-channel multi-channel SDR SDR made made the thesystem system more more signal acquisition of Iridium-Next bursts. Using one multi-channel SDR made the system more adaptiveadaptive for for changing changing the the centercenter frequenciesfrequencies and sampling sampling times times of of receiving receiving signals. signals. Although Although the the adaptive for changing the center frequencies and sampling times of receiving signals. Although the BladeRFBladeRF would would notnot bebe able to to record record two two far far sampling sampling frequencies frequencies at the at same the same time, time,it can itchange can change the BladeRF would not be able to record two far sampling frequencies at the same time, it can change the thecenter center frequency frequency rapidly rapidly with with negligible negligible delay. delay. At Atthe the time time of ofexperiment, experiment, one one Orbcomm Orbcomm satellite satellite center(Orbcomm frequency FM-110) rapidly with withdownlink negligible transmitting delay. centAt theer frequencies time of experiment, of 137.2875 one and Orbcomm 137.7375 MHz satellite (Orbcomm FM-110) with downlink transmitting center frequencies of 137.2875 and 137.7375 MHz was (Orbcommwas visible. FM-110) Also, two with Iridium-Next downlink transmitting satellites were cent detecteder frequencies overhead. of 137.2875The Welch and Fast 137.7375 Fourier MHz visible. Also, two Iridium-Next satellites were detected overhead. The Welch Fast Fourier Transform wasTransform visible. (FFT) Also, power two spectralIridium-Next density satellites analysis waswere implemented detected overhead. for recorded The Orbcomm Welch Fastsamples, Fourier (FFT) power spectral density analysis was implemented for recorded Orbcomm samples, as depicted Transformas depicted (FFT) in Figure power 8. Also,spectral Figure density 9 shows analysis the PSD was analysis implemented of one Ringfor recorded alert and Orbcomm one Quaternary samples, in Figure8. Also, Figure9 shows the PSD analysis of one Ring alert and one Quaternary message asmessage depicted bursts in Figure of Iridium-Next 8. Also, Figure before 9 shows burst the frequency PSD analysis filtering. of one The Ring peak alert frequency and one Quaternary of the bursts of Iridium-Next before burst frequency filtering. The peak frequency of the Quaternary message messageQuaternary bursts message of Iridium-Next was detected asbefore 1626.1346 burst MH frequencyz, and the frequencyfiltering. Theof 1626.3013 peak frequency MHz was theof the was detected as 1626.1346 MHz, and the frequency of 1626.3013 MHz was the FFT peak of the Ring QuaternaryFFT peak of message the Ring wasalert detectedburst. as 1626.1346 MHz, and the frequency of 1626.3013 MHz was the alert burst. FFT peak of the Ring alert burst. The average bandwidth of bursts for Ring alert and Quaternary messages were between 30 and 35 kHz. Furthermore, message bursts had a higher magnitude compared to the Ring alerts. The Doppler tracking loop for each satellite can be initialized by a simple calculation of the difference between the obtained and determined frequencies. Also, the Doppler tracking loop for the Iridium constellation was continuous for each burst’s duration. As a result of this, the initial Doppler value for Ring alert and message bursts were 30.32 and 30.30 kHz for Iridium 104, and 29.55 and 29.62 kHz for Iridium 144, respectively. Likewise, for Orbcomm constellation, the lower band frequency was considered for positioning with an initial Doppler value of approximately 2.4564 kHz. Figure 10 shows the result of − the Doppler tracking block after Orbcomm signal acquisition over a duration of 30 s. The results were used as the pseudorange rate measurements of the Orbcomm constellation for Doppler positioning.

SensorsSensors2020 2020, 20,, 20 5866, 5866 1111 of 17of 17 Sensors 2020, 20, 5866 11 of 17

Figure 8. Power Spectral Density (PSD) analysis of acquired Orbcomm signal. Figure 8. Power Spectral Density (PSD) analysis of acquired Orbcomm signal.signal.

(a) (b) (a) (b) Figure 9. (a) PSD of Quaternary message burst of Iridium-Next and (b) PSD of Ring alert burst of SensorsFigure 2020 9., 20(, a5866) PSD of Quaternary message burst of Iridium-Next and (b) PSD of Ring alert burst 12 of 17 ofFigureIridium-Next. 9. (a) PSD of Quaternary message burst of Iridium-Next and (b) PSD of Ring alert burst of Iridium-Next. The average bandwidth of bursts for Ring alert and Quaternary messages were between 30 and 35 ThekHz. average Furthermore, bandwidth message of bursts bursts for hadRing a alert high ander magnitude Quaternary compared messages towere the between Ring alerts. 30 and The 35Doppler kHz. Furthermore, tracking loop message for each bursts satellite had can a highbe initializeder magnitude by a comparedsimple calculation to the Ring of the alerts. difference The Dopplerbetween tracking the obtained loop for and each determined satellite canfrequencies. be initialized Also, by the a Dopplersimple calculation tracking loop of thefor differencethe Iridium betweenconstellation the obtained was continuous and determined for each frequencies. burst’s duration. Also, theAs aDoppler result of tracking this, the loop initial for Doppler the Iridium value constellationfor Ring alert was and continuous message bursts for each were burst’s 30.32 duration. and 30.30 As kHz a resultfor Iridium of this, 104, the and initial 29.55 Doppler and 29.62 value kHz forfor Ring Iridium alert and144, messagerespectively. bursts Likewise, were 30.32 for and Orbc 30.30omm kHz constellation, for Iridium the104, lower and 29.55 band and frequency 29.62 kHz was forconsidered Iridium 144, for respectively.positioning withLikewise, an initial for Orbc Doppleromm value constellation, of approximately the lower –2.4564 band frequency kHz. Figure was 10 consideredshows the for result positioning of the Doppler with an tracking initial Dopplerblock afte valuer Orbcomm of approximately signal acquisition –2.4564 over kHz. a Figureduration 10 of shows30 s. Thethe resultresults of were the Dopplerused as thetracking pseudorange block afte rarte Orbcomm measurements signal of acquisition the Orbcomm over constellation a duration of for 30Doppler s. The results positioning. were used as the pseudorange rate measurements of the Orbcomm constellation for Doppler positioning. FigureFigure 10. 10.Doppler Doppler shift shift tracking tracking for for Orbcomm Orbcomm FM110 FM110 in in 30 30 s measurements. s measurements.

Also,Also, Figure Figure 11 11 demonstrates demonstrates the the extracted extracted Doppler Doppler shift shift points points from from Iridium’s Iridium’s simplex simplex bursts. bursts. TheThe duration duration of eachof each simplex simplex signal si wasgnal 90was ms 90 [30 ],ms so [30], approximately so approxim 72 Dopplerately 72 pointsDoppler were points attained were afterattained 30 s of after the experiment30 s of the experiment for both Ring for alertboth andRing Quaternary alert and Quaternary message bursts. message The bursts. Doppler The tracking Doppler systemtracking tracked system the tracked Doppler the shift Doppler in each shift burst in duration each burst and ﬁnally,duration each and point finally, was each calculated point aswas thecalculated average ofas Dopplerthe average in 90 of ms. Doppler The measurement in 90 ms. The ofmeasurement the Orbcomm of the constellation Orbcomm was constellation continuous was andcontinuous in contrast, and the in measurementcontrast, the measurement of the Iridium of constellation the Iridium constellation was based on was the based burst on durations. the burst durations. The Interpolation method was used for the Doppler measurements of Iridium constellations, followed by the same sampling frequency for synchronizing the measurements of both constellations.

(a) (b)

Figure 11. Doppler points for two Iridium satellites using (a) Ring alert bursts and (b) Quaternary message bursts.

The proposed EKF-based Doppler positioning method was implemented and tested in MATLAB, using the obtained Doppler shift measurements of the designed multi-constellation software-defined receiver. The Doppler measurements of one Orbcomm satellite and two Iridium- Next satellites were injected into the positioning system. The experiment was performed one time using Ring alert, and the other time using Quaternary message bursts. Moreover, the positioning result is compared to a single constellation mode. Figure 12 demonstrates the estimated and true reference position for a stationary receiver.

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Figure 10. Doppler shift tracking for Orbcomm FM110 in 30 s measurements.

Also, Figure 11 demonstrates the extracted Doppler shift points from Iridium’s simplex bursts. The duration of each simplex signal was 90 ms [30], so approximately 72 Doppler points were attained after 30 s of the experiment for both Ring alert and Quaternary message bursts. The Doppler tracking system tracked the Doppler shift in each burst duration and finally, each point was calculated as the average of Doppler in 90 ms. The measurement of the Orbcomm constellation was Sensorscontinuous2020, 20, 5866and in contrast, the measurement of the Iridium constellation was based on the12 ofburst 17 durations. The Interpolation method was used for the Doppler measurements of Iridium constellations, followed by the same sampling frequency for synchronizing the measurements of both The Interpolation method was used for the Doppler measurements of Iridium constellations, followed by constellations. the same sampling frequency for synchronizing the measurements of both constellations.

(a) (b)

FigureFigure 11. 11.Doppler Doppler points points for for two two Iridium Iridium satellites satellites using using (a )(a Ring) Ring alert alert bursts bursts and and (b )(b Quaternary) Quaternary messagemessage bursts. bursts.

TheThe proposed proposed EKF-based EKF-based Doppler Doppl positioninger positioning method method was implemented was implemented and tested and in MATLAB, tested in usingMATLAB, the obtained using Dopplerthe obtained shift measurements Doppler shift of measur the designedements multi-constellation of the designed multi-constellation software-deﬁned receiver.software-defined The Doppler receiver. measurements The Doppler of one measurem Orbcomments satellite of one and Orbcomm two Iridium-Next satellite and satellites two Iridium- were injectedNext satellites into the positioningwere injected system. into the The position experimenting wassystem. performed The experiment one time usingwas performed Ring alert, andone thetime otherusing time Ring using alert, Quaternary and the other message time using bursts. Quat Moreover,ernary message the positioning bursts. Moreover, result is compared the positioning to a singleresult constellation is compared mode. to a single Figure constellation 12 demonstrates mode the. Figure estimated 12 demonstrates and true reference the estimated position and for true a stationary receiver. Sensorsreference 2020, 20 position, 5866 for a stationary receiver. 13 of 17

Figure 12. PositioningPositioning results results for for a stationary receiver using single-constellation (Orbcomm) and Multi-constellation (Orbcomm and Iridium-Next) receiver modes.

The estimated positionspositions were were obtained obtained using using continuous continuous Doppler Doppler measurements measurements of Orbcomm of Orbcomm and andpoints points measurements measurements of Ring of alertRing and alert messaging and messaging bursts forbursts Iridium-Next for Iridium-Next satellites. satellites. The initial The value initial for valuethe north-direction for the north-direction and east-direction and east-direction position axes posi of thetion receiver axes of werethe receiver chosen aboutwere 20chosen km away about from 20 kmthe trueaway reference. from the Also, true byreference. knowing Also, the height by know of theing building the height (roof of of the the building ETS university), (roof of where the ETS we university),carried out thewhere experiment, we carried the out initial the valueexperiment, of the altitudethe initial axis value was of selected the altitude with a axis 100 was m di selectedﬀerence. withTable a2 100shows m difference. the results Table of the 2 designed shows the Doppler results positioningof the designed using Doppler single andpositioning multi-constellation using single andmethods. multi-constellation According to Tablemethods.2, the According positioning to using Table measurements 2, the positioning of a multi-constellation using measurements receiver of a wasmulti-constellation more precise in receiver messaging was burst more mode precise than in Ringmessaging alert burst burst mode. mode than Ring alert burst mode.

Table 2. Comparison between Root Mean Square (RMS) error of each method.

2D RMS 3D RMS Altitude RMS Mode Single Constellation 0.751 km 0.7658 km 0.150 km Continuous (Orbcomm) Multi-Constellation 0.176 km 0.2136 km 0.121 km Ring alert bursts (Orbcomm + Iridium) 0.132 km 0.1771 km 0.118 km Messaging bursts

The messaging bursts usually have a more powerful magnitude, which can be a more useful signal for positioning. However, the results have shown significant improvement compared to the single constellation mode using both Ring alert and messaging bursts. As no altimeter was used in this experiment, the altitude estimation is the most challengeable issue, however; using an accurate altimeter or initializing the positioning system with true altitude, can expressively increase the system’s precision. As a result, the 3D Root Mean Square (RMS) for messaging burst mode is about 177 m compared to the real location, which shows about 76% accuracy advancement compared to the single constellation method. Also, this RMS value using Ring alert bursts is about 213 m with 72% improvement with no altimeter aiding.

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Table 2. Comparison between Root Mean Square (RMS) error of each method.

2D RMS 3D RMS Altitude RMS Mode Single Constellation (Orbcomm) 0.751 km 0.7658 km 0.150 km Continuous Multi-Constellation 0.176 km 0.2136 km 0.121 km Ring alert bursts (Orbcomm + Iridium) 0.132 km 0.1771 km 0.118 km Messaging bursts

The messaging bursts usually have a more powerful magnitude, which can be a more useful signal for positioning. However, the results have shown signiﬁcant improvement compared to the single constellation mode using both Ring alert and messaging bursts. As no altimeter was used in this experiment, the altitude estimation is the most challengeable issue, however; using an accurate altimeter or initializing the positioning system with true altitude, can expressively increase the system’s precision. As a result, the 3D Root Mean Square (RMS) for messaging burst mode is about 177 m compared to the real location, which shows about 76% accuracy advancement compared to the single constellation method. Also, this RMS value using Ring alert bursts is about 213 m with 72% improvement with no altimeter aiding.

6. Discussion The principal perspective of this research was to design and present a novel adaptive architecture for most types of LEO satellite receivers in multi-constellation mode. The Doppler frequency, clock bias, and clock drift of satellites are known as the main measurements in Doppler positioning algorithms. The designed measurement model can be selected alternatively, with regards to the number of satellites and constellations, also, burst and continuous downlinks are considered in the proposed architecture. The importance of LEO satellite receivers can be proved when the accuracy of measurements for Doppler positioning methods is being investigated. In the continuous mode of downlink signals, like the Orbcomm constellation, the receiver utilizes the Doppler tracking mode by detecting the center frequency of overhead satellites. In contrast, for the burst-based constellations, like Iridium, the bursts should be detected and tracked, which leads to a discrete Doppler trajectory. The operated SDR in the proposed experiment is BladeRF 2.0 micro with a frequency range of 47 MHz to 6 GHz and the ability of automatic gain control and automatic IQ and DC offset correction. It should be discussed that because of a significant difference between the center frequency of two used constellations, the BladeRF should be used in switch mode for changing the center frequency between two constellations. Figure 13 presents the Doppler curve of each downlink signal of LEO satellites during the same pass time of the satellite. The higher Doppler frequency means a higher elevation angle between the satellite and the receiver. As the satellite approaches the receiver’s location, the Doppler will tend to zero, oppositely, negative Doppler shows the inverse direction and movement away from the receiver. It should be mentioned that the complete curve will be obtained when the satellite passes through the receiver. The experiment in this research estimated the Doppler shift from recorded data over a duration of 30 s. This time duration was selected for two main reasons. First, visibility time for Orbcomm satellites is usually between 1 and 2 min, in contrast, Iridium-Next satellites in outdoor environments are visible most of the time. Furthermore, to perform the experiment in multi-constellation mode, the duration should be selected in a way that both constellations be visible. Second, using huge amounts of measurements over a long duration cannot assess the accuracy of the receiver in static mode. To obtain the static location of the receiver, using less measurements can validate the accuracy of the proposed method and its capability for real-time implementations. Sensors 2020, 20, 5866 14 of 17 constellations, like Iridium, the bursts should be detected and tracked, which leads to a discrete Doppler trajectory. The operated SDR in the proposed experiment is BladeRF 2.0 micro with a frequency range of 47 MHz to 6 GHz and the ability of automatic gain control and automatic IQ and DC offset correction. It should be discussed that because of a significant difference between the center frequency of two used constellations, the BladeRF should be used in switch mode for changing the center frequency between two constellations. Figure 13 presents the Doppler curve of each downlink signal of LEO satellites during the same pass time of the satellite. The higher Doppler frequency means a higher elevation angle between the satellite and the receiver. As the satellite approaches the receiver’s location,Sensors 2020 the, 20 Doppler, 5866 will tend to zero, oppositely, negative Doppler shows the inverse direction14 of 17 and movement away from the receiver.

FigureFigure 13. 13. ApproximationApproximation ofof the the Doppler Doppler curve curve for LEOfor downlinkLEO downlink signals signals in different in different elevation angles.elevation angles. The method does not have any augmentation like a GPS reference initializer or altimeter. AsIt the should main purposebe mentioned of this researchthat theis complete the design curve and validationwill be obtained of presented when multi-constellation the satellite passes throughLEO-SDR the receiver, receiver. the The validation experiment was performedin this resear inch static estimated mode to the show Doppler the improvement shift from recorded of obtained data measurements in a simple Doppler localization system. As a result, in the Ring alert burst mode, over a duration of 30 s. This time duration was selected for two main reasons. First, visibility time for the RMS error of positioning decreased from 765 to 213 m, likewise, in messaging bursts mode, the error Orbcomm satellites is usually between 1 and 2 min, in contrast, Iridium-Next satellites in outdoor reached 132 m in a no-augmentation situation. The receiver also showed moderate improvement in environments are visible most of the time. Furthermore, to perform the experiment in multi- altitude error. constellation mode, the duration should be selected in a way that both constellations be visible. Second,7. Conclusions using huge amounts of measurements over a long duration cannot assess the accuracy of the receiver in static mode. To obtain the static location of the receiver, using less measurements can In this paper, an adaptive multi-constellation software-defined LEO satellite receiver is designed validate the accuracy of the proposed method and its capability for real-time implementations. and implemented. The receiver’s architecture is compatible to be used for Doppler positioning with The method does not have any augmentation like a GPS reference initializer or altimeter. As the LEO satellite SOPs. Nav-SOP has been under investigation by researchers as an important alternative mainof GNSS purpose navigation, of this research in recent is decades.the design However, and validation coverage of presented and visibility multi-constellation of LEO satellites LEO-SDR over a receiver,long-term the duration validation are the was key performed issues of using in thisstatic kind mode of navigation. to show Designingthe improvement a multi-constellation of obtained measurementsreceiver is the in first a simple step to utilizeDoppler the localization pseudorange syst rateem. measurements As a result, ofin variousthe Ring LEO alert satellites. burst mode, It can the RMSmake error the of navigation positioning more decreased trustable from for flight765 to and 213 groundm, likewise, vehicles, in messaging due to its bursts dependency mode, onthe the error reachedmeasurements 132 m in of a variousno-augmentation constellations. situation. Also, The Nav-SOP receiver can also be integratedshowed moderate with INS improvement to cope with in altitudeGNSS-challengeable error. environments or situations, in which the GNSS is inaccessible. In the proposed architecture, the multiple antennas can be used for acquiring the LEO signals 7. fromConclusions different constellations. For more than two satellites, it is essential to use more SDRs for recording theIn data this at paper, the same an adaptive time with multi-constellation different center frequencies. software-defined The receiver LEO satellite is designed receiver to detect is designed the satellites transmitting center frequency and also to recognize the burst for burst-based satellites like and implemented. The receiver’s architecture is compatible to be used for Doppler positioning with Iridium. The Doppler tracking is managed to follow the Doppler measurements with special sampling LEO satellite SOPs. Nav-SOP has been under investigation by researchers as an important alternative frequency for all kinds of LEO satellites. The accuracy of Doppler positioning using measurements of of GNSS navigation, in recent decades. However, coverage and visibility of LEO satellites over a long- the proposed receiver is completely dependent on initial values and EKF parameters. term duration are the key issues of using this kind of navigation. Designing a multi-constellation The system can be useful in LEO-INS integration applications, collaborative multi-constellation receivernavigation is the designs, first step and to timingutilize the systems. pseudorange It is an openrate measurements research issue toof investigatevarious LEO the satellites. design of It acan tracking loop for burst-based satellites to obtain more accurate measurements. Moreover, the EKF can be designed to estimate the position and velocity of LEO satellites, as well as the receiver’s states. The dependency of the system on the downloaded orbital information from the TLE file leads to a basic error due to the inaccuracy of LEO information from TLE files. Apart from that, the positioning for dynamic flight and ground vehicles can be studied in multi-constellation modes. Although the designed receiver showed acceptable results for stationary receivers, using an altimeter or other aiding measurements is expected to improve the positioning accuracy, especially Sensors 2020, 20, 5866 15 of 17 in-flight dynamic experiments. In addition, a deep comparison between the results of the architecture using various loop filters and phase discriminators can provide future research topics. The designed system can be used in experiments of GNSS-SOP-INS integration with a GNSS cut-off time in dynamic and static situations for drones, Unmanned Aerial Vehicles (UAV), ground vehicles, and submarine unmanned vehicles. Finally, in some cases, the feasibility of LEO-SOPs for enhancing the heading precision can be studied in many indoor and outdoor positioning and localization systems.

Author Contributions: F.F. designed the algorithm, prepared the literature review, and wrote the contents of the paper. R.L.J. contributed to modifying the algorithm and supervising the project. The experiments, simulations, analysis, and conclusion were performed by F.F. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: I sincerely would like to thank Rene Jr. Landry who provided all the necessary resources and equipment to complete this research. I also wish to appreciate our research assistant, Hamza Benzerrouk, for his encouragement and supports. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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