RADIO PULSAR RECEIVER SYSTEMS FOR SPACE NAVIGATION

Transcription

1 RADIO PULSAR RECEIVER SYSTEMS FOR SPACE NAVIGATION D. Brito 1, G. Tavares 1, J. Fernandes 1, A. Noroozi 2, and C. Verhoeven 2 1 INESC-ID, Instituto Superior Técnico, Universidade de Lisboa, Portugal 2 Delft University of Technology, The Netherlands 1 {diogo.brito, goncalo.tavares, jorge.fernandes}@inesc-id.pt 2 {a.noroozi, c.j.m.verhoeven}@tudelft.nl ABSTRACT Pulsars emit broadband electromagnetic radiation, ranging from radio to X-ray and gamma-ray frequencies, with an individual signature (period and shape). For navigation purposes the pulsars of interest are fast rotating neutron stars that emit short stable periodic pulses, with periods between milliseconds and seconds [1]. By detecting a set of known pulsars one can use them as beacons for navigation in celestial coordinates, being currently seen as the only truly navigation solution for deep-space navigation [2]. In this paper we argue that using recent advances in microelectronics and antenna technologies it is possible to design a radio pulsar navigation system in a more accessible, robust and compact way. System block specifications for the radio pulsar receiver are shown and the study on the system accuracy shows that a 3.25 km accuracy is achievable after 1 hour of integration time using an antenna with an effective area of 10 m 2. Key words: Pulsar, Navigation, Space, Radio, Receiver. 1. INTRODUCTION Pulsar navigation in deep-space is an important research topic for NASA and ESA [2, 3], since there is no other viable solution for navigation in outer-space. Previous studies [2, 3] have shown that radio pulsars were disadvantageous in terms of area, volume and weight when compared to the use of X-ray pulsars, since large antennas were required to detect the radio signal. However, recent developments on phased array antennas and sub-micron microelectronics, allow to overcome such disadvantages. Pulsars are broadband pulsating radio sources, received anywhere in our solar system, that emit electromagnetic radiation emission ranging from radio, to X-ray and gamma-ray frequencies. Their pulsating nature, which originates from in their rotation movement, makes them very similar to light-houses, whose light is only seen for a very short fraction of the period. Each pulsar has its own period, between milliseconds to seconds [1], with an accuracy which can surpass that of atomic clocks. Furthermore they have their own particular shape or profile, which grants each pulsar an unique signature, as shown in the examples in Fig. 1. The radio pulsar signals are not blocked by the atmosphere, therefore they are detectable on Earth. This allows more knowledge to be acquired on radio pulsars than on the known X-ray pulsars, both in number and accuracy on the obtained characterization. In addition, since rad io pulsars are not blocked by the atmosphere, they can be used for navigation both on Earth and in space. Due to the very weak pulsar signals, commonly below the background noise, most of the pulses require coherent addition of several pulses in order to origin an integrated profile, which becomes visible above the noise level. On Earth, to detect such a weak signal, large radio telescopes are used. For space navigation, such systems are not feasible. Since we are only aiming to detect known pulsars, and its parameters (period and shape) the system specifications can be relaxed in comparison with those used on radio telescopes to find new pulsars. This paper is organized as follows: Section 2 presents the relevant pulsar signal characteristics. In Section 3, a brief explanation on navigation using pulsars is presented. Section 4, presents the general system specifications, regarding the antenna and frontend. A brief evaluation on the system accuracy is also performed. Finally the conclusions are drawn in Section 5.

2 The signal-to-noise ratio (SNR) of the pulsar signal, has an extremely high influence on the accuracy of the system, since for lower values of SNR, more integration time is required do achieve the same precision of a pulsar with a larger SNR. The received pulsar power for a pulsar i is given by S r (i) = αa e S i p ( frec f ref ) β i p B [W ] (2) Figure 1: Different pulsar profiles. where 0 < α < 1 is the polarization parameter (α = 1/2 for a single polarization receiver), A e (m 2 ) is the effective area of the receiver antenna, Sp i (Jy) is the pulsar flux measured at a reference frequency f ref (GHz), β p is the pulsar spectral index, f rec (GHz) is the receiver (observation) frequency and B (Hz) is the receiver bandwidth. The quantity Sp( i frec f ref ) βi p is the pulsar flux at the receiver central frequency f rec, expressed in W/Hz/m 2. The total noise power is given by N i = k B (T rec + T back + T gal + T sol )B [W ] (3) Figure 2: Pulsar signals entering the mathematical model. 2. PULSAR SIGNAL In absence of noise, the pulsar signal s p (t) is described as a random signal with time-varying statistics and can be modeled by where k B = (J/K) is the Boltzmann constant, T rec (K) is the receiver noise temperature, T back = 2.7 K is the background cosmic noise temperature, T gal 6frec 2.2 (K) is the background noise temperature from the galaxy and T sol = (72f rec )A e 10 (Asl/10) d 2 (K) is the solar system noise temperature with the contributions from the Sun and also from Jupiter. The parameter d (AU) is the distance from the observation location to the Sun and A sl (db) is the antenna main side lobe attenuation. A quiet Sun is considered since during solar storms, the solar noise temperature raises dramatically (up to 250 times) and will render pulsar navigation unfeasible. From (2) and (3) we can write the SNR when detecting the pulsar i as s p (t) = a(t).p rot (t) = a(t) n= p rot (t nt p ) (1) where a(t), is the pulsar intrinsic process, which is wideband (GHz), and p rot (t) is the periodic signal due to the pulsar rotation, as it is seen in Fig. 2. For time-of-arrival (TOA) estimation, we must detect the peak of the pulse. However, since the signal is below, by -50 db to -60 db, the noise level, the detection of the profile peak requires some amount of integration time (to decrease the noise variance). SNR i = αa e S i p( frec f ref ) βi p k B (T rec + T back + T gal + T sol ) (4) From (4), we have drawn the plot in Fig. 3, where it is observable a decay in the SNR as the frequency increases. Furthermore, a maximum SNR value is observable around 1 GHz, for the majority of the pulsars. The presented pulsar signal characteristics will guide the receiver parameters selection, as well as the performed study to estimate the achievable positioning accuracy.

3 0 Φ = τ k T k < 1) information. During one pulsar period T k, the signal travels a distance D k = ct k (the pulsar spatial period) and thus an ambiguity equal to an integer number of D k exists and must be solved. We start with an initial SSB-referred phase Φ SSB k (t 0 ) obtained or known at an earlier time t 0. For small t t 0 an accurate phase estimate at time t may be obtained using the pulsar frequency f k = 1 T k and a first-order phase model as [1, 2]. Figure 3: SNR in function of the observation frequency. Φ k (t) = [Φ(t 0 ) + f k (t t 0 )] 1 (5) where [x] 1 = x + m stands for modulo 1 reductions (m is an integer which solves this equation and that needs to be determined). If the spacecraft produces a phase estimate ˆΦ k (t) it may be referred to the SSB system as ˆΦ k (t) = [Φ SSB k (t τ k ) + n k ] 1 (6) where n k is the noise associated with the estimation of ˆΦ k (t). Using the phase model (5) in (6) gives Figure 4: Representation of a pulsar navigation system. 3. PULSAR NAVIGATION The pulsar navigation process is based on the receiver time-of-arrival (TOA) of the signal from different pulsars. To obtain a positional fix, an inertial observation reference is required. Due to orbital motion neither aircraft nor even the Earth can be taken as such inertial references but the solar system center of mass (solar system barycenter, SSB) can [1]. Available pulsar data is transformed to SSB coordinates using some planetary ephemeris. The navigation process is explained with the aid of Fig. 4 which depicts the relative position of the spacecraft, the SSB and two arbitrary located pulsars. In this figure T k is the (known) pulsar period, u k is the (known) unitary vector from the SSB to the kth-pulsar, x is the vector from the SSB to the spacecraft location and τ k = ut k x c is the spacecraft delay with respect to the SSB (c is the speed of light). Because the distance between pulsars and the SSB is very large (typically larger than 1kpc and much larger than x ) incoming pulsar signals are considered as plane wavefronts. Since the envelope of the pulsar signal is periodic, there is an inherent ambiguity in any distance measured using the TOA estimate τ k (also represented as a normalized phase ˆΦ k (t) = [Φ SSB k (t 0 ) + f k (t t 0 τ k ) + n k ] 1 = Φ SSB k (t 0 ) + f k (t t 0 τ k ) + n k + m. (7) Substituting the delay τ k as a function of the unit vector u k and x yields finally ( ˆΦ k (t) = Φ SSB k (t 0 ) + f k t t 0 ut k x ) c (8) This equation contains five variables: the three components of x (the desired location), the time difference t t 0 and the integer variable m. The estimation of m solves the ambiguity problem and must be done offline, prior to the estimation of the other unknowns using conditional maximum-likelihood (ML) methods with Bayesian prior information [2]. Therefore, the online estimation of t t 0 and x, which may be done from Eq. 8 using standard ML methods, requires the reception of at least four different pulsar signals. The set of samples n k are assumed to be Gaussian, independently distributed random variables. If more than four pulsar signals are available, the estimation of these parameters may be improved. In addition, if some uncertainty exists on the pulsar frequency f k value (or in any other parameter e.g. the unitary vectors u k ) then the estimation procedure to obtain a navigation solution becomes iterative with the estimation residuals of the current estimation step (which will in this case exhibit a linear trend) used to correct f k in the next step [1]. Another pulsar navigation impairment is the geometric dilution-of-precision (GDOP) effect, common to

4 (a) (b) Figure 6: (a) Planar single spiral wire antenna [4]; (b) Antenna array beam steering [5]. Figure 5: SNR as a function of the antenna area. other navigation systems. This effect is due to the angular position of the pulsars with respect to the spacecraft and may render poor estimates of both position and relative time [2]. 4. RADIO PULSAR NAVIGATION SYS- TEM In this section a set of specifications and the achievable position accuracy for a radio pulsar navigation system are presented. The system is divided into three major subsystems: the required antenna, the radio frequency (RF) front-end and the estimated positioning accuracy Antenna The antenna is the first interface with the signal and the system SNR is strongly related with its area, as shown in Fig. 5. The selection of the antenna has to take into account two main constraints; is to be mountable on a spacecraft and its bandwidth should be large (as will be defined in Section 4.2). To achieve large antenna areas in spacecrafts, deployable structures are commonly used because the aerodynamic of the spacecraft is not important. This allows to have higher gains since planar antennas can be mounted on a foldable surface, and deployed after launch. However, its use should be avoided, since they have commonly very complex structures. Even if they are built with ultra light materials, they comprise an heavy part of the payload of any spacecraft. In this paper we show that the use of smaller antennas, such as one with an area of 1 m 2 are sufficient to allow a position estimate with an acceptable error for space applications. Planar antennas, are formed on a thin surface, which can be embedded, virtually, on any surface of the spacecraft. There are different planar antenna types with different characteristics, being the most important features for this purpose, the large flexibility in designing them for different central frequencies and bandwidths. The planar spiral antenna is one such antenna configuration, depicted in Fig. 6(a). Because the antenna frequency characteristics are defined solely by the different angles, a frequencyindependent antenna results. Furthermore, for navigations purposes it is of most importance to be able to receive multiple pulsars at the same time. Thus, placing multiple small antennas to form an array is required and planar antennas are perfect for this purpose, providing both high gain and directivity, as its required for tracking multiple pulsars [5]. The planar antenna arrays are capable of electronically steering the beam and even simultaneously tracking multiple targets, as demonstrated in Fig. 6(b), where the steering of a linear antenna array in 2 dimensions is shown. In this configuration, array elements are placed in a line along the x-axis separated by a distance d. By applying proper delays to the signals of each element, the beam pattern can be rotated in the desired direction. If the array elements are placed in a planar fashion, a 3-dimensional scan will be achieved. Multi-beam operation is possible using these antenna arrays, since it can simultaneously form multiple narrow beams to scan different angles. The antenna patterns can be adaptive and flexible while accurate [6]. This property can be useful, for our application, since the antenna array may face small deformations affecting the antenna pattern, depending on which surface it is applied to.

5 flo1 LNA 90 o VGA Gain Control VGA ADC ADC Figure 7: Low-IF architecture block diagram RF Front-End DSP The RF front-end for pulsar signals, has to deal with extremely weak signal strengths due to the distance at which the pulsars are emitting (for a 1 m 2 antenna the pulsar received signal can be lower than -180 dbw). In outer space the sources of noise are already considered, and there are no interferers, therefore, the receiver dynamic range is comprised between the pulsar signal level and the electronic thermal noise. This absence of interference allows more relaxed design specifications, when compared with a similar situation on Earth, where high interference exist. A conventional wideband low-if receiver is proposed in Fig. 7, which is the most common architecture found on the radio telescopes used to detect radio pulsars on Earth. The Low-IF receiver allows to reduce the filter and the analog-to-digital (ADC) specifications, by using a low intermediate frequency. Furthermore, it is a compromise between the homodyne receiver (zero- IF), which is immune to the image frequencies problem and the heterodyne (high-if), which has no offset problems. This front-end topology will only degrade the SNR value, since the received signal is already below the noise and the receiver will add extra noise to the signal. This means that the system noise should be kept as low as possible. Regarding Fig. 3, in order to obtain the best input SNR possible, the receiver should use a central frequency around 1 GHz. Furthermore, the used bandwidth should be as large as possible, to obtain as much signal from the pulsar as possible, as can be concluded from Eq. 2. The selection of the central frequency and the bandwidth, defines the allowed LO frequencies and also the ADC Nyquist sampling rate. Therefore, the selection of the intermediate frequency should be as low as possible, to allow a lower ADC sampling rate specification. However it should also be high enough to be far from pink noise sources (as flicker noise in electronic devices). Since operation is in the absence of interference, to obtain the best available SNR from the pulsar signals, the central frequency is selected at the optimal point 1 GHz, leading to the selection of 250 MHz as intermediate frequency, which allows to use a LO frequency of either 750 MHz or 1.25 GHz. A bandwidth of 400 MHz is selected, since beyond this value technical limitations exist, namely on the ADC, that has a sampling rate at least two times the signal bandwidth. The receiver system noise follows the Friis noise equation, as shown in (9). Therefore, the low noise amplifier (LNA) should amplify the signal as much as possible, while keeping the noise low, in order to diminish the noise contribution of the remaining blocks. Furthermore, since it is a tuned LNA for the selected central frequency, it will also act as first filtering stage to band-limit the signal. State-of-the-art cooled LNAs can have noise figures close to 0.2 db, therefore these are the values that should be considered for such a system. F rx = F LNA + F BP filter 1 G LNA + F Mixer 1 G LNA G BP filter +... (9) Since no interference is considered, the band pass filter is only required to band-limit the input signal. Therefore, it should be tuned for 1 GHz, with 400 MHz bandwidth and its insertion losses should be as low as possible. The mixer block is required to combine both the input signal, centered at 1.0 GHz with the LO frequency, in order to down convert the signal to 250 MHz. Furthermore, the following stage, the lowpass filter is used to band-limit the signal in order for it to be sampled by the ADC. The ADC sampling frequency should be twice the value of the signal bandwidth, therefore at least 900 MSps. Since we are only sampling noise, a very reduced number of bits is required, in the limit a single comparator can be used. Following (10), considering the worst case temperature near Mars, where T a = 250 K [7] and a bandwidth of B = 400 MHz, the thermal noise power is approximately N i = dbw. The temperature T a can be as low as 44 K when close to the Pluto orbit, which gives a thermal noise power N i = dbw, therefore increasing the SNR. N i = k B T B (10) Since, as stated earlier, the pulsar signal power is about -180 dbw, the receiver SNR can be as low as -60 db (c.f. Fig. 3). The SNR increase is achieved after sampling through the use of digital processing algorithms. Table 1, shows the defined specifications

6 for system blocks to be used in the receiver. The values were derived considering state-of-the-art offthe-shelf blocks which are available on the market at the present day. Furthermore, the evolution of the signals along the block chain is also shown in terms of power level. This receiver will only add 0.2 db to the noise level, being this system input SNR= 57.4 db and the output SNR= 57.6 db. Furthermore, it amplifies the noise signal to 43.2 dbw and the pulsar signal to dbw, being these the levels sampled by the ADC Positioning Accuracy The estimation of the pulsar TOA, can be obtained by employing the maximum likelihood (ML) criterion, assuming that the pulsar is a cyclo-stationary signal immersed in Gaussian noise as shown in Section 2. This enables the definition of a pulsar quality factor as Q p (i) = S 2 p(i)q timing (i) (11) where Q timing is the intrinsic pulsar quality for timing estimation which depends only on the pulsar mean profile and the sampling period used in the pulsar profile and S 2 p(i) is the squared pulsar average flux. The quality factor in (11) is useful to evaluate and quantify the suitability of each individual pulsar for navigation purposes. Starting from the 50 pulsars listed in [2], a subset of 45 pulsars were classified in terms of quality for timing estimation. The remaining five from the list, were not used since important information was missing. Such information was obtained using the European Pulsar Network (EPN) profiles and Stokes parameters and the Australia Telescope National Facility pulsar catalogue (ATNF) [8]. For the navigation solution accuracy estimation an uniform distribution of the used pulsars is assumed. In other words, it is assumed that these pulsars are available independently of the spacecraft location. Furthermore, it is also considered that the selected pulsars are able to solve the geometrical ambiguity as well as the dilution of precision problem. The set of receiver specifications is as follows: The polarization parameter is set at α = 1/2, therefore a single polarization is assumed; The receiver noise temperature is T rec = 15 K; The observation frequency is 1 GHz; Figure 8: Localization RMS error as function of the integration time. The main side lobe attenuation is taken as A sl = 40 db; Two antenna effective areas are considered A e = 1 m 2 and A e = 10 m 2 ; The receiver bandwidth is set as B = 400 MHz. To solve the ambiguity problem the reception of N p = 5 pulsars is considered (the first ones shown in Tab. 2), since it represents a practical scenario. The position error can be estimated as σ x T rec αa e B Tint (12) where T int is the receiver integration time in seconds. These assumptions lead to the results shown in Fig. 8, which should be regarded as upper bounds on the achievable performance by a real navigation system. Fig. 8 shows that using an antenna size as small as A e = 1 m 2, it is possible to have a positioning with an accuracy of 10.5 km after 280 min ( 4.5 hours) of integration time. For an antenna with A e = 10 m 2 the same accuracy can be achieved after 2.8 minutes, therefore an increase in area by 10 times, decreases the integration time by 100 times for the same accuracy or improves the accuracy by a factor of 10, for the same integration time. 5. CONCLUSIONS In this work guidelines for the design of a radio pulsar navigation system are reported. The advantages of radio pulsars for navigation when compared with X-ray pulsars are stated. Solutions for the use of antennas in space vehicles are presented. Furthermore,

7 Table 1: Low-IF receiver block specifications. LNA BP Filter Mixer LP Filter VGA Total Gain [db] NF [db] NF rx (cumulative) [db] Pulsar Signal Power [dbw] Thermal Noise Power [dbw] Table 2: 5 Best Pulsar for Navigation Purposes. Pulsar Name Flux S p (i) 1 GHz Period T p (s) Q p (i) [db] SNR [db] B B B B B system block specifications are defined for a Low-IF front-end receiver architecture, revealing its feasibility with state-of-the-art off-the-shelf system blocks. In addition, the results of a study on the expected accuracy of such a system is presented, leading to the conclusion that sufficient accuracy may be achieved in reasonable time for space vehicles navigation. ACKNOWLEDGEMENTS This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with references UID/CEC/50021/2013 and Incentivo/EEI/LA0021/2014 and also through Pulsar Plane Project (FP7-AAT-2012-RTD-L0) ( Part of this research has made use of the data base of published pulse profiles and Stokes parameters maintained by the European Pulsar Network ( 5. Sophocles J Orfanidis. Electromagnetic waves and antennas. Rutgers University New Brunswick, NJ, Victor Rabinovich and Nikolai Alexandrov. Antenna arrays and automotive applications. Springer Science & Business Media, RL Patterson, A Hammond, JE Dickman, S Gerber, E Overton, and M Elbuluk. Electrical devices and circuits for low temperature space applications RN Manchester, GB Hobbs, A Teoh, and M Hobbs. The ATNF pulsar catalogue REFERENCES 1. D.R. Lorimer. Handbook of Pulsar Astronomy. Cambridge Observing Handbooks for Research Astronomers. Cambridge University Press, Josep Sala, Andreu Urruela, Xavier Villares, Robert Estalella, and Josep M Paredes. Feasibility study for a spacecraft navigation system relying on pulsar timing information. ARIADNA study, G.S. Downs. Interplanetary navigation using pulsating radio sources Constantine A Balanis. Antenna theory: analysis and design. John Wiley & Sons, 2012.