Ultra-Tight Integration of Pseudolites with INS

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					     Ultra-Tight Integration of Pseudolites with INS
                                                   Ravindra Babu and Jinling Wang
                                         School of Surveying and Spatial Information Systems
                                                   University of New South Wales
                                                       Sydney - 2052, Australia

                                                                         foliages, and the effects due to interference can be mitigated. If
Abstract - Ultra-tight integration of GPS with INS has been              used along with the GPS constellation, the number of ranging
proposed to address various problems associated with these
                                                                         signals also increases providing better robustness. These
individual systems. However, a low cost INS may not sustain
prolonged GPS signal losses which frequently occur in indoors,           advantages have led to the augmentation of Pseudolites with
foliages, urban environments etc. Moreover, the upcoming                 GPS in safely critical applications such as aircraft precision
applications such as LBS require positioning systems to work in          approach and landing, and deformation monitoring. In fact, a
all these environments and this stimulates the interests in              ‘Pseudolite-only-Navigation’ is possible where GPS signals
developing alternative positioning systems. A ‘Pseudolites-only’         cannot be received or very weak.
constellation which artificially simulates the GPS-constellation is                A different set of PRN codes are used for both the
an ideal choice to provide positioning solutions in these non-           GPS and Pseudolite constellations. While PRN codes 1 to 32
benign environments. The main advantage in using the                     are assigned for satellite network, the PRN codes 33 to 36 are
pseudolites is its flexibility - the geometry and the signal
                                                                         used for ground-based Pseudolites. The power output from the
characteristics can be optimized for a particular application. To
combat signal degradation due to reflecting/refracting                   Pseudolite transmitters is usually quite high. When this high
environments and receiver dynamics, the pseudolites can be               power reaches the receiver tracking both GPS/Pseudolite
integrated with INS to improve the overall system robustness.            signals, they can jam the weak GPS signals and as well saturate
          Two problems that affect the receiver performance in           the receiver RF-front end. This is called the near-far problem.
using ‘Pseudolite-only’ constellation are: higher rate changes in        To resolve this, the Pseudolite transmitters are usually pulsed
Doppler due to large geometry changes, and signal fluctuations.          with duty cycles ranging from 10 to 30%. For a typical 10%
This paper proposes the ultra-tight integration of pseudolites with      duty cycle per C/A code epoch, the transmitter is ON for 100
INS to address these potential problems. Firstly, the tracking loop      µsec and OFF for 900 µsecs. Therefore, when averaged over
performance in dynamic scenarios is enhanced by integrating the
                                                                         one complete epoch the averaged received signal power is
INS measured dynamics with the carrier tracking loops.
Secondly, as the tracking loops are closed by the integration            closer to the satellite power, i.e. -130 dBm. The atmospheric
Kalman filter, any larger fluctuations in the Pseudolite I and Q         effects are also quite different compared to a GPS signal. The
signals will not severely affect the receiver tracking. In this paper,   tropospheric influence is predominant for Pseudolite signals as
a series of numerical experiments are performed to study the             they propagate only through this atmospheric layer.
performance of the pseudolite/INS ultra-tight integration. The                     Despite having multitude of advantages, the
results show a significant improvement in measurements                   Pseudolite signals are vulnerable in indoor environments where
accuracy, acquisition times over conventional ultra-tight                the signals get degraded significantly due to the presence of
integration which uses only GPS signals. The propagation effects         several reflecting and moving objects. Though the degradation
of the pseudolite signals, its characteristics and their effect on
                                                                         usually will be momentary, nevertheless, this will affect the
tracking loops are also discussed in detail.
                                                                         overall system performance. By augmenting with additional
                                                                         sensors, these short-gaps can be bridged. One of the obvious
                   I.        INTRODUCTION                                choices for the augmentation sensors in navigation is the
                                                                         Inertial Navigation System (INS). Though autonomous in
         Pseudolites, also known as Pseudo-Satellites, are               nature, these sensors exhibit errors and when integrated in time
ground based GPS signal transmitters that transmit the ranging           during the mechanization process, these errors grow.
signals on the same GPS L1 frequency of 1575.42 MHz. They                Therefore, they need to be continuously calibrated. An
can also be considered as additional satellites placed on ground         extended Kalman filter integrates both Pseudolite and INS
to improve the reliability, availability and the overall geometry        measurements to calibrate the INS errors. The focus of this
that leads to improved receiver performance. One of the main             research is to integrate both these data sets in ultra-tight mode,
advantages of the Pseudolites is its flexibility. By placing them        i.e., I (in-phase) and Q (quadrature) measurements from
at appropriate locations the overall geometry can be                     correlator are integrated with Position, Velocity and Attitude
strengthened, in particular, the vertical geometry can be                from INS. A Doppler signal can be extracted from the
improved resulting in better vertical accuracy [6] [7].                  corrected INS, and when this gets integrated with receiver
Furthermore, as the Pseudolite signals are stronger at the               tracking loops, any dynamics on the GPS signal caused by the
receiver due to shorter distances, the navigation can be                 user motion is removed. With dynamics removed, the tracking
performed in indoors and                                                 bandwidth can be reduced resulting in several advantages.
          The objective of this research is to demonstrate the       most of the modern-day commercial receivers tend to operate
advantages of integrating Pseudolite and INS in ultra-tight          in such non-benign environments where either the signal
mode for providing high availability, reliability and positioning    strength is too weak or completely blocked. To mitigate these
accuracy in indoor environment. Simulation experiments were          effects and to have a seamless navigation in indoors and
performed with both ‘Pseudolites-only’ mode and                      foliages, the Pseudolite/INS integration technique has been
‘Pseudolites/INS’ integration mode and the results are               proposed in this paper. By placing the Pseudolites at
provided. For the sake of comprehensiveness, the ultra-tight         appropriate locations, a receiver can navigate virtually in any
integration philosophy is also given. The results show that the      place as the signal strength from Pseudolites is higher than
measurements accuracy improves using the Pseudolite/INS              GPS.
integrated system.                                                            The advantage of using Pseudolites for navigation is
                                                                     the improved geometry, defined by GDOP (Geometric Dilution
                                                                     of Precision) which is provided by the trace of the position
                                                                                                T    −1
         II.      PSEUDOLITE CONSTELLATION                           covariance matrix A = ( H H ) where H is the measurement
                                                                     matrix, which improves the overall accuracy, and also
          The use of GPS signals for indoor navigation is very       enhancing the availability and reliability of tracking. The GPS
limited as the signal gets heavily attenuated as it penetrates the   signals can also be augmented to this to further improve the
walls and other structures before reaching the receiver antenna.     performance; however, this can be limited only to outdoor
The rule of thumb for attenuation is approximately 10 dB/floor;      applications as the GPS signals may not be tracked in indoors.
however, this depends on the constituents of the structures. For     By placing the Pseudolites at suitable locations, the operating
example, if the receiver is placed on the ground floor in a 3-       environment can be optimized for both geometry and
floor building then the received signal strength will be of the      availability of signals.
order of -160 dBm. To extract such weak signals, high
sensitivity or weak signal algorithms have to be implemented
which are complex. Any further reduction in the signal
strength will render even these techniques ineffective. In fact,

                                              Fig. 1. Pseudolite Constellation
          In using the ‘Pseudolite-only’ constellation, an          receiver are only in the order of meters, when the receiver
important consideration that should be given is the errors in the   approaches a transmitter, the received power from that
signal modeling, as this would be significantly different from      transmitter starts increasing significantly which is termed as a
the errors on the GPS signals. The atmospheric and multipath        near effect, whereas the power drops down much faster from
errors are considerably different for Pseudolite signals when       the other transmitters which is the far effect. This higher
compared to GPS, whereas the receiver noise is common to            power from one transmitter subduing other signals is termed as
both the signals. As the Pseudolite signals propagate only          a near/far problem, and this is of paramount importance to be
through troposphere and also at lower elevation angles, the         addressed in the case of Pseudolite systems due to the smaller
modeling for the tropospheric errors would be different. The        geometries involved.
tropospheric error component is spatially correlated, i.e. the
errors will be almost same for receivers within a boundary.
These spatially correlated errors can be reduced by using
differential techniques. However, the uncorrelated errors such
as multipath and receiver noise require sophisticated signal
processing.     It should be noted that multipath is the                        Far Effect
predominant error component in the indoor navigation as the
received signal bounces off from several reflectors which                                Normal Operation
comprises the environment. For a stationary receiver, the
multipath error would be a constant which can be easily
accounted for, whereas for a dynamic receiver the multipath                                     Near Effect
becomes a time varying component which requires
sophisticated signal processing techniques and customized
antenna designs. The ionospheric error term can be discarded                                      Pseudolites
from the signal model as the signals will not pass through
          The Pseudolite constellation that is used for the
experiments is shown in Fig. 1. Four Pseudolite transmitters
are placed at right angles to each other to give the best

III.     PSEUDOLITE SIGNAL PROPAGATION EFFECTS                                 Fig. 2. Representation of Near/Far Effect

          Despite several advantages of the Pseudolite systems,              Fig. 2 is the representation of the near/far effects that
there are some serious issues that need to be addressed before      are encountered in typical Pseudolite systems. As shown in the
its application. Two of the major issues are: Near/Far Problem,     figure, for best performance the receiver should be in the
Multipath.                                                          middle layer which is the normal operation zone. In both the
                                                                    near and far zones, the effects of one transmitter would start
A. Near/Far Problem                                                 taking precedence over the others degrading the overall
         It is well known that GPS and Pseudolites are Code-        performance. The solution to this effect is the pulsing. Instead
Division Multiple Access Systems (CDMA), i.e.                       of transmitting the signals continuously, the Pseudolites
Pseudorandom noise (PRN) sequences of appropriate length            transmit in pulses defined by the duty cycle. The typical duty
are modulated with the data messages to spread its spectral         cycle is about 20% for Pseudolite systems, i.e., the transmitter
density over a wider bandwidth to improve the efficiency of         is ON for only 20% of the time and transmits about 200 chips
transmission. Since the signals from all the satellites are         instead of the full 1023 chips. This has the effect of reduced
transmitted on the same frequency, the isolation between            received power thereby mitigating the near/far effects.
different satellites in the receiver is obtained from the cross-
correlation properties that can be achieved with the PRN codes.
A cross-correlation of 21 to 30 dB is achieved in the case of       B. Multipath
GPS signals, and as the GPS satellites are about 20,000 km                    Another issue that needs to be resolved is the
away from the receiver on the surface of the earth this property    multipath. In the case of indoor navigation, as there are many
is maintained for all the satellite signals. However, in the case   hindrances to the direct signal transmission, the signal at the
of Pseudolite systems, due to the proximity of the receiver to      receiver is a superposition of a direct and several
the transmitters this cross-correlation property cannot be          reflected/refracted signals. The effect of this is the signal
guaranteed always. The power received at the receiver is            fluctuations which result in the threshold degradation in both
inversely proportional to the square of the distance the signal     the acquisition and tracking loops of the correlator. The
travels. As the distance between Pseudolite transmitter and the     simulated multipath used for these experiments is shown in
Fig. 3. A 1st order butterworth filter with a time constant of 1             error modeling is removed [4][5]. The I and Q measurements
second is used to simulate the multipath errors.                             for a Pseudolite receiver can be mathematically modeled as

                                                                                          ( n + 1) T       [sin ( w e t + φ e ) ] d t + T k p + d rk p + (1)
                                                                             I =      ∫   nT
                                                                                                        d m kp + ε kp

                                                                                           ( n + 1) T      [co s( w e t + φ e ) ] d t + T k p + d rk p +       (2)
                                                                             Q =      ∫   nT
                                                                                                        d m kp + ε kp

                                                                             where w e = w − w ' and φ e = φˆ − φ ' are the frequency and
                                                                             phase errors respectively.   w & φˆ are the local estimates
                                                                             generated by the tracking loops and w ' & φ ' are the reference

               Fig. 3. Indoor Multipath Error Simulation                     frequency and phase components respectively.                                  Tkp is the
                                                                             tropospheric delay, drk is the pseudolite location error,
C. Pseudolites Propagation Model                                             dmkp is the multipath error, ε kp is the measurement noise. k
        Normally, the mathematical models for the receiver                   and p denote the receiver and the pseudolite respectively. It
measurements such as I, Q, Pseudo-range, carrier phase                       can be observed from equations (1) and (2) that there is no
comprises the ionospheric correction term for GPS signals.                   signal propagation correction term for ionosphere, as both the
However, as the Pseudolite signals are propagated within the                 transmitters and receiver are placed on ground.
troposphere, the ionosphere component in the measurement

                                                  Integrate &
                                                  D um p

(ca rrie r+ d ata)
                                        NCO                     L oop                          D iscrim i
                                                                Filter                         nator


                                                                                                                      K alm an Filter
                                               Integrate &                                                  Q                                 P,V, Att
                                               D um p

                                               Interpola                 D oppler
                                               tor                       E stim ate

                                   ∇v, ∇θ         Strapdow n                                           P,V ,A tt
                      IM U                        M echanizat

                                                      Fig. 4. Ultra-tight integration
IV.      ULTRA-TIGHT PSEUDOLITE/INS INTEGRATION                             The terrestrial psi-angle error model is used for
                                                                    process modeling.
         The integration of GPS with INS for robust navigation
is well known in the field of navigation. Both these systems        dr = − ρ * dr + dv
have been integrated in loosely-coupled and tightly coupled         d v = − (Ω * w ) * d v + ∇ − ψ * f                           (3)
modes for about 2 decades. The start of this decade has              dψ = − w *ψ + ε
witnessed the development of ultra-tightly coupled architecture
in which the tracking loop measurements, I and Q, are                dr is the position error vector, dv is the velocity error vector,
integrated with the INS data. In addition, a Doppler signal is       dψ is the attitude error vector, ρ
                                                                                                            is the true frame rate with
derived from the Kalman filter estimates in conjunction with        respect to the Earth, Ω is the Earth rate vector, w is the true
the ephemeris which reflects the Doppler on the GPS signal          coordinate system angular rate with respect to the inertial
due to user movement. This derived Doppler signal when
                                                                                                                       f is the specific
integrated with the tracking loops remove the Doppler on the        frame, ∇ is the accelerometer error vector,
GPS signal caused by the user motion. As the dynamics on the        force vector, and  ε is the gyro drift rate vector.
GPS signal is reduced substantially, the tracking loop
bandwidth can be optimized to track only the clock dynamics         C. Measurement Model
[1]. Since the Pseudolite signals are similar to GPS signals, the            The measurement model which relates the I, Q
baseband loops can be easily configured to receive the              measurements from the Pseudolites with the P, V, A from INS
Pseudolite signals, i.e. PRN 33 to 36. The quadrature signals, I    is given as [2]
and Q, from the correlator are fed to a 17-state extended
Kalman filter, 3 position, 3 velocity, 3 attitude, 3 gyro bias, 3
                                                                    H = [{hxi , hyi , hzi ,1},{hxi , hyi , hzi ,1}]i =1:n        (4)
accelerometer bias, 1 clock bias, 1 clock drift, which estimates
the inertial sensor biases.        The ultra-tight integration
architecture is shown in Fig. 4.                                    where ‘n’ is the number of satellites visible and

A. Data Processing
                                                                           ∂E[ I ] ∂φe ∂E[ I ] ∂we 
         The Pseudolite measurements at the receiver input are      hx1 =             +                                        (5)
computed based on the receiver trajectory. To maintain                     ∂φe ∂x       ∂we ∂x 
consistency with the GPS signals, the signal power is               and
maintained at -130 dBm with an SNR of -20 dB. The
trajectory is simulated for indoor environment, and therefore,
appropriate multipath noise is added to the signal. As the                 ∂E[Q ] ∂φe ∂E[Q ] ∂we 
                                                                    hx1 =            +                                        (6)
baseband loops in the correlator are updated at every 1 msec,              ∂φe ∂x      ∂we ∂x 
the I, Q measurements are generated at the same rate, and since
this data rate is higher for the Kalman filter to process, the      where we and φe are the frequency and phase errors
measurements are first decimated by a factor of 10. The signal
processing based decimation algorithm was applied, though it        respectively, and E [I] and E[Q] are defined as
was observed that a down sampler produced about the same
performance. The simulated INS measurements are also                           − A  c o s ( w e ( n + 1) T + φ e ) − 
obtained at a rate of 100 Hz. After synchronizing these two         E[I ] =                                                    (7)
                                                                               2 we  co s(we n T + φ e )             
data sets, they are fed to a centralized Kalman filter which
estimates the inertial sensor errors. The system equations for
                                                                                 A  s in ( w e ( n + 1) T + φ e ) − 
Kalman filter are derived from the number of error states           E [Q ] =                                                    (8)
chosen and the noise models. A 17-state Kalman filter is used                  2 w e  s in ( w e n T + φ e )        
to generate the error estimates in position, velocity, attitude,
gyro and accel bias, receiver clock errors. The Doppler derived
from the INS position and velocity is interpolated by a factor of                         V.         SIMULATIONS
10 to synchronize with the update requirements of the
correlator loops.
         The Kalman filter estimates the errors by recursively               It is convenient to use the simulations to develop the
running the process and measurement models. Both these              proof-of-concept models, and therefore, the same approach is
models are extensively covered in literatures [3] [8] [9], and      taken for this research also to test the performance of the ultra-
therefore, only the equations are provided for comprehensive        tightly integrated Pseudolite/INS in indoor environment.
sake.                                                               Several software components have been developed, the major
                                                                    being – receiver trajectory generation, Pseudolite/INS signal
B. Process Model                                                    generation, software based tracking, and ultra-tightly integrated
                                                                    Kalman filter.
                                                                      measurements. These measurements were generated at a 100
                                                                      Hz rate.

                                                                      B. Software Receiver Performance
                                                                               The simulated Pseudolite signals are fed to the Data
                                                                      FusionTM Corporation’s Software receiver to test the
                                                                      performance of acquisition and tracking loops [10]. The
                                                                      receiver is tested in two different modes: i) in a stand-alone
                                                                      mode ii) in ultra-tightly integrated mode where the INS-derived
                                                                      Doppler signal is fed to the baseband loops.

                                                                      Mode 1
                                                                                Since the total Doppler was within +/- 25Hz and the
                                                                      total frequency bin size was 667 Hz, the number of search bins
                                                                      was limited to 1. The signals are searched in both the code and
                                                                      carrier domains by Delay Locked Loop (FLL) and Frequency
                                                                      Locked Loop to acquire the carrier frequency and code phase
                  Fig. 5. Reference Trajectory
                                                                      respectively. Both the I (in-phase) and Q (quadrature) phase
                                                                      measurements are accumulated and the envelope
A. Trajectory, Signals Generation
                                                                         I 2 + Q 2 is compared against the threshold. As the number
          The user trajectory which is defined by the position,
velocity, attitude and time is created in segments. The               of frequency bins is 1 in this case the search is performed in
reference trajectory that was used for the experiments is shown       only code domain which reduces the acquisition time, however,
in Fig. 5. In a typical indoor environment, the trajectory does       in adverse indoor conditions the loops frequently looses lock
not contain any significant dynamics, so a user velocity of 1m/s      leading to signal fluctuation.        The performance of the
was considered for the experiments.             For the sake of       acquisition loops is shown in Fig. 6.
simplicity, a smooth trajectory was created. The initial co-                    It can be observed from the plot that there is a
ordinates and the simulation duration are required to initialize      significant degradation in the acquisition performance with the
the software. The trajectory profile is then stored in a text         total power dropping down. The performance of the PL36
format which is then used for the Pseudolite and INS                  signal was significantly degraded compared to the other
measurements generation.                                              signals, as this may be caused due to the poor geometry
          The generation of pseudolite signals is similar to the      between the user trajectory and the Pseudolite transmitter. It
generation of GPS signals except that the Pseudolites use PRN         must be noted that the code loop has considerable influence on
codes 33 to 36. However, some points worth considering in             the acquisition Doppler performance.             The tracking
the simulation of the signal are: i) the ionospheric errors are not   performance is shown in Fig. 7. The vertical axis in the figure
considered as the signal do not propagate in ionosphere ii)           corresponds to the Doppler changes. Due to the signal
standard tropospheric model is used for the preliminary               fluctuations the tracking performance also gets degraded, and
experiments iii) the signals are modeled with multipath errors        most of the time the loops come out of the tracking stage and
iv) as the distance between the Pseudolite transmitters and the       jump back to acquisition. The Fig. 7 shows that the Doppler
receiver trajectory is known, appropriate noises such as biases,      variations are about 15 Hz. As the carrier tracking bandwidth
errors and measurement noises are added to the signal. The            is set at 12 Hz, the loops go back to the previous stage of
software receiver processes IF signals only, therefore the            narrowband FLL acquisition.
Pseudolite signals are generated at an IF frequency of 21.25
MHz. The Doppler modulation for the signals is derived from
the relative velocities between the Pseudolite transmitter and
the receiver. The signal is stored as a 1 byte integer format
which is read by the Software receiver.
          From the user trajectory, the raw INS measurements,
incremental angular and linear velocities, are generated, and
accelerometer and gyro biases/scale factor errors, random
noises, earth’s rotation are added to form the ‘true’ INS

                                      Acquisition Performance (stand-alone mode)

                                        Fig. 7. Tracking Performance (stand-alone mode)

Mode 2                                                      strapdown algorithms generate the position, velocity and
        The same experiments are performed by integrating   attitude which are input to the 17-state extended Kalman filter.
the INS. After mechanizing the INS measurements, the        The filter estimates the INS errors by incorporating
the correlator measurements during the measurement update        acquisition and tracking performance improves as shown in
process. From the corrected INS, a Doppler signal is generated   Fig.s 8 and 9 respectively.     The Fig. 8. shows that the
which reflects the user dynamics. This Doppler signal also       envelope power from the acquisition loop is stable. Another
contains a residual component resulting from unmodeled           reason for the improved performance of the loops is due to the
errors. When integrated with the tracking loops, it mitigates    usage of medium grade INS (1 deg/hr gyro bias, 10 mg accel.
the Doppler on the GPS signal. Though the amplitude              bias). However, the loops performance can get degraded even
fluctuations are still the same, nevertheless, the external      for momentary loss of signal if a low cost INS is used.
Doppler from INS helps lock the loop and therefore both the

                                      Fig. 8. Acquisition Performance (ultra-tight mode)

                                            Fig. 9. Tracking Performance (ultra-tight mode)
         VI.      KALMAN FILTER ESTIMATION                          alone Pseudolite system. Furthermore, the Kalman filter
                                                                    results also confirm the improved performance of the
         The error estimates between the reference trajectory       integrated system. These are only some of the preliminary
and the filter estimated values are shown in Fig. 10. The           results, and more research is expected to be conducted in due
Kalman filter was run at 100 Hz rate, i.e. GPS measurements         course.
are processed at that rate. As the I and Q estimates from the
tracking loops are within bounds in ultra-tight mode, the
Kalman filter position estimates (North and East error                                ACKNOWLEDGMENT
components) are smooth and convergent as shown in the
figure. It should be noted that there were no big anomalies                   This research is supported by an ARC (Australian
despite the multipath due to the bridging capability of high        Research Council) – Discovery Research Project on ‘Robust
quality INS.                                                        Positioning on Ultra-tight integration of GPS, Pseudolites and
                                                                    inertial sensors’.


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