Performance Analysis And Architectures For INS-Aided GPS .

despite a brief line-of-sight blockage. This capability canprevent carrier-phase cycle slips, and therefore haspotential applications in high performance navigationsystems where robustness to cycle slips is of paramountimportance [12,15].It should be noted that the term “tightintegration” has been used in a broader context toencompass both the tight and ultra-tight architecturesintroduced here, as done in [16].INERTIALf and ωMEASUREMENTUNIT(IMU)This analysis was performed with the use of aGPS software receiver, which was developed specificallyto study the details of ultra-tight integration. Thesoftware receiver tracks GPS sampled signals (real orsimulated) stored in data files, and gives standard GPSoutputs such as position, velocity, and attitude (if twosignals are used).INERTIALNAVIGATIONALGORITHMS f and ω (sensor biases)GPS-INERTIALBLENDINGEstimated Doppler (OR NCO commands) ALGORITHMSGPSRECEIVER(s)Figure 3.IntegrationPosVelAttPR, CP, Doppler (OR I&Q Samples)GPS/INSSystemwiththe system feature a modified phase-lock loop that utilizesexternal Doppler estimates, and a rate-aided delay-lockloop for maintaining code tracking during brief signaloutages. Although much of the discussion involvesdetails of the GPS tracking loops, some attention is alsogiven to external Doppler-frequency and clock-errorfrequency estimation. Other important design issues suchas GPS receiver clock drift and inertial sensor quality arealso covered, and evaluated versus system performance.Ultra-TightThe topic of ultra-tight integration is relativelynew, and is being developed by a few organizations,including Interstate Electronics Corporation [3], TheAerospace Corporation, and Draper Laboratories [11].The approach taken in their implementations involves theuse of a single large filter, or smaller multiple filters thatuse in-phase and quadrature samples from the GPSreceiver channels as measurements for updating the filterstates. Control of the replicated carrier and codegenerators also comes from navigation filter outputs,which are propagated with IMU measurements to achievehigh bandwidth carrier-phase tracking and anti-jamcapability. This more complex architecture variant ofultra-tight integration is also termed “deep integration”,and is characterized by implementing the closed-loopsignal tracking for all channels through the navigationfilter itself, thus precluding the need to maintain separatecode and carrier tracking loops [16].The integration structure presented in this papershows a simpler approach to ultra-tight integration thatutilizes classical control theory. The concepts that will bepresented can be used to study the theory andperformance gains of a GPS/INS navigation system withultra-tight integration, without the added complexity ofoptimal estimation. The straightforward architecture ofthe system is not limited to be a simple learning tool, butcan also potentially be implemented to realize a basicultra-tightly coupled system. The remaining sections ofthis paper will focus on the development of this simplearchitecture and its performance. The GPS receivers ofII. GPS TRACKING LOOPSThis section reviews some of the basic conceptsof traditional GPS phase and code tracking loops,including modeling and implementation. The ideas thatwill follow in the development of tracking loops thatincorporate inertial aiding will build upon thesetraditional loop structures to realize the structure of a GPSreceiver with ultra-tight integration. A more detailedtreatment of these concepts can be found in [6].A. The Phase-Lock Loop (PLL)After the GPS signal passes through the RF frontend and is sampled, the discrete signal is centered at anintermediate frequency (fIF), typically around 1-20 MHz.The GPS signal consists of the superposition of all GPSsignals in view of the antenna, and is processed byparallel channels in the receiver, where each channeltracks (or searches for) the signal from one satellite.After a satellite has been acquired, the PLL for thechannel tracks the phase and frequency of the carriersignal. A typical model of a second-order PLL is shownin Fig. 4.PhaseDiscriminatorϕ r (s)w(s)δϕ (s)"Σ"f PLL (s)Loop FilterK1τ 1s 1sϕ r ( s ) reference phasew( s) external phase noiseδϕ (s) measured phase errorf PLL ( s ) frequency tracked by PLLϕˆ ( s ) tracked phaseFigure 4. Model of Second-Order PLLNCO1 ϕˆ (s)s

In this model, the plant in the PLL model is anumerically controlled oscillator (NCO), which iscontrolled by fPLL. The loop filter is a compensatordesigned to track the reference phase with a typicalbandwidth of 15-30Hz. It is important to note that theloop filter design is a compromise between bandwidth andnoise suppression, because the reference phase and thephase noise are treated by the same transfer function,shown below:(1)ϕˆ ( s ) H1 ( s)(ϕ r ( s ) w( s ) )H1 ( s ) K1 (τ1s 1)2s K1τ1s K1(2)By maintaining lock on the phase of the carriersignal, the PLL also tracks any deviations of the carrierfrequency from the intermediate frequency. In Fig. 4, fPLLrepresents the frequency deviation from fIF.Thecomponents of fPLL include the Doppler frequency of thesignal (fdopp), due to relative motion between the receiverand the satellite, as well as frequency errors due to thelocal reference oscillator (fclk). The clock frequency errorsare introduced through the down-conversion and samplingprocess in the RF front end. Mathematically, fPLL can beexpressed as:fPLL fdopp fclk fnoise(3)The frequency content of fdopp can besignificantly higher than that of fclk, depending on the userplatform dynamics. As will be discussed later in thedevelopment of an ultra-tight integration structure, theknowledge of the satellite motion and user platformdynamics can be used to estimate the Doppler frequencyexternally. Providing this estimate to the PLL will thenpreclude the need to track the fast dynamics of fdopp withinthe loop, and will allow tightening the loop-filterbandwidth to improve noise performance. This principleis the crux of the ultra-tight integration concept.Figure 5 shows the actual structure of a PLL,including components like mixers and “accumulate anddump” (A&D) operations which perform averaging overone or more code periods.The oscillator generates in-phase and quadraturereplicas of the carrier signal for the channel, with afrequency equal to the sum of fPLL and fIF. The signalreplicas are used to mix the incoming signal to basebandfor extracting the navigation bits and measuring the phaseerror. As shown in Fig. 5, the PLL also utilizes theprompt CA code provided by the delay-lock loop, whichin turn, depends on the in-phase and quadrature basebandsignals provided by the PLL.B. The Delay-Lock Loop (DLL)The function of the DLL is to track the CA codecomponent of the GPS signal. In addition to generatingthe prompt code needed for tracking the carrier in thePLL, the code phase from the code generator is also usedto determine the pseudoranges for position determination.Although the structure of the DLL will not change withthe implementation of ultra-tight integration, someexplanation is necessary as to why a rate-aided DLLshould be used to complement the robustnessenhancements in the PLL through ultra-tight integration.Figure 6 shows the model of a noncoherent DLL.The code generator (CG) produces a replica of the CAcode at a frequency imposed by the loop compensator,which is usually a simple gain. The error signal in thismodel (δτ(s)) represents the difference between the phaseof the reference CA code (τr(s)) and that of the replicatedCA code (τr(s)).Compensatorτ r (s)GPSDataNCOfPLLK1sτ1 1ssinQuadratureTo DLLKCDLLCode rateCompensatorτ r (s)"Σ"K2DLL1 τ (s)sFigure 7. Model of Rate-Aided DLLA&DFigure 5. Structure of PLLPhaseDiscriminator1 τ (s)sFeed-forward branchData BitsLoop FiltercosK1DLLA rate-aided DLL uses the less noisy frequencyestimate determined by the PLL to aid the code-trackingloop, as shown in Fig. 7.fPLLIn-phaseδτ (s)Figure 6. Model of DLLPrompt CA Code(from DLL)A&D"Σ"CGFigure 8 shows the structure of a rate-aided DLL.As shown, the error signal is the difference of the earlyand late powers, which are computed by mixing the

replicated carrier (in-phase and quadrature) with early andlate code replicas.The gain that converts the PLL frequency to thecode rate is denoted KCDLL. With this configuration, thegain of the compensator can be reduced to improve noiseperformance, since the necessary bandwidth needed tomaintain code lock is provided by the feed-forwardbranch. However, the closed-loop configuration is stillneeded to track the slow and unpredictable drifts causedby code-carrier divergence [6]. In addition to improvednoise performance, a rate-aided DLL can also provide asynchronized code despite brief outages in the GPSsignal, as long as the external frequency aiding isuninterrupted and the outages are not long enough toallow significant code-carrier divergence. This advantagewill be exploited when uninterrupted aiding is availablewith ultra-tight ratorA&D( )2A&D( )2A&D( )2A&D( )2latepromptTo PLLFromPLLδτIn-phase carrierQuadrature carrierFigure 8. Structure of Rate-Aided DLLIII. DOPPLER AND CLOCK-ERRORFREQUENCY ESTIMATIONAs explained in section IIA, a traditional PLLtracks the Doppler and clock error components of thecarrier signal. If these components can be estimatedexternally, they can be used to aid the PLL to track withmore efficiency and robustness. The Doppler frequencyof the carrier can be estimated from the outputs of anInertial Navigation System (INS), an attitude reference,and satellite ephemeris data. As will be discussed later,the accuracy of these Doppler estimates depends on thequality of inertial sensors used.A. Doppler Frequency EstimationThe Doppler frequency of the carrier signal canbe expressed simply as the velocity of the receiverrelative to the transmitter, projected onto the line-of-sight(LOS) vector. The relationship is expressed in Eq. 4:K K1 Kf dopp (V RX V S ) 1 S(4)λwhereλK Wavelength of carrier at L1 frequencyVK RX Velocity of receiver antennaSVK S Velocity of satellite1 Unit LOS vector from receiver to satelliteThe components of Eq. 4 can be computed in any Earthfixed reference frame, such as Earth-Centered-EarthFixed (ECEF) or local East-North-Up (ENU). Thetransformation matrix between these two reference framesis easily computed as a function of latitude and longitude.The computation of the ECEF satellite velocityfrom ephemeris data is a well-known procedure,described in [13]. Another very simple and relativelyaccurate method for computing satellite velocity is toestimate the time derivative of its position.Thecomputation of the ECEF satellite position fromephemeris data is described in [19]. Using this method tocompute the satellite position as a function of GPS timeof-week, the velocity of the satellite can be approximatedas the discrete time-derivative of its position, with a smalltime-step ( t 1ms):R S (t t ) R SE (t )V SE (t ) E(5) twhereV SE (t ) ECEF velocity of satellite at GPS time of week tR SE (t ) ECEF position of satellite at GPS time of week tThe ENU velocity of the antenna is one of thecommon measurements from GPS receivers, but it doesnot have sufficient bandwidth to aid the PLL in afeedback fashion. However, an integrated GPS/INSsystem (as shown in Fig. 3) can provide velocitymeasure

of a low-cost GPS/INS attitude system for automobiles, and deep integration of INS systems with GPS tracking loops. Dr. Demoz Gebre-Egziabher is an assistant professor of Aerospace Engineering and Mechanics at the University of Minnesota, Twin Cities. His research interests are in the areas of navigation, guidance and control with an