GPS Receiver Performance Using Inertial-Aided Carrier Tracking Loop

Transcription

1 GPS Receiver Performace Usig Iertial-Aided Carrier Trackig Loop Tsug-Yu Chiou Staford Uiversity, Staford, CA BIOGRAPHY Tsug-Yu Chiou is a Ph.D. cadidate i the Aeroautics ad Astroautics Departmet at Staford Uiversity. He received his B.S. i Aerospace Egieerig i 1998 from Tamkag Uiversity, Taiwa ad his M.S. from Staford i. His research curretly focuses o the performace aalysis ad validatio of Iertial-aided GPS carrier-trackig loop. ABSTRACT Radio frequecy iterferece (RFI) has bee a perplexig problem, affectig the avigatio quality of the Global Positioig System (GPS). The presece of the RFI, or eve hostile jammig, will reduce the effective received sigal power, ad thus degrade avigatio accuracy, cotiuity, ad itegrity of the system. A proposed ext geeratio aircraft avigatio system for the U.S. military called the Joit Precisio Approach ad Ladig System (JPALS) [1, ] is a example of a system that requires high performace eve i severe RFI eviromets. Previous research has proposed usig iertialaided GPS carrier-trackig loops as a compoet of the ati-jam solutios [3, 6]. It is believed that a iertialaided GPS receiver is more robust to wide-bad RFI. By elimiatig the eed to track platform dyamics, the iertially-aided GPS trackig loops ca operate at arrow oise badwidths, thus lowerig the trackig thresholds to a lower carrier-to-oise (C/N). As a result, the lower C/N thresholds icrease robustess to the RFI. The purpose of this paper is to verify the performace of a iertial-aided GPS receiver experimetally, sice the performace has ot bee fully validated. A metric to evaluate the iertial-aided GPS receiver is, i wide-bad RFI eviromets, the tolerable degradatio of carrier-to-oise ratio (C/N) ad its correspodig loop badwidth. A uique ad flexible iertial-aided GPS test-bed has bee developed to coduct experimets to iclude various combiatios of iertial measuremet uits (IMUs) with GPS receiver clocks. I additio to differet choices of IMU, the GPS carrier-trackig loop ca be implemeted ad modified usig differet orders of trackig-loop filters ad various oise badwidths. Moreover, the level of C/N is tuable by ijectig various power levels of white Gaussia oise ito the same collected GPS frot ed sigals. Future work will cosider details of clock dyamics i iertial-aidig techiques. As show i this study, the receiver clock phase error iduced by the vibratig platform sigificatly limits the performace of the itegrated GPS/INS avigatio system. A accurate measuremet of the power spectral desity (PSD) of the receiver clock vibratio ad a precise estimate of the acceleratio sesitivity vector are two buildig blocks for advacig this iertial-aidig techique. A better improvemet of C/N is expected if a higher quality clock, such as a atomic clock, were used to drive the GPS receiver. I the low oise badwidth rage, the clock dyamics domiate the GPS receiver trackig performace. I. INTRODUCTION The Joit Precisio Approach ad Ladig System (JPALS) [1, ] is the ext geeratio ladig system for the U.S. military. JPALS will provide joit operatioal capability for U.S. forces to accomplish both covetioal ad special missios i a wide rage of eviromets, which iclude ot oly various meteorological ad terrai coditios, but also hostile radio-frequecy iterferece (RFI) circumstaces. Thus, itegrity ad cotiuity are the two most striget requiremets for JPALS. For example, the required itegrity ad cotiuity for the Sea-based JPALS, the Navy variat of the system, are 1-7 / approach ad 1-6 / 15 sec., respectively[]. ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 895

2 However, the RFI poses a severe threat to GPS itegrity ad cotiuity. Therefore, mitigatig RFI is a priority for the JPALS program. There are several techiques cosidered to reduce the effects of RFI o system itegrity ad cotiuity [3]. For istace a jammig-to-oise ratio (J/N) meter [4], receiver frot-ed filterig techiques, arrowbad iterferece-processig techiques, or with atea ehacemet. This paper focuses o yet aother techique: code/carrier trackig loop aidig. This is accomplished by applyig exteral aidig ehacemets ito code / carrier-trackig-loops. I this research, the exteral aidig source is a IMU. I this itegrated GPS/INS scheme [5, 6], the structure of the traditioal GPS carrier-trackig loop is chaged to eable the fusig of the exterally estimated Doppler frequecy, provided by iertial measuremet uits, ito the carrier-trackig loop. This iertially-aided trackig loop allows the reductio of the carrier-trackig loop badwidth, by elimiatig the eed to track the platform dyamics. The extra Doppler frequecy shift caused by the motio of the GPS receiver defies the platform dyamics. The above frequecy shift usually chages rapidly with time, ad therefore icreases the burde of the carrier-trackig loop to lock i the phase. With a iertially-aided trackig loop, the IMU defies the extra dyamics, so that the trackig loop does ot have to track these rapid frequecy shifts. A lower oise badwidth is sufficiet, makig the receiver more able to reject oise. As a result, it is more robust to the widebad RFI. Previous research i [7] has show that a additioal 4 to 5 db-hz margi o carrier-to-oise ratio (C/N) ca be achieved usig the iertial-aidig techique. Based o previous studies, a experimetal validatio is implemeted i this study to test the GPS performace i a wide-bad RFI eviromet. A flexible test-bed has bee developed to validate the iertial-aidig techique. Usig this test-bed, we ca test the performace of carrier-phase measuremets for combiatios of differet orders of carrier-trackig loops, differet coherece itegratio times, differet receiver oscillators, ad differet iertial measuremet uits, ad all uder varyig wide-bad iterferece. Specifically, this paper provides results focusig o the performace for differet orders (secod ad third-order loops) of carrier-trackig loops, combied with two types of GPS receiver oscillators. Furthermore, the results are evaluated based o various oise badwidths ad differet C/N coditios. The tuable badwidth is accomplished usig a software receiver ad the adjustable C/N is achieved by ijectig white Gaussia oise ito the sampled GPS frot-ed sigals II. OVERVIEW OF GPS CARRIER-TRACKING LOOPS To uderstad the iertially aided carriertrackig loop ad the results of this paper, uderstadig how the GPS carrier-trackig loop fuctios is essetial. This sectio presets a overview of GPS carrier-trackig loops. More thorough discussios of the GPS carriertrackig loop are provided i [3, 8 ad 9]. A GPS L1 sigal cosists of the avigatio data, the Coarse/Acquisitio (C/A) code, ad the Radio-Frequecy (RF) carrier. The GPS atea captures the GPS sigals i view; the sigals the pass through the RF frot ed ad are sampled as well as dow-coverted to a proper itermediate frequecy (IF) (1-MHz). At this poit, the GPS sigal superimposes all the sigals from the satellites. Numerous parallel chaels are required to acquire ad track the sigal from each satellite. At each chael, upo acquirig a sigal from a satellite, a phase-locked loop is used to track the phase ad frequecy of the carrier. Figure 1 shows the structure of a geeric GPS phase-locked loop [3], with or without Doppler-aidig iput. Figure 1: GPS carrier-phase trackig loop To extract the avigatio data, the digital IF iput must be further dow-coverted to the basebad. This is called a carrier wipeoff operatio which is performed by multiplyig the carrier replica, as show by the first pair of multiplicatio i Figure 1. The frequecy of the replica carrier used for this dow-coversio is obtaied by measurig the frequecy ad phase offset due to platform motio ad clock dyamics. As a result, this is the heart of the PLL. The device geeratig the replica carrier is usually a voltage-cotrolled oscillator (VCO) or mathematically represeted by a umerically-cotrolled oscillator (NCO). The upper brach multiplied by the cosie carrier replica is called the i-phase chael (I), while the lower brach multiplied by the sie carrier replica is called the quadrature chael (Q). I ad Q ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 896

3 sigals here are primarily the result of the multiplicatio of the thermal oise ad the replica digital cosie ad sie wave, respectively. I other words, the desired sigal is still buried uder the thermal oise floor. To collapse the I ad Q sigals to the basebad, a code-strippig process is required. This code wipeoff process is achieved by multiplyig the I ad Q chaels by the prompt code replica. Thereafter, the sigal has bee dow-coverted to the basebad, ad the predetectio itegratio process is executed i a itegrate ad dump operatio, which performs measuremet-averagig over at least oe or more code periods. The loger the averagig time is, the more oise is suppressed. The output of this process is the iput to a phase discrimiator, which measures the phase offset betwee the true carrier ad the replicated iphase carrier. Oe example of the phase discrimiator is the arctaget of Q/I. The output of the phase discrimiator is the phase agle of the vector sum of I+Q with respect to the I-axis. This phase agle is the used as a cotrol commad to the loop filter. The loop filter is a compesator desiged to track the phase (ad frequecy) of the iput carrier with the desired dyamic rage ad oise suppressio performace. The output of the loop filter is a frequecy commad for the NCO, which steers the replicated carrier frequecy to lock i the phase. As a result, the objective of the carrier-trackig loop or phase-locked loop (PLL) is to maitai the phase error betwee the replica carrier ad the iput GPS carrier sigals at zero. Therefore, the phase error is a importat parameter to characterize the performace of the PLL. To aalyze the phase error of the PLL, a liear model illustrated i Figure is usually used. The iput ϕ i is the phase of the icomig digital IF sigal. The output ϕ o is the phase steered by the PLL to track the iput ϕ i. The summatio symbol i Figure represets the phase discrimiator i Figure 1. Thus, δϕ is the phase error betwee ϕ i ad ϕ o. Ideally, δϕ stays exactly at zero oce the phase is locked i. However, the icomig phase sigal ϕ i is iflueced by the thermal oise, the dyamics of the platform, ad eve the satellite clock dyamics. Furthermore, the replica carrier phase ϕo is affected by the receiver clock dyamics ad a extra phase istability iduced by the platform vibratio. As a result, the phase error source icludes the thermal oise, platform dyamics stress error, receiver ad satellite clock dyamics, ad the receiver clock error iduced by the platform vibratio. A higher badwidth PLL has better performace o trackig the dyamics. However, a higher badwidth PLL demostrates poor quality o oise suppressio. Therefore, a trade-off is eeded whe desigig a PLL. The phase error respose is a parameter for judgig the proper PLL badwidth. The stadard deviatio value (1- sigma) of the steady state phase error is of iterest i this paper. 1-sigma phase error is used as a metric to characterize the performace of the PLL aloe or the iertially-aided PLL. Note that the PLL phase error is the phase differece betwee the local replica ad the icomig sigal. The 1-sigma phase error ca be represeted as equatio (A13). Figure : A Lier Model of a Phase-Locked Loop III. INERTIALLY AIDING CARRIER-TRACKING LOOP Followig the above discussios of PLL phase error, oe ca cosider removig the dyamic stress error by applyig iertial aidig. Note that the iertial aidig cotributes to the PLL by providig the estimated Doppler frequecy due to ay motio betwee the receiver ad the satellite. Figure 3 shows a liear model of the PLL with Doppler aidig. f PLL represets the carrier-frequecy deviatio from the itermediate frequecy (IF). As discussed i the previous sectio, this frequecy deviatio is primarily comprised of three compoets: the Doppler frequecy ( f dopp ) due to the relative motio betwee the receiver ad the satellite; frequecy errors due to receiver or satellite oscillators ( f clk ); ad errors due to thermal oise ad iterferece ( f oise ). Equatio (1) represets f PLL i terms of these compoets. fpll = fdopp + fclk + foise. (1) Figure 3: A Lier Model of a Phase-Locked Loop with Doppler-aidig ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 897

4 Iertial aidig is implemeted by addig the exteral Doppler-frequecy estimate to the output of the loop filter. This exteral iput may be calculated from a GPS/INS avigatio filter, whose avigatio outputs are primarily based o iertial measuremets i the short term. Iclusio of the exteral Doppler-frequecy estimate removes the task of trackig vehicle dyamics from the PLL, but may itroduce a differet form of dyamic stress i the form of errors from the exteral Doppler estimates. Therefore, the PLL with Doppler-aidig must be desiged to track phase-dyamics due to the receiver oscillator istability ad Doppler-estimate errors. As a result, the value of the loop-filter frequecy output for a iertialaided PLL is show i Figure 5, mouted o a rigid frame fixed o the test-vehicle s roof rack. f f + f δ f. () PLL clk oise dopp Assumig that the dyamics of the Doppler-estimate errors are slower tha vehicle dyamics, the use of Doppler-aidig allows for oise badwidth reductio whe compared to a traditioal PLL, hece, improvig its oise-suppressio performace. The focus of this paper is to provide the experimetal results of the iertial-aidig techique, usig the test-bed developed by the GPS lab at Staford Uiversity. I the sectio highlightig test results, the performace of 1-sigma phase error as a fuctio of PLL closed-loop oise badwidth as well as C/N is evaluated. Figure 4: The Horizotal Speed of the Collected Data GPS Ateas Automotive IMU IV. DATA COLLECTION AND EXPERIMENTAL SETUP Data Collectio Experimet The data collectio experimet was coducted with a automobile drive o a top level of a three-story parkig structure. To iclude both static ad dyamic data, the followig drive-test sceario was used: the vehicle was static for 4 miutes, ad the drove oe loop aroud the top level of the parkig structure (about oe miute of movemet). Figure 4 illustrates the profile of the horizotal speed i km/hour. The same data collectio scheme was repeated with two differet GPS referece oscillators: a ove-cotrolled crystal oscillator (OCXO), ad a temperature compesated crystal oscillator (TCXO). I additio to the GPS data, a automotive grade IMU was icluded to provide the exteral Doppler estimate, such that the phase error performace could be studied for differet combiatios of GPS clock with the IMU. A set of three ateas i a equilateral triagle cofiguratio was used as part of a automobile GPS attitude system, to measure the vehicle attitude as part of the measuremet vector for the avigatio filter[13]. The IMU ad GPS ateas are Figure 5: The Triagular Atea Array ad the IMU The atea array show has 1 meter baselies; the IMU is mouted ear the geometric ceter of the atea array to simplify the kiematic equatios of the avigatio filter. Three Novatel Allstar GPS receivers are coected to the three ateas, ad to a commo clock to allow attitude determiatio with sigle-differece carrier-phase measuremets. Data Collectio Hardware Setup Figure 6 depicts the data collectio hardware setup. The frot ed of a NordNav software receiver dow-coverts the L1 GPS sigal to a MHz IF; the streamer samples the data at MHz. As show, oe of two GPS referece oscillators could be used, ad two sets of GPS frot-ed data were collected, oe for each type of referece oscillator. The secod brach of the data-collectio setup icludes three ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 898

5 Novatel receivers ad a automotive grade IMU. A GPS/INS attitude system was utilized to provide attitude measuremets at 1 Hz, i additio to the 1Hz velocity ad Hz positio measuremets provided by the GPS receivers. I additio, the attitude system icludes circuitry to geerate a 1Hz-samplig sigal, sychroized to the pulse-per-secod sigal from oe of the Novatel receivers, which allows for the GPS timetaggig of IMU measuremets. Table 1 summarizes the key compoets used for this experimet. Figure 6: The Data Collectio Hardware Setup Table 1: Key Experimet Hardware Equipmet Fuctio GPS 1 NordNav R3 Receiver 3 Novatel Allstar Receivers Provides the degree of freedom to modify the trackig loops, such that the estimated Doppler ca be adopted. Collects, dow-coverts ad samples the GPS data by the frot ed, so that the collected GPS data ca be post-processed repeatedly usig differet trackig-loop filter orders/oise badwidths, differet C/N, ad differet combiatios of receiver clock with the IMU. Form the triagular atea array providig the iitial calibratio to the IMU. Provide the pulse per secod iformatio to a avigatio filter, so that the GPS ad IMU data ca be sychroized. 1 TCXO Drives the NordNav R3 Rx. 1 OCXO Drives the NordNav R3 Rx. 1 Automotive grade IMU IMU Provides the positio, velocity, ad attitude to calculate the estimated Doppler frequecy for the NordNav receiver. Others Atea Array Provides a rigid framework to calculate the iitial attitude. Laptop PCs Ru the required programs ad store the data. V. POST PROCESSING PROCEDURE The post-processig procedure cosisted of two steps. First, the recorded GPS measuremets from the Allstar receivers (positio, velocity, attitude) ad sychroized IMU data were passed through a GPS/INS avigatio filter; the filter s velocity estimates were used alog with satellite ephemeris data to compute Doppler estimates. Secod, the Doppler estimates were used to implemet iertially-aided phase-trackig o the recorded GPS IF samples. This step was accomplished usig a modified NordNav software receiver, customized to process exteral Doppler iformatio i replay mode. Figure 7 illustrates the post-processig procedure. As show, the two key compoets are the GPS/INS avigatio filter ad the modified NordNav software receiver. The details of the avigatio filter are beyod the scope of this paper, but it is importat to ote that the dyamic equatios are writte for the overall car positio ad velocity, icludig its suspesio dyamics. I additio, the avigatio filter velocity estimates always represet a bleded GPS/INS solutio; as a result o GPS outages have bee icluded i the data at this time. It will be show that the IMU sesor istability is egligible i the accuracy of Doppler estimates while GPS calibratio is available at a high rate (1Hz i this case), but sesor istability is expected to have a sigificat impact o dead-reckoig mode whe the GPS avigatio solutio is ot preset. Fially, data pass through the other key compoet-the modified software receiver. The carriertrackig loops are modified such that the estimated Doppler frequecy from the GPS/INS avigatio is fused ito the phase-lock loop of the software receiver. The estimated Doppler is added directly to the origial commad output from the loop filter. After a trasitio period, the Doppler term i the origial commad output from the loop filter drops dow to zero, as the dyamics have bee removed by the exterally estimated Doppler. Oe should ote that this aidig scheme is equivalet to applyig a frequecy step ito the PLL, uless the itegrator outputs i the loop filter are reset whe Doppler-aidig is applied. A iitial frequecy step that is too large would cause the loss of lock, sice the frequecy step may exceed the pull-i rage of the PLL. Therefore, oe possible scheme for the trasitio ito a iertially-aided mode is to icrease the frequecy-aidig ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 899

6 gradually, so that the PLL ca track the smaller rate of chage i iput frequecy. Figure 7: Post Processig Procedure VI. RESULTS AND DISCUSSIONS Figure 8: Chael Frequecies with TCXO Estimated Doppler Frequecy As discussed previously, the PLL phase error performace depeds o its badwidth, sigal-to-oise ratio, the quality of GPS referece oscillator, ad i the case of a iertial-aided PLL, the accuracy of exteral Doppler estimates. Before showig the phase error performace with a differet combiatio of GPS clocks ad the IMU, it is istructive to illustrate the quality of receiver clocks ad the quality of the estimated Doppler from the bleded GPS/INS avigatio filter. Figures 8 ad 9 show the chael frequecies usig the two differet clocks ad the correspodig estimated Doppler frequecies, computed with velocity outputs from the GPS/INS avigatio filter (usig the automotive IMU). The chael frequecies o each plot reflect the sceario of the test drive: for the first 3-4 miutes, the vehicle was statioary ad bega to move oly at the begiig of the last miute. The blue lie i Figures 8 ad 9 serves as a referece for the estimated Doppler from the GPS/INS avigatio filter. This lie is the estimated Doppler frequecy, calculated usig the surveyed startig poit of the tests ad the satellite positios. Obviously, this estimate is valid oly whe the receiver is static. As ca be see i Figures 8 ad 9, the estimated Doppler frequecy captures the dyamics detected by the GPS receiver. The residual errors are those due to GPS clock dyamics, vibratio iduced errors, ad thermal oise. Note that these remaiig error sources are ot icluded i the estimated Doppler to aid the traditioal PLL. As ca be see i Figure 9, the Doppler frequecy calculated by the GPS receiver (the red lie) with OCXO is excessively ustable. This pheomeo is uexpected, but it causes a sigificat degradatio i the phase error performace, as will be see i the later plots. Figure 9: Chael Frequecies with OCXO 1-Sigma Phase Error versus PLL Noise Badwidth It is importat to ote that the followig 1-sigma phase error show o the plots is measured durig the dyamic period. The improvemet of the PLL whe the GPS receiver is i motio is more importat tha the improvemet whe the receiver is static. Thus, the 1- sigma phase error here represets the steady state 1-sigma phase error whe the receiver platform is i motio. Moreover, i Figures 1, 11, 1 ad 13, the left ed of each lie of the experimetal results idicates the lowest tolerable oise badwidth i this ivestigatio. This criterio is selected i order to fid the lowest threshold of the test-bed. At the PLL desig poit, a 1-sigma phase error criterio (15 degrees for example [3]), would be used to determie the performace of the PLL. Note that, for all the data show i this paper, the coheret itegratio time (Tcoh) of the GPS trackig loops is 1 msec. Havig a loger Tcoh, the GPS trackig loops average out more oise, as a result, ca tolerate ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 9

7 lower C/N thresholds. 1 msec. is chose as a baselie for this paper; ivestigatig the dyamic trackig performace ad validatig the model is a essetial startig poit for examiig the iertial-aidig techique. Oe may be curious about the differece i performace betwee a secod-order PLL ad a third- PLL, with or without iertial aidig. Therefore, both orders of PLL have bee implemeted i the modified PLL of the software receiver. Figures 1, 11, 1 ad 13 show the experimetal results as well as the model results of the phase error performace i terms of various oise badwidths. The most importat iformatio i Figures 1, 11, 1, ad 13 is the badwidth reductio cotributed by the iertial-aidig techique. For example, i the secodorder PLL i Figures 1 ad 11, the lower tolerable oise badwidth is reduced from 7 Hz (uaided PLL) to 3.5 Hz (aided PLL). Note that the above values are read from the left stop poits of the both blue curves. If the 15 degrees threshold is used as a metric, for example, the badwidth reductio usig the secod-order PLL is.7 Hz. It should be oted that the relative badwidth reductio depeds o the receiver motio. I additio to examiig the badwidth reductio, it is more importat to explore the allowable oise badwidth whe the PLL is aided, give the C/N ad coheret itegratio time. Whe the oise badwidth is high (>=Hz), it is expected, for both clocks, that there will be o differece i either secod ad third-order or uaided ad aided PLL. I the high badwidth regio, the thermal oise is domiat. Thus, chagig the loop order or applyig iertial aidig does ot improve the performace at all. Aother highlight poit i Figures 1, 11, 1 ad 13 is the fact that the secod-order PLL has a larger badwidth reductio give the same phase error, or a larger phase error reductio, give the same badwidth tha those of the third-order PLL. The reaso for these pheomea is that as expected, the third-order PLL has a better dyamic trackig performace without iertial aidig tha the secod-order PLL. Cosequetly, the foregoig leads to a iterestig result, which is the almost equal improvemet gaied from iertial aidig compared to the secod-order PLL ad the third-order PLL. This fact ca be see from the circle marked red ad blue squared curves i Figure 11. A theoretical model [7], the solid gree ad dashed blue curves i Figure 11, also idicates this fact. The Appedix gives the details of the derivatios for the 1-sigma phase error model of a PLL. Figure 1: PLL Performace Drive by the TCXO with respect to the Noise Badwidth ad Compariso with Model Results for the case of Uaided PLL Figure 11: PLL Performace Drive by the TCXO with respect to the Noise Badwidth ad Compariso with Model Results for the case of Aided PLL Figure 1: PLL Performace Drive by the OCXO with respect to the Noise Badwidth ad Compariso with Model Results for the case of Uaided PLL ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 91

8 third-order aided PLL is ot ecessary outperform the secod-order aided PLL. Figure 13: PLL Performace Drive by the OCXO with respect to the Noise Badwidth ad Compariso with Model Results for the case of Aided PLL The reaso that the aided third-order PLL is ot always superior to the aided secod-order is iterestig. The foregoig poit highly depeds o the trasiet respose of the PLL to the imperfect estimated Doppler frequecy from the avigatio filter ad to the GPS clock dyamics. To highlight the respose chage related to the iertial aidig, I would like to discuss the impact of imperfect aidig. Without losig geerality, we ca model the aidig error by a.1 Hz frequecy step iput to the PLL [7]. From Equatios (A9) ad (A3) i the Appedix, the residual phase error due to the imperfect Doppler frequecy estimate is give by the followig Equatios (3) ad (4) for secod-order ad third-order PLLs, respectively. where Δf θed= 86 BW i deg rees. (3) Δf θe3rd= 9 BW i deg rees, (4) Δ f the frequecy step i Hz; BW is the oise badwidth (Hz) of the trackig loop. Figure 14 shows the plots of Equatios (3) ad (4) ad idicates the miimal differece betwee the two orders of the aided PLLs whe a TCXO is used. This pheomeo ca be see from experimetal results i both cases of oscillators. However, the model show i Figure 13 idicates a cotradictio way. The reaso is that the clock dyamics give by equatios (A) ad (A1) behave differet betwee TCXO ad OCXO. For the case of OCXO, the differet resposes of the two PLLs to clock dyamics overcome the differece show betwee equatios (3) ad (4). As will be see i the later sectios, the clock model has to be further ivestigated. I short, equatios (3) ad (4) as well as the experimetal results suggest that the Due to the excessive istability of the OCXO as show i Figure 9, it is more costructive to look at results usig TCXO. The experimetal results ad the model, show i Figures 1 ad 11, match to each other relatively well at the high operatig oise badwidth rage ( > Hz). It is clear that the thermal oise error domiates the phase error at high badwidth regime ad the model also predicts aalogous phase error. However, the model is too optimistic at the low badwidth regio. The discrepacy betwee the model ad the experimetal results i the low badwidth regio is due to the vibratio model. The vibratio PSD, as show i Figure A1, used for the model is obtaied from a aircraft dyamics. This PSD may ot be idetical to the car dyamics especially i low frequecy part. Aother depedet factor is the g- sesitivity of the oscillator. It is assumed to be 1^-9 parts/g across the whole spectrum of the vibratio PSD. The actual coditio of the oscillator, however, is chagig with time, temperature etc. Therefore, it is critical to have a higher fidelity of the vibratio PSD for a car movemet ad a accurate kowledge of the oscillator g-sesitivity. Figure 14: Residual Phase Error due to Imperfect Iertial Aidig (Model Results Usig TCXO) 1-Sigma Phase Error versus C/N The other metric used to evaluate the effectiveess of iertial aidig is the allowable reductio of C/N that maitais the phase lock uder dyamic coditios. As idicated, Figures 15 ad 16 show the 1- sigma phase error with respect to various C/N values. Note that the oise badwidth for both plots is 7 Hz ad the coheret itegratio time is 1 ms. Obviously, give the same C/N, the phase error has bee reduced by ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 9

9 applyig the iertial aidig. The improvemet i iertial aidig is miimal whe the GPS receiver operates at a relatively high badwidth. At low badwidths, the dyamic stress domiates the phase error. Therefore, iertial aidig beefits are apparetly i the low oise badwidth rage. The 1-sigma phase error does ot chage with C/N whe the C/N is above 4 db-hz. It is as expected sice the phase error is domiated by the dyamics whe the oise badwidth is fixed at 7 Hz. As the C/N becomes lower, the thermal oise error starts to domiate the total phase error. The model results are also show i gree-solid ad blue-dashed curves for aided secod order PLL ad third order PLL, respectively. Therefore, i Figures 15 ad 16, the blue-circled ad red-circled curves should lie up with the gree-solid ad blue-dashed curves, respectively. As ca be see i Figures 15 ad 16, the discrepacy betwee the model ad the experimetal results is relatively flat whe the C/N is high. This costat offset idicates that the clock model ad the vibratio PSD used for the study do ot truly represet the coditio of this experimet. However, this discrepacy decreases as the C/N decreases sice the thermal oise domiates the total phase error. Comparig this pheomeo with the high badwidth regio show i Figures 1 ad 11, we have a higher fidelity for the thermal oise model. Figure 16: PLL Performace Drive by the OCXO with respect to C/N; BW = 7Hz VII. CONCLUSIONS The techique of iertially aidig GPS trackig loops has bee show to effectively mitigate the RFI. This improvemet is accomplished by applyig the exterally estimated Doppler frequecy to the GPS carrier-trackig loop, so that the badwidth required to track high dyamics is elimiated. Therefore, a lower oise badwidth ca be maitaied i a high dyamic eviromet as well as whe the RFI is preset. The experimetal results show that we ideed have the improvemet i the RFI, achieved by a iertial aidig techique. However, the amout of the RFI improvemet is costraied by various factors such as receiver clock quality, the residual error of the iertial aidig, ad eve the stability of the power supply to the experimetal set-up. Oe would expect a better result if a atomic clock were used. Therefore, the results of this paper provide a baselie model verificatio of the iertialaided trackig loops. Figure 15: PLL Performace Drive by the TCXO with respect to C/N; BW = 7Hz The other iterestig poit is that the secodorder loop performs better tha the third-order loop whe iertial aidig is applied. The reaso is illustrated i Equatios (3), (4), ad Figure 14; the peak phase error of the secod ad third-order PLLs due to the residual error of the exteral frequecy estimate is early equal. The foregoig is based o the assumptio that the residual of the Doppler estimate is a frequecy step. Ideed, the experimetal results show that the assumptio is reasoable. The impact of receiver clock quality o the GPS/INS itegrated system is show i Figure 17, which illustrates the extra phase error iduced by acceleratio (or vibratio). The two curves i Figure 17 idicate the extra iduced phase error caused by platform acceleratio. ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 93

10 These are experimetal results foud as the differece betwee the 1-sigma phase error before ad after car motio. Sice the iduced clock phase error must be tracked by the PLL but ot rejected, it is therefore a fuctio of the oise badwidth of the carrier trackig loop. From Figure 17, we otice that the iduced phase error restricts the amout of PLL badwidth reductio, which is the beefit of usig the iertial-aidig carrier trackig loop. Whe the oise badwidth is reduced below 1 Hz, the phase error is domiated by the clock dyamics. Eve were the Doppler frequecy itroduced by the platform motio perfectly removed, the phase error due to clock dyamics eats up the margi origially preserved for the thermal oise phase error. Therefore, it is essetial to uderstad the clock sesitivity to the acceleratio ad vibratio modes of the receiver platforms. Give this uderstadig, the itegrity requiremets ca be met by suitable adjustmet of the phase error boud. Figure 17: Additioal 1-sigma phase error iduced by receiver clock acceleratio (TCXO) The other iformatio we ca read from Figure 17 is the discrepacy betwee the model ad the experimetal result. This is due to the PSD used for the model is from a aircraft eviromet, which is ot equivalet to the car movemet. As metioed, the g-sesitivity of the oscillator is also a importat factor eeded to be cosidered. Each oscillator has differet reactios to vibratio ad acceleratio. I coclusio, a test-bed for the iertial aided carrier trackig loop has bee fully implemeted. The performace of this aidig techique is limited by the clock dyamics. To predict the performace by the model, a further validatio o the model has to be coducted. The discrepacy betwee the model ad the experimetal results has bee idetified, which is the clock dyamics icludig clock phase oise as well as the clock sesitivity to vibratio ad acceleratio. VIII. FUTURE WORK As observed i this paper, the GPS receiver clock plays a importat role i the trackig loop ehacemet techique. To study the clock dyamics, a elaborate experimet is eeded. Applyig acceleratio o differet cut sectios of a crystal oscillator will excite differet modes of clock oise ad the vibratio-iduced errors. Thus, coductig a experimet o a shake table would be a subtle way to ivestigate the clock dyamics. Furthermore, a shake table ca duplicate the vibratio modes collected from real eviromets. Especially for JPALS applicatios, various vibratio dyamics o a aircraft ca be duplicated o a shake table. IX. ACKNOWLEDGMENTS The author gratefully ackowledges the sposor of JPALS research at Staford Uiversity, the U.S. Navy (Naval Air Systems Commad, Air Traffic Cotrol ad Combat Idetificatio Systems PMA 13). I would like to sicerely thak Professor Per Ege, ad Dr. Jey Gautier at Staford Uiversity GPS Lab for their advice ad support of this paper. A special thaks to Dr. Satiago Alba at Staford Uiversity for his help o the data collectio phase of this paper. I wat to express appreciatio to Professor Demoz Gebre- Egziabher, Alireza Razavi (Uiversity of Miesota, Twi Cities), ad Professor Deis Akos (Uiversity of Colorado, Boulder) for their costructive commets ad advice regardig this paper. I also give special thaks to Per-Ludvig Normark, Gle MacGouga, ad Christia Stalberg at NordNav Techologies for their patiet ad cotiuous advisig o modifyig the carrier-trackig loop framework of the software receiver. APPENDIX The performace of the carrier-trackig loop depeds o the system order, system type, ad the system oise badwidth. The loop filter is desiged to reduce oise, as well as to hadle the sigal dyamics. I this study, a first order ad a secod-order filter are implemeted i the software receiver. Sice the NCO is a itegrator, the overall system is secod-order ad third-order, respectively. The followig paragraphs provide the trasfer fuctios ad system characteristics of these two differet orders of PLL. Secod-order Loop For a secod-order PLL, a proportioal itegral (PI) low-pass filter is cosidered first. The trasfer fuctio of the PI filter is give as follows: ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 94

11 Fs () 1+ τ s =. (A1) τ1s Sice F(s) icludes a pole at s=, the system show i Figure is a Type II system. This meas that the steadystate error of the closed loop system is zero with a phase ramp iput, which is equivalet to a frequecy step iput. The resultig closed-loop trasfer fuctio with this PI filter is 1 If we choose the dampig ratio ξ = =.771, the e H () s =. (A7) 1+ 4 ϕ GsFs () () ξ s+ H() s = = =, (A) ϕ ξ where o 1 + GsFs ( ) ( ) s + s+ i 1 τ, ξ = ad =. τ1 is called the atural frequecy of the secod-order loop; ξ is called the dampig ratio. A importat characteristic of the PLL is its sigle-sided, closed-loop oise badwidth ( BW ), which is defied as follows [1]: BW = H( j π f) df. (A3) Evaluatig Equatio (A3) for this secod-order loop PLL, gives the relatioship betwee BW ad as [1]: 1 BW = ( ξ + ), (A4) 4ξ where the uits of BW ad are Hz ad rad/sec, respectively. For further aalysis of the phase error i later sectios, calculatig the phase error to iput trasfer fuctio ( He() s ) is eeded. Equatio (A5) gives the defiitio ad the specific expressio of He() s. δϕ s He() s = = 1 H() s =. (A5) ϕ s + ξ s+ Of iterest is the term H () s e = i H () e s. Let s = j, the [4ξ ] (A6) Third-order Loop Secod, a third-order loop is cosidered. The secod-order filter F(s) is expressed as follows: s + s+ =. (A8) s 3 () Fs Thus, the overall system is third order, which has three ope loop poles at s=. Hece it is a Type III system. With this Type III system, the steady-state phase error is zero, eve if the iput is a phase acceleratio. Give F(s) i Equatio (A8), the resultig closed-loop trasfer fuctio is the as expressed follows: ϕ s + s+ H() s = =. (A9) ϕ 3 o 3 3 i s + s + s+ As defied i Equatio (A3), the sigle-sided, closed-loop oise badwidth ( BW ) of this third-order loop is [9] BW =. (A1) 1. The phase error to iput trasfer fuctio ( He() s ) is the defied as: 3 δϕ s He() s = =. (A11) ϕ s + s + s+ 3 3 i As we have doe for the secod-order-loop, we eed to calculate the magitude square of H () s. By lettig s = j, ad calculatig e H () s = 1 H () e s, we have e. (A1) ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 95

12 Track Loop Errors The performace of a PLL ca be determied by measurig its phase error. The total phase error icludes phase jitter ad dyamic stress. The 1-sigma value of the phase error is expressed as follows [3]: θe δϕ = δϕw + δϕsv + δϕrx + δϕv +, (A13) 3 where δϕw = 1-sigma phase error due to thermal oise; δϕsv = 1-sigma oscillator phase oise from the satellite s oscillators; δϕrx = 1-sigma oscillator phase oise from the receiver s oscillators; = 1-sigma vibratio iduced oscillator jitter; δϕv θ e = dyamic stress i the PLL trackig loop. Thermal Noise ( ) δϕw The thermal oise is the most domiat error source of PLL if the system oise badwidth is i traditioal rage (1 to Hz). Otherwise, the sigal dyamics will cause most of the phase errors. The trackig loop phase error due to thermal oise is give as [3]:, (A14) C/ N T C/ N BW 1 δϕ w = 1 + coh where BW is the carrier-trackig loop oise badwidth i Hz; C/ N is the carrier-to-oise ratio; T coh is the coheret itegratio time. Equatio (A14) is obtaied whe the sigal discrimiator i Figure 1 is a product detector, I*Q. Equatio (A14) holds for a o-coheret carrier trackig loop. The term icludig T coh i the bracket of (A14) is called squarig loss. It is obvious that a loger T coh ad a stroger sigal (larger C/ N ) will mitigate the thermal oise phase error degradatio due to squarig loss. If we have perfect kowledge of the carrier phase of the icomig sigal, a coheret carrier trackig loop ca be implemeted. Therefore, the thermal oise phase error, Equatio (A15), does ot iclude the squarig loss term [8]. I [11], it is show that the 1 ta ( Q/ I) phase discrimiator is superior to the I*Q phase discrimiator, ad approaches the performace of the coheret carrier trackig loop [11]. BW δϕw =. (A15) C/ N I this study the coheret itegratio time is chose to be fixed as 1 ms. Receiver Oscillator Phase Noise ( ) δϕrx The secod phase error source is cotributed by the receiver oscillator phase oise especially at a low oise badwidth. Oe ca icrease the oise badwidth such that the PLL ca track the clock dyamics. However a higher oise badwidth itroduces more effects o the phase error caused by the thermal oise. To determie a appropriate oise badwidth, we eed to ascertai the carrier phase-oise spectrum. The phase-oise power spectral desity (PSD) (oe-sided) of oscillator ca be writte as [1]: ( ) k rx = k, l h k = 4. (A16) G f h f f f f Outside of the frequecy rage, the PSD is zero. I this study fl is set to be zero, while f h is equal to 5 Hz sice the coheret itegratio time is 1 ms [7]. The coefficiets hk are derived experimetally. The coefficiets for TCXO ad OCXO used i this study are give by [13] as follows: h k TCXO OCXO h 5 * 1 ^ * 1 ^ -8 h * 1 ^ -5 5 * 1 ^ -5 1 h 9.6 * 1 ^ * 1 ^ -4 h.6 9 * 1 ^ -7 3 h.6 1 * 1 ^ -7 4 Note that these coefficiets are already ormalized for the case that the oscillator s ceter frequecy, f, is 1.3 MHz. The 1-sigma oscillator phase oise is the defied as follows [1]: δϕ rx e rx = H () s G ( f) df. (A17) ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 96

13 Substitutig (A16) ito (A17), we have h h h h () δϕ = H s h df rx e f f f f (A18) Sice f h = 5Hz, without losig the accuracy, we ca igore the last two terms i the bracket. So Equatio (A18) becomes H s df. (A19) () h4 h3 h δϕ rx = e f f f Evaluate (A19) by substitutig (A7) ad (A1) ito (A19) for the secod-order ad the third-order loops, respectively. Remember that = π f ad chage the variables by lettig formula: x = ; apply the followig m 1 x π dx =, < m <. 1+ x mπ si( ) We have 1-sigma oscillator phase oise from the receiver s oscillators for the secod-order loop expressed as: ( π) h π ( π ) h π ( π) h π δϕrx = i rad^ ad for the third order loop: ( π) h π ( π ) h π ( π) h π δϕrx = i rad^. Fially, if we apply the relatioship betwee BW ad give i (A4) ad (A1), we would have δϕrx i terms of BW. 1 Secod order loop ( ξ = =.771): ( π) h π ( π ) h π ( BW ) ( BW ) 4 ( π) h π + ( BW ) ( rad ^ ) ( A) δϕrx = + 3 Third order loop: 3 ( π ) h4 π ( π ) h3 π δϕrx = + 3 (1. BW ) 6 (1. BW ) 3 3 ( π ) h π + ( rad ^) ( A1) (1. BW ) 3 Note that the uit BW is Hz. Usig (A) ad (A1) to evaluate the variace of phase error due to TCXO ad OCXO phase oise for the secod-order ad the thirdorder loops, respectively. Satellite Clock Error Other tha the receiver oscillator o the earth that produces phase oise, the clock oboard i the orbit could also geerate phase oise i the sigals. From [14], the omial satellite clock error power spectral desity (PSD) ca be modeled by the PSD of TCXO; except that the omial satellite clock error power spectral desity (PSD) has to be scaled such that the phase jitter is.1 rad whe BW is 1 Hz as specified i [15]. Therefore, for the secod-order loop, the 1-sigma oscillator phase oise from satellite s oscillators is = 1. (A) δϕsv δϕrxtcxo For the third-order loop, the 1-sigma oscillator phase oise from satellite s oscillators is = 6. (A3) δϕsv δϕrxtcxo Phase Error Due to Vibratio The third phase error is due to the vibratio iduced oscillator jitter. The PSD of this phase error is give as [7]: G g ( f) Gv( f) = ( kgnf), (A4) f where f is the oscillator s ceter frequecy; N is the ratio betwee the carrier frequecy ad the local ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 97

14 oscillator s ceter frequecy; k g is the oscillator s g- sesitivity i parts/g. I this study, f =1.3 MHz ad, f therefore, N = L 1 =154. A typical value of k f g is 9 1 parts/g [14]. Duplicatig the plot from [14], we have the PSD of phase error due to vibratio Gv ( f) as show i Figure A1. Dyamic Stress ( θ e ) Due to the abrupt motio, the PLL would experiece excessive phase error. Of iterest is the peak error, i.e., the phase error trasiet respose of the phase acceleratio or phase jerk. For the secod-order loop, the phase error due to dyamic stress (phase acceleratio) is give by [9]: Δ f θe =, (A6) where Δ f is a frequecy step i Hz. If ξ =.77 8ξ = BW, the (1+ 4 ξ ) from Equatio (A4), ad Figure A1: Mechaical Vibratio PSD From Figure A1, we ca have the fuctio Gv ( f ) i followig forms: G ( ).5*1 v f Hz 3 f 4 < f < 1Hz Gv ( f) =.5*1 *( ) 4 ( ) 4*1 4 Gv f = 1 < f < 5Hz 4 f 5Hz < f Gv ( f) = 4*1 *( ) 5 Give the PSD G ( f ), we ca evaluate the variace of 3 = f < 4 v the phase error due to vibratio usig the followig equatio: δϕ v e v = H () s G ( f) df. (A5) Substitutig H () e s for the secod-order ad the thirdorder loop as well as the PSD Gv ( f ) ito Equatio (A5), we ca obtai the values of δϕv at the various loop oise badwidths. Note that the above calculatio is accomplished by umerical itegratio sice there is o close form for this value. Δ f.7599amax θe = i cycles, (1.885 BW ) λl 1BW Δ f.7599amax θ = π i radias, (A7) e (1.885 BW ) λ BW L1 where a max is the maximum value of lie-of-sight phase acceleratio (g) experieced by the GPS receiver. For a car motio test, we use a value of a is.5g. max Similarly, for the third-order loop the phase error due to dyamic stress (phase jerk) is give by [9]: Δ f π (5.67) j θe = i radias, (A8) max 3 3 λl 1BW where jmax is the maximum value of lie-of-sight jerk experieced by the GPS receiver. A typical value of j is.5g/sec. max So far, we have covered every term for the phase error give i Equatio (A13). The followig two figures show the plots of Equatio (A13) with respect to oise badwidth. As ca be see i Figures A ad A3, the uaided third-order PLL has a better phase error performace at a give oise badwidth tha the secodorder PLL. These two plots also idicate the fact that thermal oise is domiat i the high badwidth regio while dyamic stress ad clock dyamics apparetly affect the phase error i the low badwidth regio. ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 98

15 Δ π Δf θe =.45 =.45 i radias. (A9) (1.885 BW ) For the third-order loop, the peak phase error due to a frequecy step is equal to the steady-state phase error i a first-order loop described i [9]. Thus, the phase error ca be expressed as the followig equatio: π Δf θe = i radias. (A3) 4B L Figure A: 1-Sigma Phase Error for a Uaided PLL (secod-order loop) Util this step, we have aalyzed of phase jitter for both uaided ad aided trackig loop. Thus, we have each term of Equatio (A13) for both cases. The followig Figures show the results of the above model aalysis whe iertial-aidig is applied. Comparig Figures A4 ad A5 with A ad A3, respectively, we ca see the improvemet usig iertial-aidig PLL. Figure A3: 1-Sigma Phase Error for a Uaided PLL (third-order loop) Figure A4: 1-Sigma Phase Error for a Aided PLL (secod-order loop) Residual Dyamic Stress Error of the Aided PLL The quatity of iterest i this paper is frequecy/phase-trackig stability, which ca be quatified by the trackig error of the PLL ad measured directly by the output of the phase discrimiator. We eed to quatify the effects of error o the exteral Doppler estimate. I [7], the upper boud of the 1-sigma Doppler estimate error is.1 Hz. We ca model this Doppler estimate error as a step i frequecy. The effect of this frequecy step is evaluated by examiig the peak phase error of the trackig loop. Give ξ =.771 for the secod-order loop, the peak error due to a frequecy step iput is illustrated i Figure.1 of [1] as: Figure A5: 1-Sigma Phase Error for a Aided PLL (third-order loop) ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 99

16 REFERENCES [1] Johso, G., Lage, M. ad et al, The JPALS performace Model, Proceedig of the ION-GPS 3, Portlad, OR, September 3. [] Peterso, B. R., Johso, G. ad et al, Feasible Architectures for Joit Precisio Approach ad Ladig System (JPALS) for Lad ad Sea, Proceedig of the ION-GPS 4, Log Beach, CA, September 4. [3] Ward, P., Satellite Sigal Acquisitio ad Trackig, i Uderstadig GPS Priciples ad Applicatios, Artech House, Washigto, D.C., pp [13] Alba, S., Desig ad Performace of a Robust GPS/INS Attitude System for Automobile Applicatios, Ph.D. Thesis, Staford Uiversity, 4 [14] Hegarty, C., Aalytical Derivatio of Maximum Tolerable I-bad Iterferece Levels for Aviatio Applicatios of GNSS, joural of The Navigatio, Vol. 44, No. 1, pp [15] US Departmet of Defese, Global Positioig System Stadard Positioig Service Sigal Specificatio, Appedix A, Secod Editio, Jue, [4] Bastide, F., Akos, D. ad et al, Automatic Gai Cotrol Cotrol (AGC) as a Iterferece Assessmet Tool, Proceedig of the ION-GPS 3, Portlad, OR, September 3. [5] Alba, S., Akos, D. ad et al, Performace Aalysis ad Architectures for INS-Aided GPS Trackig Loops, Proceedigs of ION Natioal Techical Meetig, ION- NTM 3. Aahiem, CA. Jauary 3. [6] Philips, R., ad Schmidt, G. T., GPS/INS Itegratio, AGARD Lecture Series o System Implicatios ad Iovative Applicatio of Satellite Navigatio, Paris, Frace, July [7] Gebre-Egziabher, D., Razavi, A., ad et al, Iertialaided Trackig Loops for SRPS Itegrity Moitorig, Proceedig of the ION-GPS 3, Portlad, OR, September 3. [8] Misra, P. ad Ege, P., Global Positioig System: Sigals, Measuremets ad Performace, Gaga-Jamua Press, Licol, Massachusetts, USA, 1. pp [9] Va Dieredock, A.J., GPS Receivers, i Global Positioig System: Theory ad Applicatios, AIAA, Washigto D.C., Vol. 1, pp [1] Best, R. E., Phase-Locked Loops:Desig, Simulatios, ad Applicatios, McGRAW-Hill, Third Editio, pp1-89. [11] Gebre-Egziabher, D., ad Razavi, A., persoal commuicatio etitled Evaluatio of GPS PLL ad FLL Architectures i RFI Eviromets, 5. [1] Spilker, J., Digital Commuicatio by Satellite, Pretice-Hall, Cambridge, Massachusetts, pp ION GNSS 18th Iteratioal Techical Meetig of the Satellite Divisio, September 5, Log Beach, CA 91