Investigationof aNavigation-Grade RLGSIMUtypeiNAV-RQH R.Dorobantu,C.Gerlach IAPG /FESGNo.16 InstitutfürAstronomischeundPhysikalischeGeodäsie ForschungseinrichtungSatellitengeodäsie München2004 Investigation of a Navigation–Grade RLG SIMU type iNAV–RQH R. Dorobantu, C. Gerlach IAPG / FESG No. 16 Mu¨nchen 2004 ISSN 1437-8280 ISBN 3-934205-15-1 Adressen: Institut fu¨r Astronomische und Physikalische Geod¨asie Technische Universit¨at Mu¨nchen Arcisstrasse 21 D-80290 Mu¨nchen Germany Telefon: +49-89-289-23190 Telefax: +49-89-289-23178 http://tau.fesg.tu-muenchen.de/ Forschungseinrichtung Satellitengeod¨asie Technische Universit¨at Mu¨nchen Arcisstrasse 21 D-80290 Mu¨nchen Germany Telefon: +49-89-289-23191 Telefax: +49-89-289-23178 http://tau.fesg.tu-muenchen.de/ Investigation of a Navigation-Grade RLG SIMU type iNAV-RQH RAUL DOROBANTU AND CHRISTIAN GERLACH Institut für Astronomische und Physikalische Geodäsie (IAPG), Technische Universität München D-80290 München, Germany (e-mails: [email protected] and [email protected]) Table of contents 1. Introduction . . . . . . . . . . 3 1.1. Strapdown-IMU characteristics . . . . . . . 4 2. Inertial sensor technology and error models . . . . . . 6 2.1. Specific-force sensors (accelerometers) . . . . . . 6 2.2. Ring Laser Gyroscopes . . . . . . . . 9 2.2.1. Dithered Ring Laser Gyroscope . . . . . . 10 2.3. Inertial sensor error models . . . . . . . . 14 2.3.1. Accelerometer errors . . . . . . . 14 2.3.2. Gyroscope errors . . . . . . . 17 3. Strapdown navigation mechanization and post processing results . . . 19 3.1. Strapdown mechanization . . . . . . . . 19 3.2. Post-processing navigation solutions . . . . . . . 22 3.2.1. Calibration and parameter identification . . . . 22 3.2.2. Kingspad-software input/output parameters . . . . . 23 3.2.3. Indoor navigation experiment . . . . . . 25 3.2.4. Land-navigation experiments (car-drive) . . . . . 26 3. Conclusions and recommendations for further investigations . . . 29 5. References . . . . . . . . . . 29 Appendix . . . . . . . . . . . 31 Appendix A: Insight in the ISA of the SIMU . . . . . . 31 Appendix B: Supplementary investigations about the static sensitivity of the SIMU . . . . . . 32 Appendix C: Investigation of an elastic damping suspension for the SIMU . . . 34 Appendix D: Some results from the direct use of the SIMU data-set for geodetic parameter determinations . . . . . 36 1 2 Investigation of a Navigation-Grade RLG SIMU type iNAV-RQH 1. Introduction The work presents a characterization and some results from evaluation experiments made with our Ring Laser Gyroscope (RLG) navigation grade Strapdown Inertial Measurement Unit (SIMU) type iNAV-RQH of the class 1 nmi/h precision. After a short presentation of the principal features of the SIMU, a description of the inertial sensor constructive principles and error models is given. In order to evaluate our strapdown IMU we have conceived laboratory and field tests, performed on a medium-precision turn-table and in the frame of a car-navigation mission, using a DGPS (Differential GPS) reference solution (in our case, an On-the-Fly (OTF) kinematic DGPS solution, delivering accurate position-references at regular epochs of integer seconds). The post-processed 3-D inertial-only or integrated GPS/INS solutions are obtained using the dedicated software Kingspad. A noise and error analysis, with concrete results from laboratory and field tests is presented too. With a position precision in the sub-dm domain (differences to the cm-precision DGPS reference trajectory, with 1- relative errors of about 1 cm) over driven σ trajectory perimeters of hundreds of meters, resp. with acceleration errors in mGal domain (after appropriate filtering over about 60…100 s) and with attitude errors in arcsec range, the RLG SIMU Type iNAV-RQH from iMAR is considered fully suitable for accurate navigation, surveying and precision gravity determinations. Some preliminary results were already given in [Dorobantu et al., 2004], the present extended form including more insides in the sensor technology and error models; supplementary experiments, like indoor INS-navigation with ZUPTs (Zero velocity UPdaTes of the Inertial Navigation System), static tilting experiments, damping-tests or SIMU’s statically evaluation, as well as more insight in the ISA (Inertial Sensor Assembly), or direct derivation of geodetic parameters from the registered SIMU data, are presented in the appendix. Fig. 1 DGPS/INS car-experiment in Munich Fig. 1 shows the car experiment made in Munich on a terrain with good GPS-satellite visibility (Theresienwiese): one can see the strapdown IMU (a RLG type iNAV-RQH from iMAR) mounted in the middle, between the two rover GPS antennas, as well as the reference basis GPS antenna (all GPS receivers are 18-channel, type Trimble- 4000SSI). Without a good understanding of the sensor error models [Grewal et al., 2000, IEEE Std. 337-1972, IEEE Std. 647-1995, Savage, 1997] it is not possible to obtain accurate solutions, therefore the following chapter is dedicated to presentation of the inertial sensor technology and their error models. 3 The post-processing navigation solution analysis, made with Kingspad (originated from the Calgary University, Dept. of Geomatics) permits a pertinent evaluation of the SIMU and also allows an estimation of sensor parameters. Chapter 3.2.2 illustrates the evaluation made for INS-only solutions (only with ZUPTs) as well as for GPS/INS integration. A short investigation about the precision of the reference GPS solution has also been made by analyzing the GPS relative position errors of the fixed distance between the two rover antennas. Finally, some conclusions from evaluation experiments are presented, with special focus on future hardware improvements and enlarged error models implementation. 1.1. Strapdown-IMU characteristics The Strapdown navigation-grade IMU iNAV-RQH, characterized by a medium-precision performance, uses a Honeywell inertial sensor cluster, based on three servo-accelerometers type QA2000-40 (selected-ones providing better parameters, such as noise figure, bias and scale factor stability, linearity, acceleration sensitivity) and three new-generation dithered Ring Laser Gyroscopes type GG1320 (also selected for better noise figure). Fig. 1 Inside-view of the SIMU An inside view of the unit’s hardware is given in Fig. 2. The inertial sensor assembly, provided with shock-mounts for mechanical protection (that can be clamped, for special experiment purposes), delivers the inertial sensor data via an electronic block of acquisition and pre-processing (anti-aliasing filters, A/D converters of the accelerometer data, provided also with temperature, scale factor, bias and misalignment compensations, etc.). The IMU (see the block-diagram in Fig. 3), controlled by an industry-PC CPU, stores the inertial sensor data (such as the 24-bit converted acceleration data or the digital RLG information) on the internal hard-disk (a 3 GB memory capacity of flash-disk type, chosen to eliminate the potential noise-source); the data are synchronized by means of an internal precision time-basis, that can also be calibrated via the external PPS (pulse per second) GPS receiver signal: the absolute calibration of the time-scale is then achieved through the use of the NMEA-0183 (National Marine Electronics Association) serial-interface signals (the four signals: GGA, GLL, RMC, VTG permit, apart from the time and date information, the receipt of GPS data, such as position and velocity, that can be stored on the IMU in binary files). Supplementary inputs are provided for event marker signals or for auxiliary odometer information. The IMU system software enables the configuration of the unit, by parameter specification, and provides calibration files for the inertial sensor cluster. Such configuration parameters are, among many others: the local position coordinates, the state-variables precisions for the on-line running of Kalman filters for coarse and fine alignments, resulting the Roll, Pitch, Yaw orientation angles (between the SIMU body-system and the local-level geodetic reference system). A special feature of this SIMU is the full access to all raw data, being available more than 40 variables: one can access the total uncompensated values (e.g., non-calibrated accelerometer data, without temperature compensations), as well as the fully corrected signals (e.g., the calibrated accelerometer data, compensated also for temperature, gravity and earth rotation rate). 4 The data, including GPS data or system-status information, can be accessed independently, via connection of an external keyboard and display directly to the IMU, or via an external PC-unit. The bi-lateral communication with the external PC (for navigation purposes often a Notebook), enabling the IMU-control or real-time navigation data display/storage under a RS232 serial interface, uses Windows or DOS programs; a post-mission off-line external data storage is made then via serial communication or Ethernet link (protocols as IPX, NetBEUI, TCP/IP or Net Use command). The recorded IMU binary data can be used directly, or in a converted ASCII form, as input for navigation post-processing programs. IMIMU U 1 PPS T T L GGGPPPSSS COM 2 T T L OODDOOMMEETTEERR NMEA CCPPUU MMSS -- DDOOSS 66..2222 T T L EEEVVVEEENNNTTT MMMAAARRRKKKEEERRR 1100......1188 VVddcc PPoowweerr SSuuppppllyy 3300 WW IISSAA 33 xx QQAA 22000000 -- 4400 33 xx GGGG 11222200 CCCooonnnfffiiiggg...tttxxxttt SSSyyysss999000777999 777...gggrrrlll222ggg ...iiimmmuuu IIMM1SUS10Uy0y0‘s‘0ss tscM tc e e mMmB SSB oo fftt 22DD GGaaddttBB aa PPPCCC SSSyyysss999777 ggg111000 ...iiimmmuuu 880000 eeMM BB 110000 MMff BB NNNeeettt UUUssseee DDaattaa DDaattaa NNNeeetttBBBEEEUUUIII COM 1 EETTHHEERRNNEETT IIIPPPXXX///SSSPPPXXX TTTCCCPPP///IIIPPP NNootteebbooookk Windows 9N5/a9v8C/NoTm2m0a0n/Xd P TTTTSSSSYYYYNNNNCCCC..DD..DDAAAATTTT RS232 COM MS-DOS Window # 1 IIIINNNNEEEERRRRTTTTIIIIAAAALLLL....DDDDAAAATTTT RS232 COM (Autoexec.bat) IIMMUU CCCoo(oCnnnffofiinggigf..ssi.gsyyy.ssss y s) cc Binary / ASCII dd IInnteterrLLininkk MS-DOS Window # 2 ee IPX (Autoexec.bat) ff CCCoo(oCnnnffofiinggigf..ssi.gsyyy.ssss y s) TTTTSSSSYYYYNNNNCCCC..TT..TTXXXXTTTT MS-DOS Window # 3 NetBEUI CC(CAoo(oCnnunffotfiionggiegf..xssi.gsyyey.sscss .y bsa)t ) IIIINNNNEEEERRRRTTTTIIIIAAAALLLL..TT..TTXXXXTTTT Fig. 3 SIMU structure and the data-exchange flow The SIMU exhibits over further remarkable special features: - total protection of the supply input - galvanic separation of IMU accesses - high acquisition rate (1 kHz now, but very soon 2 kHz, about three times higher then the dithering frequencies) - electronically switchable accelerometer full-scale range (2g/10g) - software dithering switch-off (for certain precision experiments). 5 The principal performance of the SIMU and its sensors are summarized in the Tab. 1 [from iMAR, 2001]. Tab. 1 Principal performance characteristics of the SIMU type iNAV-RQH from iMAR 2. Inertial sensor technology and error models The selected highly sensitive QA2000-40 balanced pendulous accelerometers and the dithered GG1320 Laser- gyroscopes (practically not sensitive to acceleration and temperature variations) assure good precision for a navigation-grade SIMU. A detailed insight concerning the principles of that inertial sensors and their errors, which permits a correct data interpretation, is presented in the next three sections. 2.1. Specific-force sensors (accelerometers) The principle of accelerometers is based on the measurement of the relative displacement that arises between the elastically suspended proof mass and the accelerometer frame subject to acceleration (inertial d’Alembert force) (see the spring-mass and balancing pendulous accelerometer principles in Fig. 4). &x& t Hinge OA IA Damper Torquer &x& PM B K PA F mm i Capacitive Pickoff K B g R OUTPUT Servo Amplifier a. Spring-mass accelerometer b. Pendulous balancing accelerometer Fig. 4 Accelerometer principles: spring-mass and pendulous balancing accelerometer 6 To attain a finite response time of the accelerometer a damped suspension of the proof-mass is used. Accelerations acting in the sensitive axis have the same effect like the static gravity (consequence of the equivalence principle), as shown explicitly in Fig. 4-a for the spring-mass accelerometer. In contrast to the spring-mass accelerometer, the IMU’s pendulous accelerometer QA2000-40 uses an antagonist torque to establish the operating Metal conducting layer point, produced by an elastic quartz suspension (see Fig. 5, 6) of the proof-mass (PM), which assures a reduced torsion constant. The input axis IA, the pendulous axis PA – situated IA along the pendular arm – and OA the output axis OA, perpendicular to the two others, PA are also depicted in Fig. 4, 5. The accelerometer employs a capacitive pick-off to command the feedback compensation through a linear electrodynamic actuator (Lorentz force), that produces a rebalancing torque. As a consequence of the continuous compensation, the proof-mass pendular amplitude is very small, resulting in a very good linearity and an Fig. 5 Physical realization of the pendulous rebalancing accelerometer almost complete lack of Honeywell QA2000 [from Lawrence, 1999] hysteresis, with the additional benefit of bias (originated from residual non-elastic moments of the suspension) and drift (caused from material fatigue) reduction. The output current/voltage signal is proportional to the magnitude of the rebalancing torque. Fig. 6 Exploded view of the QA2000 Honeywell accelerometer, from [AlliedSignal, 1998] The equilibrium of the acting torques – the active torque, due to the system acceleration (M =m(cid:215) a(cid:215) l , with m a MC the equivalent pendulum mass, concentrated in the centre of mass, and l the pendular arm), the antagonist one MC (torsion momentum:Mt =τ (cid:215) θ , with the pendulum elastic restraint and the deflection angle of the pendulum-arm τ θ with respect to the accelerometer case), the compensation torque (M =F (cid:215) l , the product between the torquer r r F rebalance force F and the torquer arm l ) and the damping (friction) torque, proportional to the angular rate r F & (M =B(cid:215) ) – permits the formulation of the differential equation for this rotating, oscillating system (using the f θ scalar form of the angular momentum theorem: K& = J(cid:215) & =∑Mext ): ω i i 7 && J(cid:215) =∑Mext, (2.1-1) θ i i where: J =inertial moment of the pendular arm, ∑Mext=the sum of all externally applied torques (see above). i i The linearity of the rebalanced sensor is entirely dependent on the high linearity property of the Lorenz-force torquer: Fr=KF(cid:215) i (i represent the applied compensation current, with the coefficientKF =Bgap(cid:215) lcoil- wire). The ~ v(s) a m(cid:215)lMC +_S +_S +_S J&q& s1(cid:215) J q& 1s q + S + KC u PID(s) Ar ur Mr Mt G(s) l B F Fr i t (cid:215) q t KF R Output i Fig. 7 Dynamic model of the pendulous accelerometer with magnetic rebalancing pendulous-accelerometer block-diagram in Fig. 7, where all the variables are Laplace transforms, shows also the capacitive-detector transfer coefficient K , in [V/rad] [see, e.g., Merhav, 1996], the rebalance-loop amplification C A (both of them considered as frequency-independent terms), respectively the PID(s) (Proportional, Integral, r Differential) regulator transfer function. In the transfer function G(s) the frequency dependent term issues from the electrical model of the balancing coil assembly. The expressions of transfer-functions in the block-diagram shown in Fig. 6 are: 1 : the transfer-function of the accelerometer sensor element, a damped elastic s²J +sB+τ pendulum; s²T T +sT +1 PID(s) = K (cid:215) d i i : the transfer-function of the lag-compensation element, of type PID sT(1+sτ ) i del Proportional-Integral-Derivative, with K the amplification factor of the PID- PID regulator, T and T the derivative and the integrating time constants, respectively, and d i τ a first-order delay term; del 1 G(s) = : the equivalent Laplace admittance for the electric part of the rebalance-torquer R+sL assembly, with R the serial resistance (winding resistance neglected) and L the total coils inductivity. We write the expression of the closed-loop transfer-function, following the above block-diagram, with explicit ~ dependencies from the applied acceleration a(s) and from the noise contributionv(s) in the form: u (s)=F (s)(cid:215) a(s)+F (s)(cid:215) v~(s), (2.1-2) out D N that is: uout(s)= K (cid:215) l + s(s²J +sRB(cid:215) +mτ(cid:215))l(MsCTiτ del +Ti)(sL+R) (cid:215) a(s)+ KF (cid:215) lF + s(sRTiτ del +Ti)(sL+R) (cid:215) ν~(s) F F KC (cid:215) KPID(cid:215) Ar (cid:215) (s²TdTi +sTi +1) s²J +sB+τ KC (cid:215) KPID(cid:215) Ar (cid:215) (s²TdTi +sTi +1) and consider the asymptotic values of the factorsF and F , for the null pulsation (s= jw =0), resp. for infinite D N ones (sfi ¥ ). Then we obtain information in a broad frequency spectrum about the dynamic sensor behavior, respectively about the noise influence: R(cid:215) m(cid:215) l F (s) = MC (2.1-3) D s=0 K (cid:215) l F F F (s) =0 (2.1-4) D sfi ¥ 8