Experiments of low-cost INS/GPS Navigation platform based on PC104
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1 xpeiments of low-cost S/GPS avigation platfom based on PC14. Hachelef, P. Lavoie, D. Li, R. Landy Depatment of lectical ngineeing École de Technologie Supéieue (TS), LACM Laboatoy 11 ote Dame Steet West, H3C 1K3 Monteal, Canada iogaphy acim Hachelef eceived a S degee in engineeing techniques at Vesailles Univesity (Fance). He is a Maste Student in Aeospace specialized in contol, at STACA Univesity, Pais (Fance). He was an exchange intenship student at École de Technologie Supéieue, Monteal (Canada) on GPS/S integation. His eseach activities involve in MMS and RLG-based S/GPS integation in simulation/eal time tests. Abstact With the state of the at innovations of navigation systems, GPS is becoming a vey impotant pat of daily life. ndeed, GPS is a vey helpful and pecise navigation system howeve its pefomance is faily vulneable due to the envionment noise, which may cause GPS signals loss and attenuation. Hence this is had to ely much on this technology. Compaed with GPS, the S is a self-contained navigation system, which has jampoof pefomances but the sensos induce eos which ae gowing with time. These two navigation systems integated togethe can compensate each othe s weakness poviding a continuous data acquisition using an adapted filte. This integated solution of GPS/S gives an accuate solution which is low-cost and jampoof. This pape pesents a low-cost GPS/S platfom developed with Mico lecto-mechanical System (MMS). Fast pototyping tools such as Matlab/Simulink ae utilized to implement/validate the algoithm. This platfom is consist of an assembly of diffeent PC14 cads such as acquisition cad, GPS cad, thenet cad, mothe boad stacked up togethe poviding the link between the sensos, the algoithm and the host compute. The softwae including S, GPS data acquisition and the Kalman filte is loaded and pocessed on the PC14 based compute. This platfom is totally self-embeddable and can be used independently without any extenal hadwae/softwae suppots. The algoithm utilized can be adapted to diffeent gade of inetial sensos by changing few paametes. 1. ntoduction High pecision netial avigation employing the expensive inetial sensos is contained to high technology applications like satellite, pobe, missiles but the emegence of low-cost MMS in the maket has facilitated the development of new applications. Theefoe, inetial systems ae expanding its maket to moe common applications such as ca navigation, video games and obots. f combined with GPS, inetial navigation system can be a vey pecise device deliveing data even when the GPS signals ae blocked. Duing the GPS loss, inetial sensos such as MMS can povide position, velocity and acceleation until the GPS can find a new available satellite constellation. n that case, the pecision is not the finest but with the Kalman filte unning, the dift caused by the sensos eos can be compensated when the GPS signals ae found. The MMS platfom is totally embeddable poviding a totally autonomous system when poweed with an embeddable powe supply. The platfom utilized is based on a PC14 bus compute by which we can integate all the needed hadwae devices. The pape is oganized as the followings. The section two gives a global view of the platfom: the devices utilized, the softwae used to communicate and the algoithm stuctue. The section thee shows the MMS test esults including simulation and eal time acquisition followed by a qualitative analysis. Section fou shows the esults by utilising the same algoithm with diffeent sensos which demonstates the vesatility of the algoithm. Finally, the esults ae shown in the pape and the futue advancement of the poject ae also discussed in the conclusion.
2 2. Hadwae and Softwae A good link between the hadwae and the softwae is a key issue fo the design of the platfom. This link is povided by the xpctaget inteface (Simulink) which gives a coect and quick link fo the communication between the host compute and the PC Hadwae The platfom is composed of seven diffeent stages stacked up togethe though the PC14 bus. This configuation makes the individual element independent fom each othes and povides a good synchonization fo the data tansmission. On the top stage thee is the inetial senso (MMS) which is not PC14 compatible but the infomation is sent via an extenal bus to the acquisition cad. This stage povides the specific foces and angula ates measuements given by the MMS. This platfom is also equipped with a gaphic cad making able to display all the data pocessed by the PC14 in eal time on a distinct sceen. On the bottom stage, thee is the PC14 motheboad whee the algoithm is loaded and executed. The benefit povided by PC14 compatible devices is that the data ae aleady synchonized because of the unique PC14 bus linking all the devices. 2.2 Softwae Thee ae two distinct pocedues detailed in the following section, one fo the simulation and one fo the eal time acquisition. The equations utilized by the softwae ae implemented into the diffeent blocks of the shown on the figue 2: Figue 2: Pogam Stuctue: S and Kalman filte Fo the simulation, the efeence tajectoies ae geneated by the softwae Micosoft Flight Simulato. The infomation povided by the softwae can be saved diectly in an ASC fomat file which is compatible to Matlab/Simulink. The useful data povided by the simulato ae the following: Figue 1: GPS/S Platfom Pototype On the next stage, thee is the GPS eceive which obtains and tansmits the position and velocity solutions to the algoithm via the PC14 bus. Following the GPS eceive, thee is a 16-bit-acquisition cad which collects the data fom the MMS via the extenal bus. Unde that, a PC14 compatible powe cad delives the powe and voltage equied to each othe cads. Then, a PC14 compatible netwok cad is added to build a TCP/P connection to a host compute. This connection is used fo two impotant tasks: fist, to send the pogams fo the eal time pocessing and second, to acquie and ecod the data pocessed in eal time. - Position expessed in tems of latitude [deg, longitude [deg and altitude [ft - Velocity expessed in tems of oth Velocity, ast Velocity and Vetical Velocity, all in [ft/s - Attitude angles expessed in tems of pitch [deg, oll [deg and heading [deg The MU simulato is a pogam designed to geneate the angula ates and specific foces fo a simulated flight tajectoy by using the aleady-known position, velocity and attitude angles. The MU data geneation takes into account the gavity and the ath s otation. n geneal, fo the sake of a bette undestanding this pogam is like a evese pocedue of the S calculation which povides the position, velocity and attitude angles fom the sensos measuements. To avoid edundancy, only the S pocess will be explained.
3 To have a ealistic simulation of the MMS, the noises and bias fo the thee axes of the acceleometes and gyoscopes have to be taken in account. This equation shows how those paametes ae added to the aw measuement in the algoithm: X = ( + M ) ( X + δx + ε ) [5 mes s tue Whee: X = measued vaiable of the senso, mes [m/s 2 fo acceleomete and [ad/s fo gyoscope X = noise fee vaiable (same units as X tue mes ) M = scaling facto matix S δ x = bias on the senso measuement ε = noise of the senso measuement = identity matix The coesponding Simulink model fo the intoduction of the petubations is shown on the figue 3: Figue 3 : Acceleometes and Gyoscopes model n this model the bias and the noise vectos ae added to the eo fee data. Then, the matix is multiplied by a scale facto to obtain the simulated aw data. The values fo those paametes ae povided by the manufactue specification datasheet. This MU model takes the main chaacteistics of the MMS in consideation. Howeve, it still can be impoved with othe chaacteistics such as influence of tempeatue and non lineaity as long as the infomation is povided by the manufactue. The est of the pogam is the same fo both simulation and eal time acquisition. The aw data coming fom the MMS o simulated with the MU simulato ae pocessed diectly by the S algoithm which pefoms all the calculations to obtain the position, velocity and attitude angles. The following equations ae used in the model and they ae integated with a method using quatenion: v = C[ a + [ g p (1) C& C& h& = Whee: = = C C S S ( S{ [ ω } + 2S{ [ ω })[ v {[ ω } S{ [ ω } C {[ ω } Z [ u [ v [ a is the measued acceleation vecto; [g p is the gavity vecto at the suface of the eath; [ ω is the tanspot ate ρ ; [ ω is the measued angula ate vecto; [ Z u is the vetical unit vecto of the avigation is the inetial fame; C is the tansfe matix fom the ody fame to the avigation fame; C is the tansfe matix fom the avigation fame to the ath fame; is the ath Centeed ath fixed (CF) fame; is the avigation fame; is the ody fame (vehicle-fixed fame); S{a} is the anti-symmetic matix of the vecto a. The fist equation (1) shows how to get the velocity popagation of the navigation fame in the navigation fame () efeed to the ath fame () fom the MU output and the gavitation model. The second equation (2) explains the popagation of the ody fame () compaed with the avigation fame (). The thid equation (3) is the popagation of the position matix. The fouth equation (4) epesents the popagation of the altitude. The whole equation allows the calculations of PVA fom the MU aw measuements independently. This means that no coection to the measuements have been done yet. The gavity model takes in consideation of the ath s mass and ath s otation: (2) (3) (4)
4 g p = g + S ( ω ). S( ω ). Whee: g p is the Plum-bob gavity vecto g is the gavity vecto S( ω ) is the ath s otation ate is the distance vecto fom cente of the ath to the mobile The ath s otating ate is also taken into account. Fo this eason, when the sensos ae static, they can measue the ath s otating ate: ω 15.4deg/hou. Concening the attitude angles the equation is the following: ω = ω + ω + ω Whee: ω is the gyoscopes measued value ω is the ath s otating ate ω is the tanspot ate i.e. the otation ate of the avigation fame with espect to the ath s fame ω is the attitude ate: otation ate of the avigation fame with espect to the ody fame The equation (5) shows the composition of the otation vecto fo ody fames. This is the pocess to obtain the gyoscopes measues by using the attitude ates, the tanspot ate and the ath s otating ate. When the GPS signals ae available, coections povided by the avigation filte ae taken into account duing the S pocess. Cuently the ole of the avigation Filte is played by a Kalman Filte that povides the necessay coections to input into the S. The ole of the Kalman filte in ou application is to estimate and coect the MU measuements (position, velocity and attitude angles) with the aid of the GPS position and velocity. The Kalman filte uses the estimated state fom the pevious time step and the cuent measuements to compute the estimated state of the cuent time step. (5) This is a geneal epesentation of the Kalman filte cycle which content two impotant pats, the pediction and the measuement update: Whee: x ) k is the estimate of the state at time k;,k is the eo covaiance matix (a measue of the estimated accuacy of the state estimate). The avigation filte and the S algoithm ae continuously being modified and impoved. Theefoe, it is essential to be able to change some pats of the algoithm apidly. Fom this point of view, Simulink is a vey convenient tool fo fast pototyping. The algoithm can be easily modified and with the eal time wokshop tool, the whole algoithm can be e-make in C, complied and then loaded on the platfom. The xpctaget libay of Simulink povides the necessay dives to ead diectly the data fom the diffeent cads. This libay can ceate the inteface with the host compute to ead and command the platfom in eal time. While fom a diffeent point of view, Simulink is not the ideal softwae to un this algoithm due to all the opeation needed to pass fom the Simulink vesion to the C vesion loaded into the platfom. This sequence of opeation can cause some unexpected poblems deceasing the pefomances of the algoithm. Theefoe, a C-code vesion of the whole algoithm package is cuently unde development.. 3. MMS Results The following section will pesent the test that has been made fo both simulation and eal time acquisition with the MMS sensos. 3.1 Simulation The Figue 4 epesents the tajectoy pocessed in simulation. The blue line is the efeence tajectoy geneated by the flight simulato and the ed line coesponds to the solution calculated by the algoithm.
5 _ Real Pofile _ stimation D estimated position vs tue P e Ve k e Vn k e Vu [ft Up othing asting 3 x 1 4 Figue 4 : 3D Position of MMS simulated sensos Position: The Kalman filte update ate can be obseved clealy on the gaph: evey 1 ms, the avigation filte povides a new estimation of the position eos. The maximal eo that is located on an axis is aound 5 metes. This peiod coespond to the high dynamic peiod duing the flight. easting nothing altitude 5-5 eu position linea model Time [s Figue 5 : Position o fo MMS Simulation P matix: This matix gives the infomation about the Kalman filte estimations pefomance. ts convegence means that the estimations ae close to the eality. The P matix of this expeiment shows that all the paametes estimations ae conveging quickly. This poves that the kalman filte is woking well giving a good estimation of the paametes. [m k e Pe k e oll k e Pn k e pitch k e Pu k e heading [m/s Figue 6 : P Matix fo MMS Simulation Velocity: The esults show that the eo fom the lowcost MMS (Simulation) neve exceeds one pecent of the total value. Consideing the MMS chaacteistics, the velocity eos shown ae good. Vel e ast Vel e oth Vel e Up 2-2 velocity eo linea model Time [s Figue 7 : Velocity o fo MMS Simulation The expeimental esults validate the algoithm design. This algoithm conveges quickly and the final esults povide a good estimation of the initial tajectoy. t is also impotant to notify the limitations of the model. n this situation, the noise, biases and all the majo eos ae added manually. That means that the values of the added noises ae known exactly howeve which is impossible in eal time wold. Anothe cucial aspect is that all those paametes ae dependent of many diffeent issues such as tempeatue, humidity, pessue, senso non-lineaity etc. Usually, an estimation of the action of the main paametes is povided by the datasheet but it is not always simple and convenient to eplicate all those effects.
6 3.2 Real Time xpeiment The expeiment shown in the this (?) section is a stand alone test that has been made with the low-cost sensos. The pupose of this test was to test the pefomances of the MMS without any aiding devices such as GPS assistance. The tajectoy is a vey simple tajectoy made inside a building which we know pecisely the length. The figue 8 coesponds to this tajectoy: This expeiment has been pefomed seveal times and it has been possible to show the epeatability of the esults. This expeiment also demonstates that this device is completely self-contained. t woks inside as well as outside always giving the same accuacy in the esults. Something impotant with MMS is that it cannot set initial conditions itself. So if used alone, it has to be manually initialized to initial position, velocity and acceleation. 4. Othe sensos Figue 8 : Real time acquisition tajectoy (MMS) Afte pocessing the algoithm, the esults ae as shown in the figue 9: MMS Tajectoy A lot of tests have been made with anothe type of sensos. The pupose fo these tests was to validate the whole algoithm, to test its pefomances and to develop a new C-code vesion of it. The algoithm has been validated in both Simulink and C-code vesion with these sensos. As it was afoementioned the algoithm is vesatile and the integation of the new sensos to the algoithm was made by changing just a few paametes which ae mostly elated to the sensos chaacteistics itself. The esults shown in the next section ae elated to a eal time oad test made in a paking lot. The dynamic of the tajectoy is low and the total length is appoximately five minutes. The figue 1 epesents the whole tajectoy: longitude(deg) latitude(deg) Figue 9 : Real time S solution (MMS) The esults coming fom this expeiment ae povided in the table 1 [2. Real MMS Total Distance 15.97m 8.3m Total o 48.2% Latitude Dist. 8.23m 5.32m Longitude Dist m 6.36m Test Duation 2.36s Table 1 : Compaative Table Duing these expeiments it is possible to obseve vaious chaacteistics of the senso. The esult shows that these sensos poduce an eo which is gowing with time making it baely eliable fo a long duation stand alone condition. Figue 1 : Real time acquisition tajectoy (othe sensos) Fo this test, the algoithm was pocessed with the C-code pogam which is faste and moe accuate than the Simulink vesion. The solution calculated is the integated GPS/S solution and the esults ae the followings:
7 Figue 11 : Latitude and longitude eos (othe sensos) Position: The position eo is epesented in latitude and longitude eo. The maximum eos found fo this tajectoy ae aound ±2x1-6 adians which coespond to appoximately.5 to 1 mete. Figue 13 : Attitude eos (othe sensos) 5. Conclusion The esults fom the MMS test shows that the position of the solution diectly depends on the time duation of the simulation. This also explains the eason that such gade of senso needs to be coected with an aiding device, in this study, GPS plays this ole. evetheless, if this senso is used fo a limited time span, it can be helpful fo its jampoof chaacteistic and it can still povide a signal when GPS is unavailable. n a few wods, MMS can be an altenative to GPS when the signals ae blocked. Figue 12 : Velocity eos (othe sensos) Velocity: The velocity eos ae epesented in mete pe seconds. The maximum eos in this expeiment ae aound 2 mete pe second and seams to occu when the dynamic is high. These eos can be caused because of the low data acquisition fequency (limited to 1Hz fo this senso) so when the dynamic is high, some data ae lost causing a lot of eos. Attitude angles: The attitude angles eos ae epesented in adians. The maximum eos ae aound.2 adians (.1 ) fo the oll and pitch and aound.5 adians (1 ) fo the heading. The oll and pitch eo ae vey small because of the natue of the tajectoy. This test was made with a ca on a plain oad so the oll and pitch ae not changing a lot duing the whole tajectoy. The esults fom this pape show that the algoithm is woking well but thee is still some wok to do to impove it. Fo example, thee is still no senso compensation such as bias compensation which could educe a lot of the difting effect on the MMS. Also, the MMS do not povide the initial position, velocity and attitude angles so they have to be set up befoe unning the algoithm. n a nea futue, an initial alignment pocess will be added to the algoithm making it able to initialize all these paametes by itself. The GPS signals used by the algoithm as an aiding device can be impoved too with the integation of a RTK solution which is also unde development. The next goal fo the poject is to test the pogam with a diffeent low-cost MMS senso on a eal fly test to see the pefomance of the whole algoithm in a high dynamic envionment.
8 Refeences [1 Gioux R. (August 24), «Capteus bas de gamme et système de navigation inetielle : ouveaux paadigmes d application», PhD Thesis, École de Technologie Supéieue, Monte, Canada. [2 Gioux R., Landy R.J., Leach. and Goudeau R. (23), «Validation and Pefomance valuation of a Simulink netial avigation System Simulato», Canadian Aeonautics and Space Jounal, Vol. 49, o. 4, p [3 Gioux R., Sukkaieh, S. and yson, M., «mplementation of a Skewed-Redundant Low-Cost S in a Fast-Pototyping nvionment», O TM 24, San Diego, USA, Januay 24. [4 Savage, P.G. (2) «Stapdown Analytics, Pat», Stapdown Associates nc, Maple Plain, Minnesota. [5 Z. ennou, R. J. Landy, R. Gioux, A. Constantinescu, G. Gavidia «Web-ased MMS netial avigation Simulato» [6 Gioux, R., Goudeau R. and Landy R.J., «xtended Kalman filte eal-time implementation fo low-cost S/GPS ntegation in a Fast-pototyping nvionment», 16 th Canadian avigation Symposium, CAS, Toonto, Canada, Apil 25. [7 MMSense « AccelRate3d vesion datasheet
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