Comparison Of Low-Cost GPS/INS Sensors For Autonomous .
Comparison of Low-Cost GPS/INS Sensors for Autonomous VehicleApplicationsG. H. Elkaim , M. Lizarraga , and L. Pedersen† AutonomousSystems Lab, Computer Engineering, University of California, Santa Cruz, Santa Cruz, CA 95064 USA† Intelligent Systems Division,NASA Ames Research Center, Moffett Field, CA 94035Abstract— Autonomous Vehicle applications (UnmannedGround Vehicles, Micro-Air Vehicles, UAV’s, and Marine Surface Vehicles) all require accurate position and attitude to beeffective. Commercial units range in both cost and accuracy,as well as power, size, and weight. With the advent of low-costblended GPS/INS solutions, several new options are available toaccomplish the positioning task. In this work, we experimentallycompare three commercially available, off-the-shelf units insitu, in terms of both position, and attitude. The compared unitsare a Microbotics MIDG-II, a Tokimec VSAS-2GM, along witha KVH Fiber Optic Gyro. The position truth measure is from aTrimble Ag122 DGPS receiver, and the attitude truth is from theKVH in yaw. Care is taken to make sure that all measurementsare taken simultaneously, and that the sensors are all mountedrigidly to the vehicle chassis. A series of measurement trialsare performed, including light driving on coastal roads andhighway speeds, static bench testing, and flight data taken ina light aircraft both flying up the coast as well as aggressivelymaneuvering. Allan Variance analysis performed on all of thesensors, and their noise characteristics are compared directly.A table is included with the final consistent models for thesesensors, and a methodology for creating such models for anyadditional sensors as they are made available.The Microbotics MIDG-II demonstrates performance thatis superior to the Tokimec VSAS-2GM, both in terms of rawpositioning data, as well as attitude data. While both performquite well during flight, the MIDG is much better duringdriving tests. This is due to the MIDG internal tightly-coupledarchitecture, which is able to better fuse the GPS informationwith the noisy inertial sensor measurements.VSAS-2GM. These are compared under three test conditions:static, road, and flight. The theory behind the models isexplained in Section III, and experimental data is used togenerate consistent models.I. INTRODUCTIONII. HARDWARE DESCRIPTIONAutonomous Vehicle applications (Unmanned Ground Vehicles, Micro-Air Vehicles, UAV’s, and Marine Surface Vehicles) all require accurate position and attitude to be effective[7]. While navigation grade IMUs have existed for manyyears, they remain very expensive, and out of reach both interms of cost and payload for all but the best funded projects.Small UAVs, even if the can afford the cost, cannot supplythe necessary power to these units.Combined MEMs based GPS/INS solutions offer lowpower, low cost, and lightweight navigation sensors forautonomous vehicles. The challenge remains to quantify theperformance versus cost. Each time a new design for anautonomous vehicle is begun, a navigation solution is picked,and rarely is the choice revisited. In order to determinewhich is the right GPS/INS navigation solution, each sensorrequires a consistent model so that a full comparison can bemade.In this work we compare two low-cost GPS/INS navigation sensors, a Microbotics Inc. MIDG II and a Tokimec USAThis work is, in essence, an attempt to compare betweentwo small combined GPS/INS units suitable for use inautonomous vehicles such as UAVs, UGVs, and ASVs. Inaddition to the two tested units themselves, a KVH FOGwas used to provide a truth reference for yaw, and a highquality differential GPS receiver, the Trimble Ag122 withcoast guard beacon differential corrections, was used toprovide a track truth reference. Each of these sensors will bedetailed below, along with a brief description of their internaloperation, and specifications. Note that two other sensors areavailable to the lab, but were not ready for testing at the timeof the flight tests, and are thus not included in this work. Thefirst is a Crossbow AHRS-400 attitude and heading referenceunit. This unit uses MEMs based gyros and accelerometersin order to calculate a traditional attitude solution, and is supplemented by a three axis magnetometer to generate absoluteheading. The accelerometers are capacitive MEMs devices,the gyros based on vibrating ceramic beams (such as the Systron Donner Horizon series [3]), and the magnetometers are1-4244-1537-3/08/ 25.00 2008 IEEEFig. 1.1133Navigation Sensors installed in the cargo area of a Cessna 172
Fig. 2.GPS antenna affixed to the rear window of the aircraftflux-gate type. The AHRS-400 has an internal DSP runninga Kalman Filter and supplies the standard 3-2-1 euler angleset at 80Hz. A detailed description of the AHRS-400 can befound in [16]. Note that our own experience with using theCrossbow unit on an autonomous ground vehicle has beendisappointing due to the unacceptable yaw rate distortionsfrom the other onboard electronics [2]. Much of this hasbeen addressed with the newer versions of the unit, and it ishoped that future testing will corroborate these conclusions.In addition, a novel low-cost MEMs based sensor head hasbeen the focus of much work in the lab [8], [6], [5]. Acontinuation of the work found in [11], [10], [9], it wasof great interest to compare this gyro-free technique to thecommercial units. Using Freescale MEMs accelerometers,and Honeywell GMR magnetometers, this attitude systemhas shown bench tests that are very promising. Unfortunately,synchronizing the measurements and performing the attitudecalculations proved to be too difficult within the time frameof the tests, and so a comparative measure of this sensorwill be left to future experimentation. The two main truthsensors are the Trimble Ag122 DGPS receiver, and the KVHDSP-3000 Fiber Optic Gyro. The Ag122 receiver uses theCoast Guard beacons for differential corrections that arereceived on a separate collocated antenna [15]. The receiveruses carrier-smoothed code on the L1 C/A code to producesub-meter accuracy. The beacon signals are automaticallytuned in based on auto power or auto distance modes, andseamlessly provide differential corrections. It is capable ofoutputting GPS fixes at up to 10Hz, though in practice, 5Hzhas much lower position noise. This same unit was tested in[4] in both static and low dynamic tests and found to havea position error of approximately 0.36m (1-σ). The KVHDSP-3000 Fiber Optic Gyro (FOG) is a high performancesingle axis gyro. The DSP-3000 can be set into either angularrate or accumulated angle mode. In angle mode, it internallyimplements bias estimation and integration schemes to outputthe angle since last reset. The internal DSP implementstemperature correction, digitization, and signal conditioningFig. 3.Simulink model used to capture IMU datasuch that angle is remarkably clean. Given the low drift rate,the FOG is used as a truth measurement once the initial angleerror is determined. The full specifications can be foundin [13].A. Tokimec VSAS-2GMThe Tokimec VSAS-2GM is a low-cost blended GPS/INSsolution that is a small, lightweight, and low-power device.It is roughly 6cm wide (not including the mounting flanges),4cm deep, and 3cm tall. It uses three MEMs accelerometersand gyros, and a three axis magnetometer as well. Though itis not specified, based on the performance detailed later, theVSAS-2GM appears to use a loosely coupled INS mechanization. It is capable of outputting position and attitude atup to 100Hz, and can provide these positions either througha standard serial connection or through a CAN bus. TheVSAS-2GM consumes 200mA at 12V, for a total powerconsumption of 2.4W. The specifications are for pitch androll to be within 2 and heading to be within 3 , with positionbeing 15m. There is no capability of calibrating the VSAS2GM, which comes set from the factory. VSAS-2GM costsapproximately 4K.B. Microbotics MIDG-IIThe Microbotics MIDG-II is also a small blendedGPS/INS solution intended for small UAV applications. TheMIDG-II is part of a full fledged autopilot suite, the Microbot1134
Fig. 4.Allan Variance and Autocorrelation for MIDG Roll sensorFig. 8.Allan Variance and Autocorrelation for MIDG Pitch sensorGPS data for static testFig. 5.Fig. 6.Fig. 7.GPS CEP (1-σ)AP, and can be used either integrated into the autopilotor as a stand alone GPS/INS. Smaller than the VSAS, theMIDG-II measures 4 x 3 x 2 cm. Like the VSAS, it uses3 MEMs based accelerometers and gyros, with a 3-axismagnetometer as well. Internally, the MIDG-II uses tightcoupling in its filter mechanization (that is, the inputs to theKalman Filter are the raw pseudo-ranges, not the computedpositions). Additionally, the mechanization is accomplishedusing an Unscented Kalman Filter, and includes various flagsin the output to rate the quality of the solution. The MIDG-IIweighs 55gm, and consumes 1.2W. Position, velocity, andHistograms of GPS static data, with Gaussian fitFig. 9.1135Allan Variance and Autocorrelation for MIDG Yaw sensor
Fig. 10.Allan Variance and Autocorrelation for Tokimec Roll sensorFig. 11.Allan Variance and Autocorrelation for Tokimec Pitch sensorFig. 13.Allan Variance and Autocorrelation for Tokimec Yaw sensorFig. 14. Allan Variance and Autocorrelation for Tokimec Yaw sensor,linear drift removedattitude are available at up to 50Hz on an RS-422 bus.The noise specifications are 5m for the position, 2 forheading, and 0.4 for pitch and roll (1-σ) [14]. The MIDGcost approximately 6K.III. SENSOR MODELINGGiven the vast differences in sensor specifications, it isimportant to develop a unified model that can be used toperform an “apple-to-apples” comparison between similarsensors. A unified model is also useful in developing simulation models for the sensors in order to be able to characterizeoverall system performance and determine the cost/benefitof different sensor configurations. We will use this modeldirectly on all of the processed outputs (euler angles) in orderto characterize the relative performance of each sensor.A general model for the sensor output follows closely theone presented in [17]:ξm (1 Sf )ξt b(t) νwwhere ξm is the measured quantity at the sensor outputand ξt is the true quantity. Sf represents a scale factorerror, b(t) represents the time varying bias or drift terms,and νw is the noise on the sensor. b(t) νw is the residualmeasurement of the sensor with no input, and can thus bemeasured when the sensor is static. The sensor noise, νwcan be assumed to be zero mean band limited white noise.This can be characterized by taking the standard deviationof the sensor’s output over a short period of time with noinput applied. In this work, we will ignore the scale factorerror (Sf 0) as this is usually calibrated out at the factoryor during initial installation.The total sensor bias b(t) is comprised of several components, and consists of an additive error:b(t) b0 b1 (t)Fig. 12.(1)Tokimec YAW channel, static test demonstrating linear drift(2)The constant null shift, b0 , is easy to determine by1136
Fig. 15.Allan Variance and Autocorrelation for KVH Yaw sensorFig. 17.Fig. 16. Allan Variance and Autocorrelation for KVH Yaw sensor, lineardrift removedcomputing the mean of the sensor over a long period oftime when no input is applied. Note that an easy estimate ofthe null shift can be accomplished by measuring the outputwhen static (as in the case of computing the bias for rategyros while sitting still).The time varying bias drift, b1 (t), is characterized as astochastic time sequence. Modeling the drift as band limitedwhite noise would be too conservative in the short term,and too optimistic in the longer term. In order to adequatelymodel this time sequence, yet retain a tractable model, wemodel the bias drift as an exponentially correlated or firstorder Gauss-Markov process:1ḃ1 (t) b1 (t) ωb(3)τwhere τ is strictly positive and is the correlation timeconstant. ωb is a Gaussian white process noise with a powerspectral density given by:2σb(4)τThe parameter τ defines the degree of correlation. If τ issmall, then the signal is highly correlated in time, and in thelimit as τ approaches infinity, the signal becomes a randomconstant (e.g.: Gaussian white noise). The slow time varyingbias drift can be completely modeled with the parameters τand σb .E {ωb (t1 ) ωb (t2 )} Fig. 18.Time sequence of Euler angles, static testHistograms and Gaussian fits to static Euler Angle dataTwo different, but complementary, techniques will beused to extract the values of τ and σb : the Allan Varianceand the autocorrelation function. The Allan Variance is astandard approach to characterize noise models originallydeveloped to analyze the stability of atomic clocks [1].Whereas the power spectral density of a signal relates thepower as a function of freqency, the Allan Variance doesso as a function of averaging time [12]. Using the AllanVariance, the signature of exponentially correlated noise canbe revealed.The Allan Variance plot will demonstrate a slope of 1/2during the time where wide-band noise is the dominantprocess. Where the slope is 1/2, the process is dominatedby correlated noise. Thus a minimum for the time constantcan be extracted from the point on the Allan Variance plotwhere the slope changes from 1/2 to 1/2 (often referredto as the “flicker floor”). Thus a signal with only wide-bandnoise would appear to drop at a slope of 1/2 throughoutthe averaging time.Using the autocorrelation plot, τ corresponds to the lagwhere the value is at 1/e from its zero-lag peak (approximately 37% of the peak value). Note that in order toextract the slowly varying time process, the sensor readingsare decimated through averaging for a variety of windowwidths, with the correlation time being consistent throughthe averaging. Likewise, it is possible to extract the Markov1137
Fig. 19.Fig. 20.Fig. 22.Road test position data, large yaw changesFig. 23.Road test position data, tracking difficultyRoad test position data, full testRoad test position data, start locationprocess noise, σb by taking the square root of the peak ofthe autocorrelation function. Again, this should be consistentacross averaging time.Using these tools, it is possible to model the bias drift of asensor in a unified and simple way. Note that many sensorsdisplay multiple correlation processes that have different timescales, but that these are beyond the scope of this unifiedmodel.IV. EXPERIMENTAL SETUPFig. 21.Road test position data, end locationIn order to synchronously capture the data from the varioussensors, a MATLAB/Simulink model was created to strobethe sensors and record the outputs into a file on a laptopPC. The simulink model is shown in Fig. 3, and uses areal time block to generate hard real time pulses at 20Hz.In addition to recording the data, the simulink model alsogenerated a trigger pulse for a camera that was pointed outthe window. These images will be later used to investigateimproved position estimation using the overlapping visualfield within each high resolution photo.All sensors were rigidly mounted to a plexiglass plate(Fig. 1) so that their relative orientations could be preciselycontrolled. This whole plate was secured to the rear cargo1138
Fig. 24.Euler angles vs. time for road test dataFig. 26.Fig. 25.Yaw angles for road testYaw angles under large dynamic maneuversFig. 27.bay of a Cessna 172 light aircraft for flight testing. Additionally, the three GPS antennae were affixed to the rearwindow, as pictured in Fig. 2. The entire setup was poweredindependently from a 12V battery, which was used to runan inverter for AC power, a power supply for regulated DCvoltages, and the data pumped back to the laptop throughseveral USB to serial converters.Three different tests were performed. First, slightly overtwo hours worth of static data was recorded for the unitssitting on a bench to generate the consistent models asdescribed in Section III. The second data set was takenwith the sensors mounted in a car driving along the coastfrom Watsonville airport (KWVI) to Santa Cruz, CA. Thisdrive included both freeway speeds as well as slower drivingalong coastal roads. The last experiment was to fly thesensors in the 172 from Watsonville up the California coastapproximately 50km to Ano Neuvo state park and return.During this flight, straight and level flight as well as tightturns and aggressive zero-g pushovers were performed.V. STATIC DATAIn order to establish baseline performance, and see ifthe units met their advertized specifications, GPS data wasgathered with the antenna situated in a relatively benignenvironment as a bench test. After removing obvious outliersfrom the data stream (most likely communication errorsError from KVH yaw histogramscaused by our data collection setup), the points are transformed into North-East-Down coordinates and plotted as ascatter plot in Fig. 4. The calculated CEP from the data areplotted overlayed upon a satellite image of the location inSanta Cruz, CA. As expected, the Trimble Ag122 is the best,with a CEP of 0.35m and beats its specification of “under 1meter.” The MIDG has a CEP of 3.7m while its specificationis for 5m, and the Tokimec is 9.3m with an advertised specof 15m. Note that all GPS receivers tested exceed theirspecifications, and the relative measured performance of eachis consistent with the advertised specification. The CEP radiiare overlaid on the same satellite image in Fig. 5.Lastly, in order to visualize the spread of the data, and toasses how close to “white” the GPS noise is, histograms ofeach GPS receiver along with an ideal Gaussian fit to thedata are presented in Fig. 6.Using the basic sensor model (Eq. 1) with the first orderGauss-Markov bias drift term (Eq. 2), each sensor was benchtested for slightly over 2 hours at 20Hz. This resulted in astream of data that was analyzed with the Allan Varianceand autocorrelation functions as detailed in Section III. TheMIDG data was analyzed first.A. MIDG ModelFig. 7 shows the short term (15 seconds) worth of data inthe top left panel. Taking the standard deviation of this we get1139
Fig. 28.Fig. 29.Fig. 30.Fig. 31.Flight GPS data overlaid onto satellite mosaicFlight GPS data vs. timeFig. 32.Flight test turn northern boundary, view from northFlight test turn northern boundary, view from aboveFlight test steep turns and pushovers, from aboveFig. 33.1140Flight test descent to landing
Fig. 34.Fig. 35.Flight Euler angles vs. timeFig. 36.Flight yaw anglesFlight Euler angles vs. time, zoomed in on maneuver sectionFig. 37.the value of σν to be 0.06 , which is the standard deviationof the sensor noise. Looking at the Allan Variance in the topright panel, we see the characteristic 1/2 slope of wideband noise out to an averaging time of approximately 100seconds. There we encounter the flicker floor, and the slopechange to 1/2 indicating the dominance of correlated noiseat these time scales. Using the autocorrelation, we find thatthe correlation time, τ is 164 seconds, and the Gauss-Markovdriving noise, σb is 0.05 . With these three parameters, theroll channel is characterized. Note that the null shift, b0 isdetermined when the unit is turned on, with the knowledgethat the aircraft or vehicle is level. The same analysis isperformed for both the MIDG pitch and yaw, and the graphspresented in Fig. 8 and Fig. 9 respectively.From the analysis, the parameters of the pitch are σν of0.1 , τ , and σb of 0.07, and those for yaw are 0.06 , 67seconds, and 0.14 , respectively. These results deserve a fewcomments. The correlation time for the pitch means that itwas not found using the autocorrelation function. However,examining the Allan Variance panel in Fig. 8 shows a likelycorrelation time after 200 seconds, but the data becomesnoisy enough to make that distinction difficult. A longerstatic test would clean up the data and allow for betterdiscernment of τ
terms of cost and payload for all but the best funded projects. Small UAVs, even if the can afford the cost, cannot supply the necessary power to these units. Combined MEMs based GPS/INS solutions offer low power, low cost, and lightweight navigation sensors for autonomous vehicles. The challenge remains to quantify the performance versus cost.
3. Overview of the Bible 2. How did the Bible come into being? 4. The First process of the Bible GPS is Understanding. 5. The Second process of the Bible GPS is Application. The Third process of the Bible GPS is Communication. 6. The Bible GPS on Galatians 5: 16-26 7. The Bible GPS on Ephesians 5: 8-20 8. The Bible GPS on Romans 3: 21-26
GPS outages. To overcome these limitations, GPS can be integrated with a relatively environment-independent system, the inertial navigation system (INS). Currently, most integrated GPS/INS systems are based on differential GPS (DGPS) due to the high accuracy of differential mode (Petovello, 2003 and Nassar, 2003). More recently, GPS-
History of GPS User Equipment Development at SMC . 180,000 units , Bosnia and OIF . Precision Lightweight GPS Receiver (PLGR) Defense Advanced GPS Receiver (DAGR) 500,000 units, since 2005 . Ground Based-GPS Receiver Application Module (GB-GRAM) 100,000 units, since 2005 . Small Lightweight GPS Receiver (S
a ship under navigation. 2 SYSTEM OUTLINE 2.1 GPS-BASED CONTROL STATION The carrier phase data for RTK-GPS positioning have been transmitted experimentally from several GPS-based control stations, which work as the reference stations of RTK-GPS via DMCA. The service is available at the moment in the following districts: the
Low-Cost GPS/INS Integrated Land-Vehicular Navigation System for Harsh Environments Using Hybrid Mamdani AFIS/KF Model 24 stability of GPS), thus providing precise and ubiquitous navigation. The INS/GPS integration is a mature topic that is widely covered in the literature when it comes to high-end systems [2-5]. However, the recent studies
Low-cost IMU Through the Use of Tightly-coupled L1 GPS Stanley Radzevicius, W. Todd Faulkner, David W.A. Taylor . approach also allows integration of sparse pseudorange measurements that are discarded in loosely coupled approach. 7 . Indoor/Outdoor Tightly Coupled GPS/INS Navigation: Short Segment Enter Building Exit Building GPS Only GPS .
Cost Accounting 1.2 Objectives and Functions of Cost Accounting 1.3 Cost Accounting and Financial Accounting — Comparison 1.3 Application of Cost Accounting 1.5 Advantages of Cost Accounting 1.6 Limitations or Objections Against cost Accounting 1.7 Installation of a costing system 1.7 Concept of Cost 1.9 Cost Centre 1.10 Cost Unit 1.11 Cost .File Size: 1MB
November 2014 HR: Getting smart about agile working WORK WORKFORCE WORKPLACE in association with . Championing better work and working lives The CIPD’s purpose is to champion better work and working lives by improving practices in people and organisation development, for the benefit of individuals, businesses, economies and society. Our research work plays a critical role – providing the .
