Intelligent vehicles and road transportation systems (ITS)

Transcription

1 ME470 Intelligent vehicles and road transportation systems (ITS) Week 3 : Positioning and navigation systems and sensors Denis Gingras Winter janv.-15 D Gingras ME470 IV course CalPoly Week 3

2 Course outline Week 1 : Introduction to intelligent vehicles, context, applications and motivations Week 2 : Vehicle dynamics and vehicle modelling Week 3: Positioning and navigation systems and sensors Week4: Vehicular perception and map building Week 5 : Multi-sensor data fusion techniques Week 6 : Object detection, recognition and tracking Week 7: ADAS systems and vehicular control Week 8 : VANETS and connected vehicles Week 9 : Multi-vehicular scenarios and collaborative architectures Week 10 : The future: toward autonomous vehicles and automated driving (Final exam) 2 13-janv.-15 D Gingras ME470 IV course CalPoly Week 3

3 Week 3 outline Brainstorming and introduction Context, history and importance of vehicle positioning in IVs and ITS Navigation system basic architectures Coordinate reference frames Global navigation satellite systems (GNSS) GPS and GLONASS Galileo and BeiDou Inertial navigation systems Accelerometers Gyrometers Compass Odometers Vehicle navigation states Maps and map matching Vehicle positioning via wireless telecommunications 3 13-janv.-15 D Gingras ME470 IV course CalPoly Week 3

4 Brainstorming Open questions and introductory discussion Brainstorming What is navigation? 4 13-janv.-15 D Gingras ME470 IV course CalPoly Week 3

5 Brainstorming Open questions and introductory discussion Brainstorming Define the following words: Positioning, heading, localization, pose, dead reckoning 5 13-janv.-15 D Gingras ME470 IV course CalPoly Week 3

6 Brainstorming Open questions and introductory discussion Brainstorming What is a coordinate reference frame? Name a few janv.-15 D Gingras ME470 IV course CalPoly Week 3

7 Brainstorming Open questions and introductory discussion Name a few technologies used for positioning of vehicles. Brainstorming 7 13-janv.-15 D Gingras ME470 IV course CalPoly Week 3

8 Brainstorming Open questions and introductory discussion Is the position accuracy requirement the same for all intelligent vehicle applications? Explain your answer. Brainstorming 8 13-janv.-15 D Gingras ME470 IV course CalPoly Week 3

9 Brainstorming Open questions and introductory discussion Brainstorming From a systemic point of view, what are the roles of positioning in intelligent vehicles? 9 13-janv.-15 D Gingras ME470 IV course CalPoly Week 3

10 Brainstorming Open questions and introductory discussion Name a few applications of vehicle positioning and car navigation systems Brainstorming janv.-15 D Gingras ME470 IV course CalPoly Week 3

11 Brainstorming Open questions and introductory discussion Brainstorming What are the main building blocks of a in-car navigation system? janv.-15 D Gingras ME470 IV course CalPoly Week 3

12 Brainstorming Open questions and introductory discussion Brainstorming Navigation is much easier since the 1960s and 70s. Why? janv.-15 D Gingras ME470 IV course CalPoly Week 3

13 Brainstorming Open questions and introductory discussion Brainstorming What is a sensor? What kind of sensors do we find in IVs? janv.-15 D Gingras ME470 IV course CalPoly Week 3

14 Brainstorming Open questions and introductory discussion Brainstorming What makes position estimates and localisation imperfect? janv.-15 D Gingras ME470 IV course CalPoly Week 3

15 A brief history of navigation Originally, navigation tools were developed for sailors. They could use the following tools: History Compass: needle giving the direction of the magnetic North of the Earth. Astrolab: You lined it up so the sun shone through one hole onto another, and the pointer would show your latitude. Quadrant: A sailor would see the North Star along one edge, and where the string fell would tell approximately the ship s latitude. Chronometer (Clock) : In 1764, John Harrison created a very accurate chronometer that would keep time at sea. Finally sailors had a tool to measure longitude at sea janv.-15 D Gingras ME470 IV course CalPoly Week 3 The North Star, also known as Polaris, helped sailors to figure out their position.

16 A brief history of navigation History Current handheld devices to provide absolute position of the vehicle Mission Navigation Localization janv.-15 D Gingras ME470 IV course CalPoly Week 3

17 Reference frames Reference frames To achieve navigation in a general way; a coordinate system is needed that allow quantitative calculations (dixit Claudius Ptolemy, ~130AD) A Reference Frame describes the coordinate system basis deploying the space in which we navigate. The definition of a 3D set of axes requires: An origin (3 quantities) An orientation (3 quantities) A scale (1 quantity) (A Helmert transformation estimates these 7 quantities to relate two reference frames). For the Earth: Terrestrial frames come in two forms: Geometric (mathematical description) Potential field based (gravity and magnetic) janv.-15 D Gingras ME470 IV course CalPoly Week 3

18 Reference frames Reference frames To navigate, one needs coordinates set-up in a reference frame. Several reference frames have been proposed, however three frames are typically used in intelligent vehicle positioning applications: 1) The Global frame, denoted E, called the Earth-Center, Earth-Fixed (ECEF) frame where the origin is at the center of mass of the earth; is used as the reference frame in the position estimation framework; 2) The Navigation frame, denoted N, which coincides with a local tangent frame with axes pointing along North, East, and Down (NED), is used to describe the trajectory in a results which is easier for human to process; 3) The Body frame is used to represent the sensor suite coordinates embedded in the vehicle janv.-15 D Gingras ME470 IV course CalPoly Week 3

19 Reference frames Reference frames ECEF Z Simple Global Reference Frame X Greenwich Meridian Center of Mass Y Geometric: Origin at the center of mass of the Earth; Orientation defined by a Z-axis near the rotation axis; one Meridian (plane containing the Z-axis) defined by a convenient location such as Greenwich, England. Coordinate system would be Cartesian XYZ janv.-15 D Gingras ME470 IV course CalPoly Week 3

20 Reference frames Reference frames Conventional coordinate system in navigation Until the mid-1950s, we used conventional coordinate systems (CCS) which rely on the direction of the gravity vector of the Earth. We had 2 different systems: A horizontal one (how far away is something) and a vertical one (height differences between points). Conventional coordinate systems are a mix of geometric systems (geodetic latitude and longitude) and potential based systems (orthometric heights). The origin of conventional systems are also poorly defined because determining the position of the center of mass of the Earth was difficult. Therefore, CCS were much more complicated to use than the simple global reference frame we use today. But how come this is simpler today? Do you know why? janv.-15 D Gingras ME470 IV course CalPoly Week 3

21 Reference frames Reference frames The global reference frame and the vehicle reference frame are represented by XgOgYg and XvOvYv, respectively. Vehicle pose is expressed by (x, y, θ) in the global reference frame, representing the position and orientation of a vehicle. The relationship between the global coordinates (x g, y g ) and vehicle coordinates (x v, y v ) of feature point P, can be expressed by: janv.-15 D Gingras ME470 IV course CalPoly Week 3

22 State space model for positioning History In the next few slides we will look at a general state space model for the vehicle position and velocity relating it to the on-board proprioceptive measurements. We distinguish two kinds of sensors: Attitude sensors Compasses and gyroscopes: provide angular and or angular velocity informations defining the attitude of the vehicle with respect to a fixed external global reference frame. Linear displacement sensors Accelerometers and wheel odometers: provide information about the longitudinal acceleration velocity and distance travelled of the vehicle with respect to an internal body frame janv.-15 D Gingras ME470 IV course CalPoly Week 3

23 State space model for positioning History Vehicle global position measured in the external frame: x x y z Vehicle linear velocity along each coordinate of the external frame x x y z Vehicle linear velocity along each coordinate of the body frame Heading (yaw) pitch and roll angles measured in the body frame frame Heading (yaw), pitch and roll angular velocities measured in the body frame T b b b b janv.-15 T E E E E T E E E E T b b b b v v v v T b b b b D Gingras ME470 IV course CalPoly Week 3

24 State space model for positioning History Vehicle global position measured in the external frame: T E E E E x x y z Vehicle linear velocity along each coordinate of the external frame T E E E E x x y z Vehicle linear velocity along each coordinate of the body frame T b b b b v v v v Heading (yaw) pitch and roll angles measured in the external frame T janv.-15 D Gingras ME470 IV course CalPoly Week 3

25 State space model for positioning History The linear velocities in the global frame and in the vehicle body frame are related by the attitude angles. v We have: where are rotation matrices. The state space equations in the global frame are given by: xe( k1) xe( k) ye( k 1) ye( k) ze( k1) ze( k) x E( k1) x E( k) ye( k1) A ye( k) wk ( ) ze( k1) ze( k) ( k1) ( k) ( k1) ( k) ( k1) ( k) b R R R x R R R wk ( ) Where is a model stationnary white noise vector with covariance matrix. A The matrix is the state transition matrix (the system (vehicle) model matrix). Q janv.-15 D Gingras ME470 IV course CalPoly Week 3

26 State space model for positioning History The observation equations (measurements) are given by: xe ( k) ye ( k) ze ( k) x E ( k) zk ( ) Hk ( ) y E ( k) ( k) z E ( k) ( k) ( k) ( k) ( k) Where is a measurement stationnary white noise vector with covariance matrix H is the state to measurement matrix (matrix mapping the sensors measurements to the vehicle states). R janv.-15 D Gingras ME470 IV course CalPoly Week 3

27 Positioning sensors Positioning Module Sensors Intro Relative sensors Transmission pickups Odome ter wheel sensors Gyroscopes Recalibration Sensor fusion Better position estimate Map matching Position on the road Absolute sensors GNSS Magnetic compasses Terrestrial radio technology janv.-15 D Gingras ME470 IV course CalPoly Week 3

28 Positioning sensors Sensors Intro Some positioning and range sensors Sensor Output Relation to position GPS Vehicle position Directly output position coordinates IMU Accelerations and angular rate Outputs can be integrated by an INS to obtain the vehicle position Odometer Inclinometer Magnetic compass Distance or increment of distance Inclination Azimuth Position coordinates are determined by dead reckoning from the distance and direction relative to a known location janv.-15 D Gingras ME470 IV course CalPoly Week 3

29 Positioning sensors Sensors Intro Some positioning and range sensors Sensors performance characteristics Definition Dynamic Range Maximum and minimum values that can be measured Resolution or discrimination Error Accuracy Precision Linearity Sensitivity Smallest discernible change in the measured value Difference between the measured and actual values, including random errors, and systematic errors Thedegreeofconformityofameasuredorcalculatedquantitytoits actual value Thedegreetowhichfurthermeasurementsorcalculationsshowthe same or similar results The variation in the constant of proportionality between the output signal and the measured physical quantity A measure of the change produced at the output for a given change in the quantity being measured janv.-15 D Gingras ME470 IV course CalPoly Week 3

30 Positioning Sensors Sensors Intro Sensor Terminology (continued) Bandwidth: frequencies seen by the sensor Systematic Errors: can be predicted and corrected with proper calibration Random Errors: cannot be predicted and exactly corrected, characterized by their pdf (probability density function) and their statistical moments (mean, variance or covariance) janv.-15 D Gingras ME470 IV course CalPoly Week 3

31 Positioning sensors Sensors Intro Some positioning and range sensors janv.-15 D Gingras ME470 IV course CalPoly Week 3

32 Positioning sensors Sensors Intro MEMs, VLSI and packaging technologies are evolving very rapidly and have a positive impact on automotive positioning systems. INS MEMS and processing ASIC side-by-side assembly Source: Tronics Microsystems Inc. Source: Fastrax Ltd., technical specifications of itrax03 Development Kit janv.-15 D Gingras ME470 IV course CalPoly Week 3

33 Dead reckoning Sensors Intro Dead reckoning (DR) is the process of calculating one's current position by using a previously determined position and advancing that position based upon known or estimated speeds over elapsed time and course. It uses estimates of distance travelled and direction of travel. Dead reckoning is subject to significant errors due to many factors as both speed and direction must be accurately known at all instants for position to be determined accurately. For example, if displacement is measured by the number of rotations of a wheel (ex. odometer), any discrepancy between the actual and assumed diameter, due perhaps to the degree of tire inflation and wear, will be a source of error. As each estimate of position is relative to the previous one, errors are cumulative. It provides relative position with respect to a previous position estimate. Integration of noisy data is involved in dead reckoning. Hence the cumulation of error similar to a random walk or a Wiener process janv.-15 D Gingras ME470 IV course CalPoly Week 3

34 Positioning Sensors Sensors Intro Dead reckoning uses estimates of distance travelled and direction of travel. Odometry uses wheel encoders to measure distance traveled. It is susceptible to errors due to tire slip, incorrect estimates of wheel circumference due to changes in tire inflation, etc. Road Rally enthusiasts can calibrate their odometry to 0.1%; this is not practical for most vehicles. Standard compasses are affected by nearby metallic objects, such as bridges or buildings. Image correlators directly measure vehicle motion by watching the ground move by under the vehicle. These systems are accurate to better than 0.1% Doppler radar is used in precision applications, where it is important to measure the relative speed of the lead vehicle as well as its range, even with significant tire slip janv.-15 D Gingras ME470 IV course CalPoly Week 3

35 Magnetic compass Compass A magnetic compass measures the direction of the Earth magnetic field. This physical principle has been used since the 1200s to navigate ships across the ocean. An original compass consisted of an iron needle floating in water, but it has been developed a lot since. When used in a modern positioning system, a compass measures the orientation of an object to which the compass is attached. The orientation is measured with respect to magnetic North. The compass information needs to be corrected because of the discrepancy between the true North and the direction of the Earth s magnetic field. Another correction is also required due to vertical magnetic equator and maximum at the poles. The magnetic compass is the only low cost absolute heading reference presently available for the automotive market. Other absolute references, such as North-seeking gyros, are far too expensive. The serious drawback for the use of a magnetic compass on a vehicle is the hostile magnetic environment of an automobile. Several manufacturers, including KVH Industries Inc., have built gyro stabilized compasses which blend the short term relative accuracy of gyro with the absolute sensing of a compass for an improved heading sensor janv.-15 D Gingras ME470 IV course CalPoly Week 3

36 Magnetic compass A magnetic compass senses the magnetic field of the Earth on two or three orthogonal sensors, sometimes in conjunction with a biaxial inclinometer. Since this field should point directly North, some method can be used to estimate the heading relative to the magnetic North pole. There is a varying declination between the magnetic and geodetic North poles, but models can easily generated this difference to better than one degree. The magnetic sensors are usually flux-gate sensors as the one shown here. MEMS technology allows new compact designs. Toroidal Wound Fluxgate Compass Sensor janv.-15 D Gingras ME470 IV course CalPoly Week 3 Compass Source: Ganssle, J. (1989). Anatomy of a Fluxgate. Ocean Navigator. No. 28. Pp In recent years magnetometers have been miniaturized to the extent that they can be incorporated in integrated circuits at very low cost and are finding increasing use as compasses in vehicles.

37 Magnetic compass Compass The operation of a fluxgate is based on Faraday s law, which states that a current (or voltage) is created in a loop in the presence of a changing magnetic field. A fluxgate is composed of a saturating magnetic core, with a drive winding and a pair of sense windings on it (only one is shown in the previous figure). The drive winding is wrapped around the core, which is normally a toroid. These sense windings are often wound flat on the outside of the core and are arranged at precisely 90 to each other. When not energized, a fluxgate s permeability draws in the Earth s magnetic field. When energized, the core saturates and ceases to be magnetic. As this switching occurs (hence the name fluxgate), the Earth magnetic field is drawn into or released from the core, resulting in a small induced voltage that is proportional to the strength and direction of the external field. Electronic/MEMS compass modules with auto calibration. Source: Unagi Net janv.-15 D Gingras ME470 IV course CalPoly Week 3

38 GNSS: the GPS GPS The Global Positioning System is a satellite-based navigation system, originally developed by the US military. It works by broadcasting very accurate time signals from a constellation of orbiting satellites. A groundbased receiver can compare the times from several satellites; the difference in apparent times gives the difference in time-of-flight of the signals from the satellites to the vehicle, and therefore the difference in distance to each satellite. Precise time measurement is therefore crucial in GNSS. This is why the satellites are equipped with atomic clocks. Simple geometry (trilateration) gives the location of the ground-based receiver and an accurate reference time. This simple picture is distorted by two phenomena: The US government deliberately introduces distortions into the civilian version of the signal, in order to reduce the accuracy of the system for potential enemies Local atmospheric effects refract the signals by varying amounts The result is that raw GPS data has an accuracy of only 10 s of meters janv.-15 D Gingras ME470 IV course CalPoly Week 3

39 GPS: Global Positioning System Satellites synchronize transmissions of location & current time GPS 4 satellites provide (x,y,z) and time correction GPS receiver is passive janv.-15 D Gingras ME470 IV course CalPoly Week 3

40 GPS: Global Positioning System GPS The GPS allows the estimation of the 3D absolute position (latitude, longitude et altitude) in a global reference frame. It does so in a continuous fashion at a sampling rate of roughly 0.1Hz. At least 4 satellites must be «seen» by the receiver. The GPS satellites constellation covers almost all the earth surface, hence the name «Global». When the receiver is mobile, Sped and motion direction can also be obtained from the GPS data. The GPS is made of 3 main components: - Space component: 24 earth orbiting satellites - Control component: composed of several tracking stations around the world. Headquarter is in Colorado. - User component: the receivers end. GPS satellites constellation janv.-15 D Gingras ME470 IV course CalPoly Week 3

41 GPS: Global Positioning System GPS GNSS is based on the following principle: a mobile receiver captures signals by at least 3 satellites and uses trilateration to compute the position. Trilateration is a mathematical method based on triangle geometry). The satellites position being known precisely, the mobile receiver s coordinates are obtained by computing the so-called pseudo-distances between each satellite and the receiver x x y y z z i s R s R s R i i i = pseudo-distance x, y, z S S S i i i = coordinates of satellite i x, y, z R R R = receiver coordinates janv.-15 Satellites coordinates are most often expressed in the ECI (terrestrial inertial frame) or in the (ECEF) frame. D Gingras ME470 IV course CalPoly Week 3

42 GPS: Global Positioning System GPS Trilateration in GPS: a simple example Say we want to localize the vehicle at point M (see figure) in the (x,y) plane. The satellite positions being known and assuming that the 3 pseudo-distances have been computed, the trilateration approach generates 3 circles using as centers the 3 satellites position. The 3 radius corresponds to the 3 pseudodistances (or pseudo-ranges). The vehicle s position correspond to the intersection of the 3 circles. Note that circles for S 2 and S 3 are tangent to each other leading in practice to large error on the estimated position. In practice four satellite minimum are being used to take time into account. S x1 3 y S 3 S 1 S x2 4 y y M S 2 S x 3 y x janv.-15 D Gingras ME470 IV course CalPoly Week 3

43 GPS: Global Positioning System GPS Trilateration in GPS: a simple example Inserting the values in the pseudorange equations, we get the 3 equations: x x y y z z i s R s R s R i i i 2 2 ( x 3) ( y 3) 34 (1) 2 2 ( x 4) ( y 1) 17 (2) 2 2 ( x 3) ( y 3) 10 (3) To get the estimated position M of the receiver, we can solve this system of equations in various ways: (1) (2) 8 y 14 x 19 and (1) (3) y 2 Finally we get: x = 0 et y = 2 (as was shown in the previous) janv.-15 D Gingras ME470 IV course CalPoly Week 3

44 GPS: Global Positioning System GPS Details on the GPS satellite signal: how to get the pseudoranges Satellites signals are transmitted on two radio wave carriers at frequencies MHz and MHz and precisely time-stamped. The signals are coded using pseudo-random sequences. A replica of the pseudo-random sequence is generated simultaneously by the receiver. Satellite. Receiver. Estimated delay, using cross-correlation techniques, between the received sequence and the local generated sequence, corresponds to propagation time between the satellite and the receiver. This delay multiplied by the speed of light in free space gives us the pseudodistance or the pseudorange. GPS accuracy and reliability depends on satellites coverage and clock precision. Sampling rate is about 100 ms, that is ten times slower that for example an INS janv.-15 D Gingras ME470 IV course CalPoly Week 3

45 GPS: Global Positioning System GPS Differential GPS In Differential GPS, a base station has a GPS receiver at a known location. It continually compares its known position with the GPS reported position. The difference is the error caused by selective availability and atmospheric distortion. The base station broadcasts the correction terms to mobile units. By applying the correction, the mobile units can reduce their errors. The accuracy of DGPS is on the order of a few meters. RTK or Carrier Phase GPS In carrier phase systems, the base station and the mobile units watch both the broadcast time code, and the actual waveforms of the carriers. By counting waveforms, they can synchronize their positions with each other to a fraction of a wavelength. A good carrier-phase system, with good conditions, can achieve accuracies of 2 cm or better janv.-15 D Gingras ME470 IV course CalPoly Week 3

46 GPS: Global Positioning System GPS DGPS: Differential GPS Differential GPS are receivers equipped with additional features allowing signal reception from fixed-based reference stations for which the exact location is know. It allows the computation of corrections from these reference signals and are usually integrated directly either in the computation of the position estimate or in the computation of the pseudo-ranges. DGPS receivers correct some common errors occurring with simple GPS receivers and thus increase the position estimate accuracy (order of 1m or even below). However, DGPS operability is limited to a region nearby a fixed-base reference station janv.-15 D Gingras ME470 IV course CalPoly Week 3

47 GPS: Global Positioning System GPS RTK DGPS receivers Real Time Kinematic (RTK) satellite navigation is a technique used to enhance the precision of position data derived from satellite-based positioning systems, being usable in conjunction with GPS, GLONASS and/or Galileo. It uses measurements of the phase of the signal s carrier wave, rather than the information content of the signal, and relies on a single reference station to provide real-time corrections, providing up to centimetre-level accuracy. With reference to GPS in particular, the system is commonly referred to as Carrier-Phase Enhancement, or CPGPS. Normally, satellite navigation receivers must align signals sent from the satellite to an internally generated version of a pseudorandom binary sequence, also contained in the signal. Since the satellite signal takes time to reach the receiver, the two sequences do not initially coincide; the satellite's copy is delayed in relation to the local copy janv.-15 D Gingras - UdeS IV course CalPoly Week 3

48 GPS: Global Positioning System GPS RTK DGPS receivers By increasingly delaying the local copy, the two copies can eventually be aligned. The correct delay represents the time needed for the signal to reach the receiver, and from this the distance from the satellite can be calculated. The accuracy of the resulting range measurement is essentially a function of the ability of the receiver's electronics to accurately process signals from the satellite. In general receivers are able to align the signals to about 1% of one bit-width.[1] For instance, the coarse-acquisition (C/A) code sent on the GPS system sends a bit every 0.98 microsecond, so a receiver is accurate to 0.01 microsecond, or about 3 metres. The military-only P(Y) signal sent by the same satellites is clocked ten times faster, so with similar techniques the receiver will be accurate to about 30 cm. Other effects introduce errors much greater than this, and accuracy based on an uncorrected C/A signal is generally about 15 m janv.-15 D Gingras - UdeS IV course CalPoly Week 3

49 GPS: Global Positioning System RTK DGPS receivers RTK follows the same general concept, but uses the satellite signal's carrier wave as its signal, ignoring the information contained within. The improvement possible using this signal is potentially very high if one continues to assume a 1% accuracy in locking. For instance, in the case of GPS, the coarse-acquisition (C/A) code (broadcast in the L1 signal) changes phase at MHz, but the L1 carrier itself is MHz, over a thousand times more often. The carrier frequency corresponds to a wavelength of 19 cm for the L1 signal. A ±1% error in L1 carrier phase measurement thus corresponds to a ±1.9 mm error in baseline estimation.[1] The difficulty in making an RTK system is properly aligning the signals. The navigation signals are deliberately encoded in order to allow them to be aligned easily, whereas every cycle of the carrier is similar to every other. This makes it extremely difficult to know if you have properly aligned the signals or if they are "off by one" and are thus introducing an error of 20 cm, or a larger multiple of 20 cm. This integer ambiguity problem can be addressed to some degree with sophisticated statistical methods that compare the measurements from the C/A signals and by comparing the resulting ranges between multiple satellites. However, none of these methods can reduce this error to zero janv.-15 D Gingras - UdeS IV course CalPoly Week 3 GPS

50 GPS: Global Positioning System RTK DGPS receivers In practice, RTK systems use a single base station receiver and a number of mobile units. The base station re-broadcasts the phase of the carrier that it observes, and the mobile units compare their own phase measurements with the one received from the base station. There are several ways to transmit a correction signal from base station to mobile station. The most popular way to achieve real-time, low-cost signal transmission is to use a radio modem, typically in the UHF band. In most countries, certain frequencies are allocated specifically for RTK purposes. Most land survey equipment has a built-in UHF band radio modem as a standard option. This allows the units to calculate their relative position to within millimeters, although their absolute position is accurate only to the same accuracy as the computed position of the base station. The typical nominal accuracy for these systems is 1 centimetre ± 2 parts-per-million (ppm) horizontally and 2 centimetres ± 2 ppm vertically.[2] Although these parameters limit the usefulness of the RTK technique for general navigation, GPS janv.-15 D Gingras - UdeS IV course CalPoly Week 3

51 GPS: Global Positioning System The GPS has many advantages: GPS - Absolute positioning in a global frame - Independent to initial position of the receiver - Global coverage (but not 100%) - Long term accuracy, no drift - Functioning 24/7 - Independent of temperature or climate - Relatively low cost receivers, affordable to the automotive industry The GPS has many problems: - Bad satellite coverage due to trees, urban canyons, tunnel etc., thus reducing the estimated position accuracy; - Not suitable for indoor applications; - Sensitive to multipath propagation (reflection on plane surfaces, such as building walls), thus introducing large biases in the position estimate. are - Sensitive to ionospheric and tropospheric perturbations generating random propagation delays. - Sensitive to satellites constellation geometry janv.-15 D Gingras ME470 IV course CalPoly Week 3

52 GPS: Global Positioning System GPS Other problems Sporadic introduction of SA: Selective Availability by the DOF: intentional degradation of the GPS signal for national security reason. It has been removed recently. Who knows when it will be reintroduced Synchronization errors between the satellites atomic clocks and those from the ephemerides (GPS satellites constellation information, orbital parameters, etc. provided by national labs and tracking stations) Receiver noise. Note that GPS receivers are considered as exteroreceptive sensors in contrast to dead-reckoning ones janv.-15 D Gingras ME470 IV course CalPoly Week 3

53 GPS: Global Positioning System GPS Error sources Standard deviation GPS (m) Standard deviation DGPS (m) Ionospheric random delays Tropospheric random delays Clocks and ephemerides Constellation geometry à Receiver accuracy Multipaths Total (UERE*) Mean STD 10m Mean STD 1m UERE: User Equivalent Range Error janv.-15 D Gingras ME470 IV course CalPoly Week 3

54 GPS: Global Positioning System GPS GPS Difficulties GPS requires a clear view of at least 4 satellites. For rural applications, or in flat, open terrain, this is not a problem. In mountainous terrain, or in urban canyons, GPS signals can be blocked or (worse) can reflect from tall objects and cause mistaken readings (multipath phenomenon). Carrier-phase GPS is very sensitive to losing lock on the satellites, and can become confused even going under a large road sign. Bottom line on GPS GPS is very useful for many automotive applications. It is not yet 100% reliable, so is not ready for control in safety applications applications. Research continues on filling in gaps in GPS satellites coverage and integrating GPS with other sensors janv.-15 D Gingras ME470 IV course CalPoly Week 3

55 Maps MAPs and GIS Accurate position is not useful unless combined with accurate maps. The first generation of digital maps were produced from paper maps, and therefore were no more accurate than the paper products. Typical quoted accuracies were 14 meters. This is sufficient only for non-safety critical invehicle navigation systems. Current generations of digital maps are produced directly from satellites and aerial photos and verified by driving selected routes with accurate differential GPS, so the accuracies are improved, typically below 1m. In that case, the digital maps accuracy is higher than the one of dead reckoning sensors and therefore the map matching results (assuming a correct match) can be used to calibrate the dead reckoning (DR) drifting error. By frequently updating new initial positions from map matching results, the DR position errors can be constrained to a reasonably small level, which, in turn, will improve the quality of map matching process as a whole. Maps for intelligent vehicle applications often include additional information, such as design speed of curves, grade of slopes, road signs such as stops and speed limits, etc. These info are used for example in ADAS such as warning drivers of excessive speed when entering a given curve janv.-15 D Gingras ME470 IV course CalPoly Week 3

56 Map matching MAPs and GIS In general map matching algorithms can be classified as Geometric methods mainly utilize geometric shapes of roads, vehicle trajectory, and road network connectivity. Conditional probability-based methods are statistical methods which attempt to improve the quality of map matching through better accounting for the uncertainty in digital maps and position estimates. Fuzzy-logic based algorithms to improve multiple factor decision-making have also been proposed because map matching is a qualitative decisionmaking process involving a degree of ambiguity. Although most of the map matching algorithms work well in rural area with sparse road networks, the reliability of these methods in urban areas is still a problem because the vehicle s position may be located to an incorrect road section (called a mismatch) due to large vehicle positioning errors janv.-15 D Gingras ME470 IV course CalPoly Week 3

57 Map matching MAPs and GIS Most mismatches in urban environment are caused by dead reckoning sensors errors. Thus, how to control these errors when GPS is not available is one of the important factors for improving vehicle navigation performance in urban areas. Moreover, algorithms for automatic mismatch detection and correction need to be implemented for any map matching processes, especially in situations where the GPS signal is not reliably available over a significant period of time. Road identification is the process of finding a road segment that a vehicle is currently travelling on. This is the most important task in the map matching process, which matches the vehicle trajectory to the road network. A match is found if a set of criteria of maximum similarity between road network and vehicle trajectory are met. Thus, in map matching, a measure for similarity is required. The criteria are usually formed from extracted features of candidate roads and the vehicle trajectory, which may include the: difference between the vehicle bearing and the candidate road direction, distance from the estimated position to candidate roads, difference of the change of vehicle bearing and the change of candidate road direction janv.-15 D Gingras ME470 IV course CalPoly Week 3

58 Map matching MAPs and GIS Position fix: is a process of determining the location of the vehicle on an identified road segment. After a candidate road is determined, a new position can be obtained from two sources: the predicted position based on vehicle velocity and road direction the measured position projected on the identified road. The final position is usually obtained by a data fusion technique involving some Kalman filter to get an optimal estimation from the two sources. We have where X E, X p and X r are the final estimated, predicted and measured vehicle positions. C p and C r are the covariance matrices of X p and X r. K is the Kalman gain matrix janv.-15 D Gingras ME470 IV course CalPoly Week 3

59 Map matching Map matching validation is a process that ensures that the vehicle location is correctly matched to the road network. It basically include functions to detect and correct any mismatches. In practice, most mismatches occur at road junctions or in situations when more than one road segments can be considered as possible road segments. Few methods have been developed to ensure quality of map-matching results, such as: During the road identification process, several number of consecutive position measurements (e.g., data from 5 epochs) are used to identify the correct road segment when the location is close to junctions. A confidence region test is applied for detecting any mismatches. This method is to generate an elliptical error region using the covariance matrix of the position estimation. Then a test is performed to check if the map-matched positions on road are within the error ellipsoid. A curve pattern match is used to compare the similarity of the vehicle s trajectory and the road network. Due to the error nature of the GPS/dead reckoning (DR) unit, the curve of the vehicle trajectory generated by the integrated GPS/DR unit is normally similar to the curve of the driving route derived from the digital road map. Consequently, the verification problem of the map matching process can be considered as a problem of planar curves-matching, which deals with junctions (points) janv.-15 D Gingras ME470 IV course CalPoly Week 3 MAPs and GIS

60 Map matching MAPs and GIS Illustration of the confidence region test The elliptical error region is created for each GPS/Dead reckoning (DR) point. The vehicle actually travels from Road N to Road L. At the junction, however, the GPS/DR positions are closer to Road M and, therefore, the vehicle positions are wrongly matched to Road M. Note: the road width (ex. 5 m) should be taken into account in carrying out the confidence test. Source: W Chen et al, An Integrated Map-Match Algorithm with Position Feedback, Journal of ITS, janv.-15 D Gingras ME470 IV course CalPoly Week 3

61 Inertial sensors Inertial sensors Inertial localization is a technique using accelerometers and gyroscopes to measure linear and angular forces (accelerations) respectively in order to continuously calculate, via dead reckoning, the position, orientation, and velocity (direction and speed of movement) of a moving vehicle without the need for external references. The position and pose (orientation) of the moving vehicle are estimated with respect to an initial starting point with known initial orientation and speed. The accelerometers and gyroscopes are usually mounted on IMU gimbals. The gimbals are a set of rings, each with a pair of bearings initially at right angles. They let the platform twist about any rotational axis (or, rather, they let the platform keep the same orientation while the vehicle rotates around it). There are two gyroscopes on the platform. IMU = Inertial measurement unit INS = Inertial navigation system Classical Inertial platform Source: Wikispace janv.-15 D Gingras ME470 IV course CalPoly Week 3

62 Inertial sensors Inertial sensors Family of sensors in inertial dead reckoning janv.-15 D Gingras ME470 IV course CalPoly Week 3

63 Inertial sensors Inertial sensors Accelerometers Accelerometers are sensors that measure inertial acceleration. Considering a vehicle as a rigid body of mass m and applying the second newton's law, we have, ma. f f mg. d b Example of an automotive low g accelerometer tower system plugin that contains an inertial sensor that can be used in automotive applications. Source where a is the acceleration of the point mass relatively to the vehicle inertial reference f d is the driving force applied to the moving vehicle modeled as a point mass, f b is the total friction force g is the gravity; The net force measured by the accelerometer becomes f f m d b f a g janv.-15 D Gingras ME470 IV course CalPoly Week 3

64 Inertial sensors Inertial sensors Accelerometer - Basic principle: If we can measure the acceleration of a vehicle we can integrate the acceleration to get velocity, then integrate the velocity to get the position. The integration of acceleration signals results in a reasonably smooth speed and position signal. Assuming that we know the initial position and velocity, we can determine the position of the vehicle at any time t. t t x adtdt x v ta t 0 0 x 0 x x janv.-15 D Gingras ME470 IV course CalPoly Week 3

65 Inertial sensors Inertial sensors The main problem is that an accelerometer cannot tell the difference between vehicle acceleration and gravity. We therefore have to find a way of separating the effect of gravity and the effect of dynamic acceleration. This problem is solved in one of two ways Keep the accelerometers horizontal so that they do not sense the gravity vector. This is the Stable Platform Mechanization. Somehow keep track of the angle between the accelerometer axis and the gravity vector and subtract out the gravity component. This is the Strapdown Mechanization. The original inertial navigation systems (INS) were implemented using the stable platform mechanization but all new systems use the strapdown system. Further details on these 2 approaches can be found in the literature on INS janv.-15 D Gingras ME470 IV course CalPoly Week 3

66 Inertial sensors Inertial sensors With the Stable Platform approach, there are three main problems to be solved: The accelerator platform has to be mechanically isolated from the rotation of the vehicle. The platform is isolated from the vehicle s rotation by means of a gimbal system. The platform is connected to the first (inner) gimbal by two pivots along the vertical (yaw) axis. This isolates it in the yaw axis. The inner gimbal is the connected to the second gimbal by means of two pivots along the roll axis. This isolates the platform in the roll axis. The second gimbal is connected to the INS chassis by means of two pivots along the pitch axis. This isolates it in the pitch axis. The vehicle travels on a non perfect spherical surface and thus the direction of the gravity vector changes with position according to altitude. The earth rotates on its axis and thus the direction of the gravity vector changes with time janv.-15 D Gingras ME470 IV course CalPoly Week 3

67 Inertial sensors Inertial sensors The gyroscopes The gyroscope informs us about the rotations and orientation of the vehicle. It measures the angular speed ω following the axis on which it is mounted in the inertial coordinate system. The measures provided by the supplied gyroscope, can determine the attitude of the vehicle (heading) throughout his movement by simple time integration of the angular velocity. We find three main types of gyroscope: Spinning Mass Ring Laser MEMS janv.-15 D Gingras ME470 IV course CalPoly Week 3

68 Inertial sensors Inertial sensors Spinning Mass Gyroscope Old It has rigidity in space. A spinning mass has a tendency to maintain its orientation in inertial space. Its rigidity (or resistance to change) depends on its moment of inertia and its angular velocity about the spin axis (INU gyros spin at around 25,000 RPM). Precession: If a torque τ is applied perpendicular to the spinning mass it will respond by rotating around an axis 90 degrees to the applied torque, i.e. ω τ Disadvantages sensitive to shock during installation and handling (Pivots can be easily damaged. requires several minutes to get up to speed and temperature Expensive Rarely used in the automotive industry janv.-15 D Gingras ME470 IV course CalPoly Week 3

69 Inertial sensors Inertial sensors Ring Laser Gyro: (RLG) in service since 1986 Advantages over spinning mass gyros: more rugged inherently digital output large dynamic range good linearity short warm up time Spinning Mass Gyroscope Disadvantages sensitive to shock during installation and handling (Pivots can be easily damaged. requires several minutes to get up to speed and temperature Expensive Rarely used in the automotive industry janv.-15 D Gingras ME470 IV course CalPoly Week 3

70 Inertial sensors Inertial sensors Stable Platform approach and gyros To keep the platform level stable, we must be able to sense platform rotations and correct for it. To do this, we mount gyroscopes on the stable platform and install small motors at each of the gimbal pivots. The gyroscopes sense platform rotation in any of the three axes and then send a correction signal to the pivot motors which then rotates the relevant gimbal to maintain the platform at the correct attitude. Before the INS can navigate it must do two things: Orient the platform perpendicular to the gravity vector Determine the direction of True North Also it must be given: Initial Position of the vehicle (given by GPS) Initial velocity: usually zero janv.-15 D Gingras ME470 IV course CalPoly Week 3

71 Inertial sensors Inertial sensors Types of Gyrocopes Gyro Type Principle of Operation Cost ($) Stability ( o /h) Rotating Conservation of Angular Momentum Fiber Optic Sagnac Effect Vibrating Piezoelecric Coriolis Effect janv.-15 D Gingras ME470 IV course CalPoly Week 3

72 Inertial sensors Inertial sensors Inertial navigation systems Principle of INS operation janv.-15 D Gingras ME470 IV course CalPoly Week 3

73 Inertial sensors Advantages Inertial sensors Accelerometers can be used to sense orientation WRT gravity vector when stationary (linear acceleration = 0) Accelerometers measures linear acceleration, they can be used to sense motion/no-motion and freefall. Instantaneous output of position and velocity Completely self contained, does not depend on terrain High sampling rate (compared to GPS) All weather global operation Very accurate azimuth and vertical vector measurement Error characteristics are known and can be modeled rather well Work well in hybrid systems (for example with GPS) Allow for miniaturization with the advent of MEMS janv.-15 D Gingras ME470 IV course CalPoly Week 3

74 Inertial sensors Disadvantages Inertial sensors Sensitive to gravity. An accelerometer measures both the dynamic linear acceleration and the static acceleration - gravity. We need to separate them. accelerometers alone cannot determine heading as it is insensitive to rotation about the gravity vector Equipment is still expensive (specially for gyros) from an automotive point of view. Drift. Position/velocity information degrade with time. No absolute positioning information (dead reckoning only) Equipment is still expensive (specially for gyros) from an automotive point of view. Calibration issues janv.-15 D Gingras ME470 IV course CalPoly Week 3

75 Inertial sensors Inertial sensors Sources of noise Unlike the wheel odometers which error sources are closely related to the terrain surface via tires deformation, the inertial sensors are subject to errors related primarily to the system. The main sources of error in INS are: The biais: corresponds to the 1st statistical moment. Correspond to a constant and can be remove rather easily during static no-motion measurements. However, it differs each time the INS is turned on. So the automotive system must correct this error while starting the car. Scale factor: comes from the sensor aging and sources of uncertainty in the fabrication process. Correction of the scale factor requires a calibration process. Measurement noise: electronic noise+ quantification noise etc. Can be modeled as stationnary additive noise white or colored. Drift: error that builds up in the integration process to estimate speed and position. Can be modeled as a random walk process (non-stationnary) janv.-15 D Gingras ME470 IV course CalPoly Week 3

76 Inertial sensors Inertial sensors Concluding remarks on INS Inertial sensors measures accelerations, then integrate accelerations to give velocities and integrating again to give the positions in each axis. Since position is doubly-integrated, small errors in acceleration build up rapidly leading to drifts. Inertial measurement is also good for sensing braking forces or for comparing wheel speed with ground speed, thus allowing to calculate wheel slip during braking. Thanks to MEMS technology, high-precision inertial navigation is gradually becoming affordable for the automotive market. Inertial measurement is useful to fill in short-term gaps in GPS absolute position measurements janv.-15 D Gingras ME470 IV course CalPoly Week 3

77 Odometer Odometer The odometer is a dead reckoning sensor, measuring the distance travelled by a vehicle. The distance is obtained by measuring and incrementing the elementary rotations of the vehicle s wheels. Incremental encoders located on the vehicle s wheels provide measurements on each wheel revolution (period). Starting from a known vehicle initial absolute position and integrating the vehicle s displacement, the current position of the vehicle relative to the initial position can thus be calculated every moment. Knowledge of the wheel diameters and the wheel axle length are required. Moreover, from the distance difference travelled by the right wheel and the left wheel, the vehicle orientation can also be monitored using differential odometry, assuming negligible wheel slip janv.-15 D Gingras ME470 IV course CalPoly Week 3

78 Odometer Odometer Let us first consider a two-wheel vehicle model. Let ω r and ω l be the angular velocities of the right and left wheels and R their diameter (assumed identical). The center of the wheel is equal to 2d. The vehicle speed V then becomes: and its angular velocity V R( r l) 2d vd vg R( d g) janv.-15 D Gingras ME470 IV course CalPoly Week 3

79 Odometer Odometer The projected speeds along the x and y axis are: V V x y V V cos sin In a recursive form, the vehicle position and heading can be estimated at time instant k + 1 from the previous ones with time increment Δt. xk1 xk V cos( k 1) t yk 1 yk Vsin( k 1) t k1 R( r l) k t l These equations are used in the measurement matrix of the state space model linking the vehicle dynamic parameters to the measurements from the 2-wheel odometer janv.-15 D Gingras ME470 IV course CalPoly Week 3

80 Odometer Similar equations can be obtained for the tricycle (3-wheel) model as shown in the figure below. In this model, considering the vehicle as having two rear wheels and one front steering wheel located in the center longitudinal axis of the vehicle. x cos( ) y sin( ) tan l Odometer Assuming that the steering angle is known at all time (ex. through an angle encoder on the steering wheel), the vehicle position and heading can be estimated at time instant k + 1 from the previous ones with time increment Δt. This yields, xk 1 xk vloncos( k) t yk 1 yk vlonsin( k) t t k1 k v lon tank l janv.-15 D Gingras ME470 IV course CalPoly Week 3

81 Odometer Odometer Advantages The principle of positioning by odometry (dead reckoning) has several advantages: Ease and low cost of implementation; High measurement sampling rate (on the order of 100 Hz); Good short term precision; Availability: odometers are relatively cheap, autonomous and very reliable. The main problem with this technique is a drift of the estimated position proportionally to the distance travelled by the vehicle. Since the position and orientation are determined by integration of the speed, angle and distance measurements accumulate errors over time janv.-15 D Gingras ME470 IV course CalPoly Week 3

82 Odometer Odometer Error sources The error sources for the odometer can be divided into two categories: Random errors related to wheels-road interface (wheel, skid, etc,).they are random in nature and depend on the quality of the road surface (irregularities, ice...) Systematic errors due to a bad mechanical setting of the vehicle or sensors model errors (wheel diameters, length of the distance, not wheel alignment, resolution of coders, inaccurate sampling...) These sources of error result in an overestimation or underestimation of the distance travelled. Some of these errors such as quantification error are generally modelled by zero mean random processes (ex. Gaussians) janv.-15 D Gingras ME470 IV course CalPoly Week 3

83 Odometric vehicle positioning Odometer This figure shows the relationship between vehicle poses at time steps i and i + 1. ICR represents the instant center of rotation. It is assumed that the vehicle s motion is locally circular. The vehicle motion model can be derived from the geometry and thus its position and orientation at time t i are given by: where (ΔS, Δθ) represent the arc length and the rotation angle between time steps i and i + 1, which can be obtained from an optical encoder fixed on the vehicle. This model can be used for example to predict vehicle poses janv.-15 D Gingras ME470 IV course CalPoly Week 3

84 Conclusion Automotive applications in a first approximation requires mainly positioning information in a 2D plane. A single sensor is not sufficient to provide the required position and localization information, accuracy, reliability and robustness. GPS is great for providing absolute position information. However it works at low sampling rate, suffers from signal outages and multipaths. INS characteristics are complementary to those GNSS techniques. They are often combined together. Other low cost sensors are useful too such as wheel-odometers and electronic compass. Digital maps are becoming an important source of information to constrain the localization and position estimation process. Still today, no unique solution is considered the ultimate best janv.-15 D Gingras ME470 IV course CalPoly Week 3

85 References Borenstein J. et al. Tech report, Sensors and Methods for Mobile Robot Positioning, Uni of Michigan, 1996 Chen, W., Li, Z., Yu, M., and Chen, Y. (2005). Effects of sensor errors on the performance of map matching. Journal of Navigation, 58, pp Drane C et al., Positioning systems in intelligent transportation systems, Artech House, 1998 Eskandarian Azim (Ed.),Handbook of Intelligent Vehicles, Chapter 13 and 14, Springer, 2012.Handbook of IVs, Springer Farell J., Aided Navigation GPS with High Rate Sensors, Chap 2, McGraw Hill, Flenniken W S., Characterization of Various IMU Error Sources and the Effect on Navigation Performance. Grewal M et al., Global positioning systems inertial navigation and integration, Wiley, Kaplan E. D., Understanding GPS, Principles and Applications, Artech House Publishers, Hein G.W., J. Godet, J. Issler and all, «The GALILEO frequency structure and signal design», proceedings of ION GPS janv.-15 D Gingras ME470 IV course CalPoly Week 3

86 References Kleeman L., Odometry Error Covariance Estimation for Two Wheel Robot Vehicles, Tech. Report MECSE-95-1 Monash Uni., EECE dept., Hadri A. Attitude estimation with gyros-bias compensation using low-cost sensors, Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference Shanghai, P.R. China, 2009 Klein L A., Sensor technologies and data requirements for ITS, Artech House, 2001 Nilsson J-O, Global Navigation Satellite Systems: An Enabler for In-Vehicle Navigation Savvides A., et al, Dynamic Fine-Grained Localization in Ad-Hoc Networks of Sensors, Proc of the 7th ACM Annual International Conference on Mobile Computing and Networking (MobiCom2001), Rome, Italy, Jul 16-21, Skog I, State-of-the-Art In-Car Navigation: An Overview, Handbook of IVs, Chap 17, Springer Skog I et al., In-Car Positioning and Navigation Technologies A Survey, IEEE Transactions On Intelligent Transportation Systems, Vol. 10, No. 1, March Waghris Georgy Jacques Ford, Advanced nonlinear techniques for low cost land vehicle navigation, PhD thesis, Queen Uni., Ont. Canada, Zhao Y., Vehicle location and navigation systems, Artech House, janv.-15 D Gingras ME470 IV course CalPoly Week 3

87 QUESTIONS? janv.-15 D Gingras ME470 IV course CalPoly Week 3