Patent Publication Number: US-2021171079-A1

Title: Positioning and odometry system

Description:
RELATED APPLICATIONS 
     The following application claims priority to U.S. provisional patent application No. 62/945,654 filed on Dec. 9, 2019, and is hereby incorporated by reference in its entirety. 
    
    
     BACKGROUND 
     Position and speed determination of a rail vehicle can be performed by a system that includes a checked-redundant vehicle onboard controller (VOBC) connected to a set of sensors. The sensors can consist of a radio frequency identification (RFID) tag reader, a tachometer/speed sensor, cameras, LIDΔR, UWB technology, radar (radio detection and ranging) and accelerometer with RFID tags installed along a guideway. The speed and positioning functions are typically part of the VOBC. 
     VOBC systems can be expensive both in sensor and support equipment cost and the manpower for installing the sensors and support equipment to operate the VOBC system. A large number of sensors are difficult to install and maintain. Each of these sensors must be maintained periodically and the maintenance is an added cost. Some sensors of a VOBC system can also be affected by environmental conditions to which a vehicle is exposed on a regular basis. Other sensors require expensive off vehicle equipment be installed on the guideway. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Aspects of the present disclosure are best understood from the following detailed description when read with the accompanying FIGS. It is noted that, in accordance with the standard practice in the industry, various features are not drawn to scale. In fact, the dimensions of the various features may be arbitrarily increased or reduced for clarity of discussion. 
         FIG. 1  is a high level diagrammatic representation of a single guideway positioning and odometry system (PAOS), in accordance with some embodiments. 
         FIG. 2  is a graphical representation of a multi-guideway PAOS, in accordance with some embodiments. 
         FIG. 3  is a graphical representation of vehicle positioning along a guideway, in accordance with some embodiments. 
         FIG. 4  is a high-level diagram of beacon speed determination, in accordance with some embodiments. 
         FIG. 5A  is a high-level diagram of a safety bag, in accordance with some embodiments. 
         FIG. 5B  is a high-level graph of position bias compensation, in accordance with some embodiments. 
         FIG. 6  is a pictorial diagram of platform beacon coverage, in accordance with some embodiments. 
         FIG. 7  is a high level flow diagram of a method for determining position and odometry, in accordance with some embodiments. 
         FIG. 8  is a high-level functional block diagram of a processor-based system, in accordance with some embodiments. 
         FIG. 9  is a graphical representation of R 1 -R 2  values as a function of longitudinal distance between anchors, in accordance with some embodiments. 
         FIG. 10  is a graphical representation of R 1 -R 4  values as a function of longitudinal distance between anchors, in accordance with some embodiments. 
         FIG. 11  is a graphical representation of R 3 -R 2  values as a function of longitudinal distance between anchors, in accordance with some embodiments. 
         FIG. 12  is a graphical representation of R 3 -R 4  values as a function of longitudinal distance between anchors, in accordance with some embodiments. 
         FIG. 13  is a graphical representation of the change in actual position and determined position, in accordance with some embodiments. 
         FIG. 14  is a graphical representation of a Standford diagram, in accordance with some embodiments. 
         FIG. 15  is a table showing change in position for along tracks position, in accordance with some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     The following disclosure provides many different embodiments, or examples, for implementing different features of the provided subject matter. Specific examples of components, values, operations, materials, arrangements, or the like, are described below to simplify the present disclosure. These are, of course, merely examples and are not intended to be limiting. Other components, values, operations, materials, arrangements, or the like, are contemplated. For example, the formation of a first feature over or on a second feature in the description that follows may include embodiments in which the first and second features are formed in direct contact, and may also include embodiments in which additional features may be formed between the first and second features, such that the first and second features may not be in direct contact. In addition, the present disclosure may repeat reference numerals and/or letters in the various examples. This repetition is for the purpose of simplicity and clarity and does not in itself dictate a relationship between the various embodiments and/or configurations discussed. 
     Further, spatially relative terms, such as “beneath,” “below,” “lower,” “above,” “upper” and the like, may be used herein for ease of description to describe one element or feature&#39;s relationship to another element(s) or feature(s) as illustrated in the FIGS. The spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the FIGS. The apparatus may be otherwise oriented (rotated  90  degrees or at other orientations) and the spatially relative descriptors used herein may likewise be interpreted accordingly. 
     In some embodiments, a positioning and odometry system (PAOS) determines vehicle position and speed using a beacon and map system. Additionally or alternatively, the PAOS also determines a vehicle stationary state and vehicle cold motion detection (e.g., detection of vehicle motion occurring while processing circuitry is powered off) in beacon coverage areas. 
     In some embodiments, the PAOS includes a beacon range measurement system with vehicle beacons installed on-board the vehicle measuring the range to guideway beacons installed trackside to determine a position of the vehicle. Additionally or alternatively, frequency modulated continuous wave (FMCW) radar, from the vehicle beacons, determines the Doppler speed (e.g., radial relative speed) together with a range and angular position (azimuth) to the guideway beacons within the vehicle beacon&#39;s field of view (FOV). In some embodiments, a six degree of freedom (DOF) inertial measurement unit (IMU) measures three dimensional (3-D) acceleration and angular speed with respect to a local coordinate system. In some embodiments, positioning and odometry algorithms maintain a high safety integrity stationary state determination and cold motion detection in beacon coverage areas. Additionally or alternatively, positioning and odometry algorithms provide safety integrity level (SIL) 4 positioning and odometry functions, stationary state determination and cold motion detection on a guideway in beacon coverage areas. In some embodiments, the SIL-4 is based on international electrotechnical commission&#39;s (IEC) standard IEC 61508, or CENELEC 50126 and 50129, herein incorporated by reference in their entirety. Additionally or alternatively, SIL-4 refers to a probability of system failure per hour ranging from 10 −8  to 10 −9 . 
     In some embodiments, the PAOS system (1) reduces VOBC system life cycle expense by a reduction in the number of trackside devices needed to support the PAOS; (2) is a less labor intensive installation and maintenance process for the sensors and support equipment as the sensors are vehicle body mounted and not bogie/wheel mounted; (3) is configured to determine cold motion detection and cold start localization in beacon coverage areas; and (4) is configured for continuous position determination. Additionally or alternatively, the safety integrity of the PAOS with and without beacon coverage satisfies a SIL-4. In some embodiments, areas with beacons also support a SIL-4 stationary state determination and cold motion detection. 
       FIG. 1  is a high level diagrammatic representation of a single guideway PAOS  100 , in accordance with some embodiments. PAOS  100  includes two or more vehicle beacons  102 A,  102 B (hereinafter referred to as vehicle beacons  102 ) installed on a vehicle  104 A at a vehicle first end  106  or vehicle second end  107 . Vehicle beacon  102  is configured to communicate with one or more guideway beacons  108 A,  108 B (hereinafter referred to as guideway beacon  108 ) installed along a guideway  110 . In some embodiments, processing circuitry ( 802   FIG. 8 ) is configured to communicate with vehicle beacons  102 . Additionally or alternatively, processing circuitry ( 802 ) is configured to: determine, before processing circuitry ( 802 ) enters a sleep state, a first vehicle position on guideway  110  using range measurements between vehicle beacons  102  and guideway beacons  108 ; determine, after processing circuitry ( 802 ) wakes from the sleep state, a second vehicle position on guideway  110  using range measurements between vehicle beacons  102  and guideway beacons  108 ; determine, after processing circuitry ( 802 ) wakes from the sleep state, any difference between the first vehicle position on guideway  110  and the second vehicle position on guideway  110 ; determine a periodic vehicle position on guideway  110  using range measurements between vehicle  104  and guideway beacons  108  taken at predetermined time periods; and determine a vehicle speed using range measurements between a single vehicle beacon  102  and a single guideway beacon  108  where speed is measured as a change in the periodic vehicle position over time. 
     In some embodiments, vehicle beacon  102  and guideway beacon  108  are beacon sensors. Additionally or alternatively, the beacons are a radio beacon that marks a location and allows direction-finding equipment to find relative bearing. In some embodiments, vehicle beacon  102  and guideway beacon  108  are radio beacons that transmit a radio signal that is picked up by radio direction-finding systems to determine the direction to each beacon. In some embodiments, the vehicle beacon  102  and guideway beacon  108  are beacon sensors using ultra-wideband (UWB). UWB is a radio technology that uses a low energy level for high-bandwidth communications over a large portion of the radio spectrum, typically from 3 GHz to 10 GHz. Additionally or alternatively, UWB beacons are configured for target sensor data collection, precision locating and tracking. In some embodiments, vehicle beacon  102  and guideway beacon  108  use frequency modulated continuous-wave (FMCW) radar, a range measuring radar capable of determining distance along with speed measurement. 
     In some embodiments, vehicle  104 A is a train having a series of connected vehicles that generally run along a railroad track (e.g., guideway or railway) to transport passengers or cargo (also known as “freight” or “goods”). In some embodiments, vehicle  104  is any vehicle that transports people or cargo. Vehicles include wagons, bicycles, motor vehicles (e.g., motorcycles, cars, trucks, and buses), watercraft (e.g., ships, boats), amphibious vehicles (e.g., screw-propelled vehicle, hovercraft), aircraft (e.g., airplanes, helicopters), spacecraft or the like. 
     In some embodiments, guideway  110  provides both physical support, like a road, as well as the guidance. In the case of fixed-route systems, the two are often the same in the same way that a rail line provides both support and guidance for a train. In some embodiments, systems use smaller wheels riding on the guideway to steer the vehicle using conventional steering arrangements like those on a car. In some embodiments, a track has two running rails with a fixed spacing that is supplemented by additional rails such as electric conducting rails (e.g., a third rail) and track rails. In some embodiments, monorails and maglev guideways are used. 
     In some embodiments, an odometry algorithm is configured to determine a vehicle&#39;s speed and motion direction. Additionally or alternatively, the odometry algorithm determines a stationary state and cold motion detection. In some embodiments, stationary references a vehicle standing still and described when the vehicle&#39;s speed is consistently less than  0 . 5 kph and accumulative displacement less than 3 cm. In some embodiments, a positioning algorithm is configured to determine the position and orientation of the vehicle on a guideway or road. In some embodiments, a dead reckoning algorithm is configured to determine a vehicle position with non-beacon sensor measurements (e.g., an IMU, tachometer, radar, or the like) in non-beacon coverage areas. Additionally or alternatively, the dead reckoning algorithm is a sub-algorithm of the positioning algorithm. 
     In some embodiments, a map is a diagrammatic representation of a guideway network in terms of nodes (e.g., platforms, beacon-coverage areas or the like) and edges (e.g., tracks, guideways or the like) connecting the nodes. Additionally or alternatively, the map is map stored in memory ( FIG. 8   804 ) as a database. In some embodiments, a digital map (e.g., a map stored in memory ( 804 ) and presented on a user interface ( FIG. 8   842  by processing circuitry ( FIG. 8   802 )) includes locations of guideway beacons  108  that have digital identifiers (ID). Additionally or alternatively, each guideway beacon  108  has a unique digital ID that is reported in real-time (e.g., part of a message transmitted by guideway beacon  108 ). In some embodiments, the map contains an association between the beacon&#39;s ID and it location in terms of earth-centered, earth-fixed (ECEF) coordinates and/or edge/offset as well. Additionally or alternatively, a position of the vehicle&#39;s reference point is determined in terms of the edge identification (ID) and the offset along the edge both in a positive and negative direction of travel (e.g., where is the vehicle on a guideway, what is its orientation and direction of motion and the like). 
     In some embodiments, orientation is the direction, with respect to the map, to the end of the vehicle (e.g., a vehicle first end  106  or a vehicle second end  107 ) with the beacon sensors (e.g. UWB beacons) used to initialize (e.g., during a cold start) the vehicle position orientation (e.g., a positive orientation for vehicle  104 A or negative orientation for possible vehicle location  104 B (indicated in dotted lines)). In some embodiments, beacon coverage area is a guideway area equipped with guideway beacons  108  enabling vehicles equipped with vehicle beacons  102  to determine the range to guideway beacons  108  installed on guideway  110  within this beacon coverage area and determine the vehicle&#39;s position and speed. Additionally or alternatively, vehicle beacons  102  are range measurement devices installed on vehicle  104  and guideway beacons  108  are range measurement devices installed on guideway  110 . 
     In some embodiments, the PAOS  100  includes one or more vehicle(s)  104 A equipped with vehicle beacons  102 . Additionally or alternatively, vehicle beacons  102  are coupled to a vehicle body  111  at a first vehicle end  106  and a second vehicle end  107 . In some embodiments, first vehicle end  106  and second vehicle end  107  are equipped with two (2) vehicle beacons  102 . In some embodiments, for positioning and odometry algorithms two (2) beacons are at a single (1) end of vehicle  104 A (either first vehicle end  106  or second vehicle end  107 ; see  FIG. 1 ) or one (1) vehicle beacon  102  at both vehicle ends  106 ,  107  of vehicle  104  (one beacon at first vehicle end  106  and the other beacon at second vehicle end  107 ) for distance and speed data for the positioning and odometry algorithms. 
     In some embodiments, guideway  110  with guideway beacon coverage is a platform area (see  FIG. 6 ). Additionally or alternatively, a switch zone (e.g., a mechanical installation enabling railway trains to be guided from one guideway to another, such as at a railway junction) or other critical location includes guideway beacon coverage to support the high level of safety integrity (e.g., SIL-4) of the positioning and odometry algorithms. 
     In some embodiments, distance and speed measurements are determined every 100 msec (e.g., beacon measurements are taken at 100 Hz). Additionally or alternatively, when the beacon measurements are taken at a higher frequency the time period is made shorter than 10 msec. In some embodiments, processing circuitry ( 802 ) determines an average position based on beacon measurements, an average position based on the dead reckoning algorithm, an average speed based on beacon measurements, an average speed based on non-beacon measurements, a dead reckoning positioning precision (a), and a non-beacon speed precision (a). In some embodiments, precision is the degree that measurements are close to each other. In some embodiments, accuracy is the degree that a measurement is close to the actual value. 
     In some embodiments, in beacon coverage areas the PAOS  100  is implemented using vehicle beacons  102  (installed on-board vehicle  104  or on vehicle body  111 ) and guideway beacons  108  (installed on guideway  110 ). In some embodiments, there are several aspects to the positioning algorithm. For example, in some embodiments, in a cold start condition, positioning algorithm determines whether vehicle  104  is positioned on the correct guideway  110 . A situation where vehicle  104  is positioned on the wrong guideway is hazardous. 
     In some embodiments, after vehicle  104  is determined to be positioned on the correct guideway, the positioning algorithm determines where the vehicle&#39;s position on the correct guideway is correct. A situation where vehicle  104  is positioned on the correct guideway, but at a wrong location or in the correct location but with a larger uncertainty than the uncertainty determined by the positioning algorithm is hazardous. 
     In some embodiments, the positioning algorithm determines a vehicle&#39;s direction of travel on guideway  110 . In a situation where the vehicle&#39;s direction of travel on the guideway is incorrect, the situation is hazardous. 
     In some embodiments, the odometry algorithm provides a vehicle&#39;s speed on guideway  110  along with a speed uncertainty and motion direction of the vehicle (i.e., in the direction of motion from second end  107  to first end  106  or from first end  106  to second end  107 ). A situation where the vehicle speed uncertainty is greater than the uncertainty determined by the odometry algorithm is hazardous. 
     In some embodiments, the odometry algorithm provides a stationary state determination to indicate if vehicle  104  is moving or stationary. A situation where vehicle  104  is moving while the system determines vehicle  104  is stationary is hazardous. Further, a situation where vehicle  104  is stationary when PAOS  100  determines vehicle  104  is moving is hazardous as well. 
     In some embodiments, the odometry algorithm provides cold motion detection to determine whether vehicle  104  moved while the processing circuitry ( 802 ) was shutoff. A situation where vehicle  104  was moved while processing circuitry ( 802 ) was shutoff and the odometry algorithm positions vehicle  104  on a guideway location known before the move is hazardous. 
     In some embodiments, positioning and odometry algorithms provide cold start guideway occupancy &amp; positioning determination with beacon range data, position update with beacon range data, speed &amp; motion direction determination with beacon range data, stationary state determination with beacon range data, cold motion detection, dead reckoning positioning in non-beacon coverage areas, and speed &amp; motion direction determination in non-beacon coverage areas. 
     In some embodiments, cold start guideway occupancy &amp; positioning determination using beacons  102  and  108  determine what guideway  110  vehicle  104 A occupies and the vehicle&#39;s position on guideway  110  upon cold start. In some embodiments, ranges (e.g., R 1 , R 2 , R 3 , and R 4 ) are measured from beacons  102  on vehicle  104 A to beacons  108  installed on guideway  110 . In some embodiments, guideway beacons  108  are installed at the extremities of multi-guideways when the beacon coverage area contains multiple guideways (see  FIG. 2 ), or at the extremities of guideway  110  if the guideway coverage area contains a single guideway (see  FIG. 1 ). 
     In some embodiments, range R 1  is determined from vehicle&#39;s right beacon  102 A to guideway beacon  108 A. Range R 2  is determined from vehicle&#39;s right beacon  102 A to beacon  108 B. Range R 3  is measured from vehicle&#39;s left beacon  102 B to beacon  108 A. Range R 4  is measured from vehicle&#39;s left beacon  102 B to guideway beacon  108 B. In some embodiments, lateral offset  112  (W A ) is a lateral offset of guideway beacon  108 A with respect to guideway centreline  114  (e.g., a positive value if lateral offset  112  is pointing left). Lateral offset  116  (W B ) is a lateral offset of guideway beacon  108 B lateral offset with respect guideway centerline  114  (e.g., a positive value if lateral offset is pointing right). Longitudinal offset  118  (Ω B ) is a longitudinal offset of guideway beacon  108 B with respect to guideway beacon  108 A (e.g., a positive value if direction is positive). Distance w is the distance between beacons  102 A,  102 B on the same vehicle  104 A. 
     In some embodiments, position determination and orientation of vehicle  104  on guideway  110  is determined as follows: the vehicle orientation is positive and in the location indicated by vehicle  104 A when 
       R 1 −R 3 &lt;−ΔR Min , and
 
       R 2 −R 4 &gt;ΔR Min .
 
     In some embodiments, ranges R 1 , R 2 , R 3 , and R 4  provide the orientation for vehicle  104 A, but also provide the position on guideway  110 . In some embodiments, ΔR Min  is a minimum range difference between two (2) range measurements required to ensure the discrimination of guideway  110  vehicle  104 A is occupying is performed with a sufficient confidence level suitable for SIL-4 applications. Additionally or alternatively, 5 cm or greater is a typical value for ΔR Min . In some embodiments, determination of ΔR Min  is considered a range measurement error for the determination of the range to guideway beacons  108 A,  108 B. For example, if a single range measurement error is 2 cm then ΔR Min  is greater than two (2) times the range measurement error. In some embodiments, the range measurement error is a property of guideway beacon  108 . Additionally or alternatively, the range measurement error is reported together with the range measurement itself and sometimes it is determined offline. In some embodiments, the range measurement error is typically expressed in terms of error (e.g. 3 cm) with a confidence level (e.g. 3σ) (e.g., 99.8% of the measurements have an error of  3 cm or less). In this example ΔR Min  &gt;4 cm+margin. In some embodiments, the shorter the range to guideway beacons  108 A,  108 B in determining the position of vehicle  104 A, the greater ΔR Min  (see  FIGS. 9-12 ). 
     In some embodiments, the vehicle position is determined and orientation is negative as shown by dotted line vehicle  104 B when: 
       R 1 −R 3 &gt;ΔR Min , and
 
       R 2 −R 4 &lt;−ΔR Min .
 
     In some embodiments, ranges R 1 , R 2 , R 3 , and R 4  provide the orientation for vehicle  104 B, but also provide the position on guideway  110 . In some embodiments, when vehicle  104 A or  104 B begin moving and the motion direction is determined then the vehicle correlation with a map is determined. In some embodiments, correlation is between the vehicle orientation and the vehicle motion direction. For example, when the orientation is positive and the motion direction is from vehicle second end  107  to vehicle first end  106 , the correlation is positive (e.g., vehicle  104 A is moving towards beacons  108 ). In another example, when the orientation is positive and the motion direction is from vehicle first end  106  to vehicle second end  107 , the correlation is negative (e.g., vehicle  104 A is moving away from beacons  108 ). In another example, when the orientation is negative and the motion direction is from vehicle second end  107  to vehicle first end  106 , the correlation is negative (e.g., vehicle  104 B is moving towards beacons  108 ). In another example, when the orientation is negative and the motion direction is from vehicle first end  106  to vehicle second end  107 , the correlation is positive (e.g., vehicle  104 B is moving away from beacons  108 ). 
     In some embodiments, the positioning algorithm determines where vehicle  104  is on guideway  110  during a cold start based on range measurements. Additionally or alternatively, a single guideway scenario, such as shown in  FIG. 1 , is not always the situation and in order to maintain a SIL-4 the positioning algorithm also operates effectively when multiple guideways are involved. 
       FIG. 2  is a graphical representation of a multi-guideway PAOS  200 , in accordance with some embodiments. In some embodiments, a non-transitory computer-readable storage medium ( 804  FIG. 8 ), comprising executable instructions ( 806   FIG. 8 ), such as positioning algorithm and odometry algorithm, that, when executed by processing circuitry ( 802   FIG. 8 ), cause processing circuitry ( 802 ) to: determine, with range measurements between one or more vehicle beacons  202 A,  202 B (hereinafter referred to as vehicle beacon  202 ) installed on an end  206  of a vehicle  204 A and configured to communicate with one or more guideway beacons  208 A,  208 B (hereinafter referred to as guideway beacon  208 ) positioned at predetermined locations along one or more guideways  210 A,  210 B (hereinafter guideway  210 ), after processing circuitry ( 802 ) wakes from a sleep state, vehicle position and guideway occupancy are determined to determine a change in the vehicle position from before processing circuitry ( 802 ) entering the sleep state; determine, with the range measurements between vehicle beacons  202  and guideway beacons  208 , a periodic vehicle position update; determine, with the range measurements between vehicle beacons  202  and guideway beacons  208 , a vehicle speed and a vehicle direction of motion on guideway  210 ; determine, with the range measurements between vehicle beacon  202  and guideway beacon  208 , a vehicle stationary state; determine dead-reckoning positioning; and determine the vehicle speed and the vehicle direction of motion in areas with no guideway beacons. 
     In some embodiments, PAOS  200  with vehicle beacon  202  on vehicle  204 A, whether on vehicle first end  206  and/or vehicle second end  207 , and guideway beacon  208  along guideway  210  are like PAOS  100  with vehicle beacon  102  on vehicle  104 A, whether on vehicle first end  106  and/or vehicle second end  107 , and guideway beacon  108  along guideway  110 . 
     In some embodiments, the positioning algorithm discriminates between two (2) or more guideways  210 A,  210 B vehicle  204 A possibly occupies. Additionally or alternatively, an orientation of vehicle  204 A on guideway  210  with respect to the map is performed by comparing the following range pairs: 
       (a) R 1 −R 3 .
 
       (b) R 1 −R 4 .
 
       (c) R 2 −R 3 .
 
       (d) R 2 −R 4 .
 
     In some embodiments, when R 1 -R 2  &gt;ΔR Min , R 1 -R 4  &gt;ΔR Min , R 3 -R 2  &gt;ΔR Min  and R 3 -R 4  &gt;ΔR Min  then vehicle  204 A occupies guideway  210 B in either vehicle location  204 C or vehicle location  204 D. Additionally or alternatively, when R 1 -R 2  &lt;R 1 -R 4  &lt;-ΔR Min , R 3 -R 2  &lt;-ΔR Min  and R 3 -R 4  &lt;-ΔR Min  then vehicle  204  occupies guideway  210 A as vehicle  204 A or at vehicle location  204 B. In some embodiments, when a guideway occupancy is known using the range equations directly above, a location on guideway  210  is determined using the equations from above: 
       Is, R 1 −R 3 &lt;−ΔR Min , and
 
       R 2 −R 4 &gt;ΔR Min  . Or
 
       Is, R 1 −R 3 &gt;ΔR Min , and
 
       Is, R 2 −R 4 &lt;−ΔR Min  
 
     As discussed above and in some embodiments, ΔR Min , is the minimum range difference between two (2) range measurements required to ensure the positioning algorithmic discrimination between guideways  210 A and  210 B for vehicle  204 A to occupy is performed with a sufficient confidence level suitable for a SIL 4 function. In some embodiments, 5 cm or greater is typical value for ΔR Min . Additionally or alternatively, determination of ΔR Min  should consider the range measurement error and the range to guideway beacons  208  as well. For example if a single range measurement error is 2 cm then ΔR Min  must be greater than two (2) times the range measurement error. In this example ΔR Min  &gt;4 cm+margin. The shorter the range to the anchors in determining the position the greater ΔR Min . See  FIGS. 9-12 . 
     In some embodiments, and with reference to  FIGS. 9-12  an example depicting R 1 -R 2  ( FIG. 9 ), R 1 -R 4  ( FIG. 10 ), R 3 -R 2  ( FIG. 11 ) and R 3 -R 4  ( FIG. 12 ) for a multiple guideway such as shown in  FIG. 2 , is shown assuming the following parameters: 
     (a) W (distance between guideway centerlines  220 )=5 m. 
     (b) w A  (lateral offset  212  to guideway beacon  208 A)=2 m. 
     (c) w B  (lateral offset  216  to guideway beacon  208 B)=2 m. 
     (d) ω (distance between vehicle beacons  202  on same vehicle)=2 m. 
     (e) Ω B  (longitudinal offset  218  of guideway beacons  208 A and  208 B)=0 m. 
     In some embodiments, as seen in  FIG. 9 , ΔR is shown for R 1 -R 2  values for guideways  210 A and  210 B as a function of the longitudinal distance from vehicle beacon(s)  202  to guideway beacons  208 . In some embodiments, at 200 m ΔR is approximately 20 cm. In some embodiments, it is possible to determine what track the vehicle is on based upon  FIGS. 9-12 . Additionally or alternatively, the sign of ΔR presents an indication as to the tracks the vehicle occupies. 
       FIG. 3  is a graphical representation of vehicle positioning along a guideway, in accordance with some embodiments. In some embodiments, PAOS  300  with vehicle beacon(s)  302 A,  302 B (hereinafter vehicle beacons  302 ) on vehicle  304 A, and guideway beacons  308 A,  308 B (hereinafter guideway beacons  308 ) along guideway  310  is like PAOS  100  and  200  with vehicle beacon(s)  102  and  202  on vehicle(s)  104  and  204 , and guideway beacon(s)  108 ,  208  along guideway(s)  110  and  210 . 
     In some embodiments, when a vehicle&#39;s guideway occupancy and vehicle orientation is determined, an along-guideway position (e.g., where is the vehicle at specifically along the guideway the vehicle has been determined to be located on) is determined based on an R 1 , R 2 , R 3 , and R 4  intersections  301  with guideway centerline  314 . Additionally or alternatively, typically eight (8) intersection points are observed; however, typically four (4) out of the eight (8) intersection points are consistent with unique vehicle positions along guideway  310 A in consideration of vehicle beacon  302 A,  302 B arrangement on vehicle  304 A and considering the vehicle&#39;s orientation. In some embodiments,  4  of the  8  intersections  301  are closely grouped at or near the along-guideway position represented by vehicle  304 A. In some embodiments, vehicle  304 A is the correct vehicle position along guideway  310 A and is consistent with 4 intersections  301 . Additionally or alternatively, dashed line vehicles  304 B,  304 C,  304 D,  304 E,  304 F, and  304 G are not consistent with any set of  4  intersection points and thus are not considered as actual along-guideway positions. 
     In some embodiments, the positioning algorithm verifies that a change in position along guideway centerline  314  is determined based on the four (4) range measurements (R 1 , R 2 , R 3 , and R 4 ) and determines the same along-guideway position with a certain acceptable tolerance. Additionally or alternatively, the along-guideway position determined based on R 1  and R 4  overshoots the actual position along guideway  310 A in the guideway direction vehicle  304 A is oriented with, and the along-guideway position determined based on R 2  and R 3  undershoots the actual position along guideway  310 A with respect to the same guideway direction. 
     In some embodiments,  FIG. 13  depicts the delta (e.g., change in position over distance) between the actual position, based on the measured ranges R 1 , R 2 , R 3 , and R 4 , and the along-guideway position, discussed above, determined for a vehicle with positive orientation on a guideway. 
     In some embodiments, delta (Δ) or change between the actual position using beacon ranges and the along-guideway position determined based on the measured ranges R 1  R 2 , R 3 , and R 4  is corrected by the positioning algorithm based on a measured range and the lateral distance between guideway beacon  308  and guideways centerline  314 . In some embodiments,  FIG. 15  depicts the delta positions for a vehicle on guideway  310 A and guideway  310 B with positive and negative orientations. 
     In some embodiments, once a vehicle&#39;s guideway occupancy, vehicle orientation and along-guideway position is determined, and the vehicle starts to move, then a motion direction and correlation are determined too. Additionally or alternatively, a single range (R 1 , R 2 , R 3  or R 4 ) measurement is sufficient to update the vehicle&#39;s along-guideway position on the guideways centerline. In some embodiments, the determination of the vehicle&#39;s guideway occupancy, vehicle orientation and along-guideway position is desired before determining the vehicle motion direction and correlation. Additionally or alternatively, positioning algorithm and the odometry algorithm actively determine any of vehicle&#39;s guideway occupancy, vehicle orientation, along-guideway position vehicle motion, and vehicle direction and correlation independently of one another with neither aspect being performed before the other is determined. However, for purposes of safety, some determinations are made before others as discussed above in detail. 
       FIG. 4  is a high-level diagram of beacon speed determination, in accordance with some embodiments. In some embodiments, guideway centerline  414  is a 3-D curve (e.g., to account for the curvature of the Earth or due to constraints imposed by the guideway construction design). Additionally or alternatively, once an along-guideway position is established and then updated in a certain refresh rate (e.g., every  100 msec or at 50 Hz), the vehicle&#39;s speed is determined based on the derivative (ratio) of dP/dt (AP [change in position]/Δt [change in time]). In some embodiments, the odometry algorithm also accounts for guideway curvature  420  to ensure that AP is the arc length between a first determine position  422  and a second determined position  424  and not a cord  426  between first position  422  and second position  424 . In some embodiments, when the refresh rate is high the difference between the two is negligible otherwise the difference is significant. Additionally or alternatively, the difference is a function of the refresh rate and the train speed. For a train moving at 100 kph, AP=1.4 m for refresh rate of 50 msec, 2.8 m for refresh rate of  100 msec, and  14 m for refresh rate of 500 mse. For a train moving at 5 kph AP=7 cm for refresh rate of 50 msec, 14 cm for refresh rate of 100 msec and 70 cm for refresh rate of 500 msec. 
     In some embodiments, the speed is derived from two (2) positions where: (1) the difference in the along guideways distance (e.g., the arc length of centerline  414 ) between the two (2) positions is greater than  10  times the positioning error; (2) the difference in the along guideways distance (e.g., arc length of centerline  414 ) between the two (2) positions is less than  100  times the positioning error. Additionally or alternatively, when the arc length of centerline  414  between first position  422  and second position  424  is not less than 10 times the positioning error (e.g., potentially causing the derived speed to be noisy (e.g., affected by the positioning error)) and not greater than  100  times the arc length of centerline  414  between first position  422  and second positon  424  to prevent inaccurate measurements the most accurate speed is derived by the odometry algorithm. Additionally or alternatively, the speed error can be expressed as V err =2P err /Δt+2ΔPt err /Δt 2 . In some embodiments, in order to avoid noisy speed, a larger Δt is preferred that typically is related with a larger ΔP too. Additionally or alternatively, the speed is calculated as a derivative of the position. In some embodiments, the derivative is noisy; therefore relaxing (e.g., lengthening) the At reduces the derivative noise. In some embodiments, this means that the derivative is not calculated based on consecutive measurements. Additionally or alternatively, a measurement is taken (e.g., P 1  at t 1 ) then the next measurement used for ΔP and At should be Pn, to not P 2 , t 2 . 
     In some embodiments, when the vehicle is in a beacon coverage area and at least a single range measurement (e.g., one of R 1 , R 2 , R 3  or R 4 ) is available, and the value of the measured range does not change, or if the value of the measured range changed within a certain predefined bound (e.g., ±ΔR stationary  5 cm) then the vehicle&#39;s state is determined to be stationary. 
     In some embodiments, before processing circuitry ( 802 ) is powered down, the along-guideway position and the trackside beacon IDs are stored within a nonvolatile memory ( 804 ). Additionally or alternatively, upon startup of processing circuitry ( 802 ) (e.g., a cold start) of a vehicle in a beacon coverage area, the vehicle&#39;s guideway occupancy, orientation and along-guideway position are determined. In some embodiments, when a change is determined with respect to the position data stored in nonvolatile memory ( 804 ) before powering down then cold motion is declared. Additionally or alternatively, when the processing circuitry ( 802 ) starts up while the vehicle is in an area without beacon coverage then cold motion is declared. In some embodiments, an alarm is sounded and/or reported to the central control as a positive or negative motion when cold motion is detected. 
     In some embodiments, beacon positioning, speed functions, dead reckoning positioning and odometry functions, beacon positioning information is independently determined and provided to the dead reckoning positioning and odometry algorithms at specified times. For example, beacon positioning information is provided on cold start (e.g., upon processing circuitry ( 802 ) powering up for operation), when the beacon coverage area is entered (e.g., when the vehicle is entering a beacon coverage area), before the beacon coverage area is vacated (e.g., when the vehicle is exiting a beacon coverage area), the time elapsed since a last beacon positioning update is greater than 2 minutes, or the distance travelled since the last beacon positioning update is greater than 1 km. Additionally or alternatively, in providing the dead reckoning algorithm with the beacon positioning information at these times, provides the dead reckoning algorithm with the most accurate positioning information before the vehicle utilizes dead reckoning positioning. 
     In some embodiments, dead reckoning positioning is a position determined using non-beacon measurements. Additionally or alternatively, a beacon coverage area is maximized with beacons and allows for coverage gaps without compromising the SIL-4 function. In some embodiments, beacon installation is in a platform area (see  FIG. 6 ) in which a guideway stretch (e.g., 2000 m) alternates beacon coverage. For example, in some embodiments, 1100 m are provided with beacon coverage while the areas without beacon coverage are no longer than 150 m. 
     In some embodiments, in beacon coverage areas, the odometry algorithm estimates the speed based on a beacon positioning error and a beacon positioning error&#39;s influence on a beacon based speed error to minimize the speed error. Additionally or alternatively, the dead reckoning positioning bias and the non-beacon speed bias are compensated and supervised. In some embodiments, the dead reckoning positioning bias, for a specified time interval, is the difference between the average position determined based on the dead reckoning positioning function (e.g., using the beacon measurements for initialization only) and the average position solely determined based on beacon measurements. In some embodiments, a dead reckoning positioning protection level is verified against the beacon position. Additionally or alternatively, the positioning precision is estimated in consideration of the dead reckoning positioning precision and the beacon positioning precision. In some embodiments, the speed precision is estimated based on the non-beacon speed precision and the beacon speed precision. In some embodiments, non-beacon speed is the speed determined using non-beacon speed measurements (e.g., IMU data). 
     In some embodiments, in areas without beacon coverage the dead reckoning positioning and its uncertainty is compared against the positioning determined based on the integration, in the time domain, of the non-beacon speed, such as an IMU, (e.g., safety bag  FIG. 5 ) to supervise its integrity. Additionally or alternatively, temporary portable beacons are installed in these non-beacon coverage areas to build the confidence level in the high safety integrity (SIL 4) algorithms. In some embodiments, uncertainty is an interval or distribution around a measured value, where the true value lies with some probability (e.g., confidence level). 
     In some embodiments, in beacon coverage areas, the along-guideway positioning is determined based on beacon measurements with a refresh rate (e.g. 5 Hz (200 ms) or higher). Additionally or alternatively, once the along guideway positioning is initialized based on beacon measurements, the position is then based on the dead reckoning positioning algorithm until the position is re-updated based on beacon measurements (e.g., typically in platform areas or switch zones). Additionally or alternatively, even though beacon measurements are available (i.e., excluding initialization) the positioning algorithm does not use the beacon measurements to determine the dead reckoning position (e.g., P Dead Reckoning  vs. P Beacon ). 
     In some embodiments, a dead reckoning algorithm is part of the positioning algorithm and is determined based on Radar and IMU, radar, tachometer/speed sensor and IMU, tachometer/speed sensor and single axis accelerometer or any other sensor arrangement that does not include localization capability. 
       FIG. 5  is a high-level diagram of a safety bag  500 , in accordance with some embodiments. In some embodiments, safety bag  500  is an external algorithm, implemented on independent processing circuitry and set to a different specification of the positioning and odometry algorithms. Additionally or alternatively, the safety bag algorithm is concerned with ensuring processing circuitry ( 802 ) operates within a safe zone represented by safety bag  500 . In some embodiments, the safety bag algorithm continuously monitors the processing circuitry ( 802 ). Additionally or alternatively, the safety bag algorithm prevents the processing circuitry ( 802 ) from entering an unsafe state. In some embodiments, when the safety bag algorithm determines that processing circuitry ( 802 ) is entering a potentially hazardous state, the processing circuitry ( 802 ) is brought back to a safe state either by the safety bag algorithm or by processing circuitry ( 802 ). In some embodiments, the safety bag algorithm is in accord with CENELEC-EN 50128 communication, signaling and processing systems software for railway control and protection systems publication that is hereby incorporated by reference in its entirety. 
     In some embodiments, in beacon coverage areas, the beacon positioning (P Beacon ) serves as safety bag  500  for the dead reckoning positioning (P Dead Reckoning ). 
     Additionally or alternatively, safety bag  500 , provided by the beacon positioning (P Beacon ) is greater than uncertainty range  502  that encompasses true position  504  and a determined position  506  associated with the dead reckoning positioning (P Dead Reckoning ). In some embodiments, when the positioning algorithm determines a position outside of safety bag  500 , an alarm is raised and the safety bag algorithm or the positioning algorithm implements a correction. 
       FIG. 5B  is a high-level graph of position bias compensation, in accordance with some embodiments. In some embodiments, in beacon coverage areas, beacon positioning  508  (e.g., P Beacon ) and dead reckoning positioning  510  (e.g., P Dead Reckoning ) are amalgamated to remove the dead reckoning positioning bias  512  and estimate positioning uncertainty  514  (that in some embodiments is safety bag  500 ) based on the summation of the beacon positioning precision  516 , dead reckoning positioning precision  518  and a certain margin. In some embodiments, the error in P Beacon  is about 10 cm. additionally or alternatively, the error in P Dead_Reckoning  starts at 10 cm and may grow to 10 m if the dead reckoning is performed over a long distance (e.g., 1 km). In some embodiments, the margin is in the range from 5 cm to 10 cm. 
     In some embodiments, beacon positioning  508  (e.g., P Beacon ) and dead reckoning positioning  510  (e.g., P Dead Reckoning ) are compared to assess dead reckoning positioning bias  512 . Additionally or alternatively, the beacon coverage area provides for accurate positioning and proper calculation of dead reckoning positioning bias  512 . In some embodiments, beacon coverage areas providing beacon positioning  508  (P Beacon ) serve as safety bag  500  for dead reckoning positioning  510  (P Dead Reckoning ). Additionally or alternatively, safety bag  500  provided by beacon positioning  508  (P Beacon ) is greater than uncertainty  502  associated with dead reckoning positioning  510  (P Dead Reckoning).    
     In some embodiments, in beacon coverage areas beacon positioning  508  (P Beacon ) and the dead reckoning positioning  510  (P Dead Reckoning ) are combined to remove dead reckoning positioning bias  512  and estimate positioning uncertainty  514  based on the sum of beacon positioning precision  516 , dead reckoning positioning precision  518  and a certain margin. Additionally or alternatively, in a beacon coverage area, beacon positioning  508  (P Beacon ) is the true  504  (e.g., actual) value with a negligible bias (e.g., &lt;5 cm) and beacon positioning precision  516  is significantly smaller than dead reckoning positioning precision  518  (e.g., beacon positioning precision  516  is less than or equal to 10 cm (±3σ)). 
     In some embodiments, in beacon coverage areas, the along guideway protection level is checked. For example, the dead reckoning positioning uncertainty (P Dead Reckoning    510  ±P Dead Reckoning  Precision  518 ) is compared against the beacon positioning uncertainty (P Beacon    508  ±P Beacon Precision    516 ). In some embodiments, when the difference is bounded by the along tracks protection level (e.g., safety bag  500 ), then the along tracks protection level is trusted; otherwise an alarm is raised. 
     In some embodiments, in areas without beacon coverage the along guideways positioning is determined solely based on the dead reckoning positioning algorithm (P Dead Reckoning ). Additionally or alternatively, in areas without beacon coverage beacon positioning  508  (P Beacon ) is not available. Therefore, dead reckoning positioning bias  512  is not determined. In some embodiments, the positioning algorithm will use the last beacon measurements before leaving the beacon coverage area to re-localize the dead reckoning positioning. In some embodiments, the positioning algorithm has two sub-algorithms: (a) localization in that the position is determined by observing a landmark with known location (P Beacon ), and (b) dead-reckoning in that the position is estimated based on the last observed landmark and speed/acceleration measurements. Additionally or alternatively, before leaving a beacon coverage area the dead-reckoning position is reset to the beacon position (e.g., +/− the error) and from that point the error will grow until the next beacon is observed. In some embodiments, positioning uncertainty  514  is still determined like beacon coverage areas (e.g., the summation of beacon positioning precision  516  (e.g., fixed value) and dead reckoning positioning precision  518  and a certain margin), but dead reckoning positioning precision  518  is determined based on error estimation techniques such as the covariance matrix of a Kalman Filter or equivalent. 
     In some embodiments, SIL-4 positioning in areas without beacon coverage is ensured by complementary measures such as supervision that dead reckoning positioning bias  512  in areas with beacon coverage is consistent and contained within a certain envelop such as ±5 m. Additionally or alternatively, safety bag  500  includes protection level supervision based on Standford diagrams (see  FIG. 14 ). In some embodiments, a consistency check checks a calculated position against the previous position in consideration of the acceleration and speed. In some embodiments, optimization of the guideway beacon installation maximizes the beacon coverage areas with beacon coverage to provide tighter position uncertainty. 
       FIG. 6  is a pictorial diagram of platform beacon coverage in accordance with some embodiments. In some embodiments, a platform area  600  with beacons  602  installed in platform area  600  have the following dimensions: platform length of approximately 150 m, vehicle  601  length of approximately 150 m, a first set of beacons  602 A installed 100 m (at each end of platform  600 ) outside of the platform edge, and a second set of beacons  602 B installed  600 m further from first set  602 A at each end of platform  600 ). Guideway beacons  602 A,  602 B,  602 C and  602 D (hereinafter referred to as guideway beacons  602 ), in some embodiments, are like guideway beacons  108 ,  208  and  308 . 
     In some embodiments, the placement of guideway beacons  602 A,  602 B will yield 2000 m of beacon coverage area that coincides with guideway distances between platforms for metro/subway systems. Additionally or alternatively, beacon coverage area will yield 1100 m with guideway beacon coverage and 900 m without. In some embodiments, the non-coverage areas are no longer than 150 m. 
     In some embodiments, when a vehicle travels more than a certain distance (e.g., twice the average distance between platforms) without encountering any guideway beacon  602  then the vehicle&#39;s position will be determined to be unknown, an alarm will sound and reported to central control, and the vehicle&#39;s position will have to re-established (e.g., a cold start performed). In some embodiments, the maximum distance without observing any beacon must be long enough to at least reach the next platform. In some embodiments, several aspects must be considered to determine the maximum allowed distance without observing any beacon. For example, when vehicle  601  is moving from right to left approaching guideway beacon  602 B and beacon  602 B is not detected by both front vehicle beacons  603 , the next opportunity to detect guideway beacon  602 B is when the vehicle&#39;s rear passes beacon  602 B. In some embodiments, when guideway beacon  602 B is detected by at least 1 of the rear vehicle beacons  605  then the distance travelled without observing any guideway beacon is at least 450 m. In this example, guideway beacon  602 B is most probably healthy and both front vehicle beacons have failed either intermittently or non-intermittently. This situation is expected to be rare as multiple beacon failure is uncommon. In some embodiments, when guideway beacon  602 B is not detected by both rear vehicle beacons then the distance travelled without observing any guideway beacon is at least 750 m. In this example, guideway beacon  602 B is most probably failed because at least four (4) vehicle beacons were not able to detect it. 
     In some embodiments, guideway beacons  602  are installed with redundancy, such as guideway beacons  602 C,  602 D. In some embodiments, the position and its associated position uncertainty, from the dead reckoning positioning algorithm (P Dead Reckoning  ±P Dead Reckoning Uncertainty ) are compared with the positioning, and its associated uncertainty, determined by the speed and its associated uncertainty. In some embodiments, when the following conditions, in the equation below where V is vehicle speed, are satisfied the dead reckoning positioning is within high level of safety integrity (SIL-4). 
       Σ (V Non-Beacon −V Non-Beacon Err )×Δt&lt;P Dead Reckoning −P Dead Reckoning Uncertainty &lt;P Dead Reckoning &lt;P Dead Reckoning +P Dead Reckoning Uncertainty &lt;Σ(V Non-Beacon +V Non-Beacon Err )×≢t
 
     In some embodiments, in beacon coverage areas the speed is determined as solely based on beacons measurements with refresh rate of Beacon refresh rate  (typically 5 Hz or higher) and referred to as V Beacon . In some embodiments, V Non-Beacon  is initialized while the vehicle is stationary and then once the speed is initialized solely based on the non-beacon speed algorithm. Additionally or alternatively, even though the beacons are available the beacons are not used to determine the non-beacon speed. In some embodiments, the non-beacon speed function is determined based on Radar and IMU, radar, tachometer/speed sensor and IMU, tachometer/speed sensor and single axis accelerometer or any other sensors arrangement that does not include localization capability as discussed above. 
     In some embodiments, the beacon speed (V Beacon ) and the non-beacon speed (V Non-Beacon ) are compared with the intent to assess the bias of the non-beacon speed. Additionally or alternatively, the assumption here is that the area covered with beacons is significant enough allowing proper calculation of the dead reckoning positioning bias. In some embodiments, in beacon coverage areas the beacon speed (V Beacon ) serves as a safety bag for the non-beacon speed (V Non-Beacon ). Additionally or alternatively, the safety bag provided by the beacon speed is greater than the uncertainty associated with the non-beacon speed. 
     In some embodiments, an amalgamation of the beacon speed and the non-beacon speed is preformed to remove the non-beacon speed bias (e.g., similar to the position bias discussed above) and estimate the speed uncertainty based on the summation of the beacon speed precision, the non-beacon speed precision and a certain margin. In some embodiments, the non-beacon speed bias, for a specified time interval, is the difference between the average speed determined based on the non-beacon speed function (e.g., using the beacons measurements for initialization only) and the average speed solely determined based on beacons measurements. Additionally or alternatively, the beacon speed is assumed to be the true (actual) value and the beacon speed precision is significantly smaller than the non-beacon speed precision (i.e. the beacon speed precision is less than or equal to 5 cm/sec (±3σ)). 
     In some embodiments, in areas without beacons coverage the speed is determined solely based on the non-beacon speed function and referred to as V Non-Beacon . In some embodiments, in areas without beacons coverage the beacon speed (V Beacon ) safety bag for the non-beacon speed (V Non-Beacon ) is not available. Therefore, the non-beacon speed bias is not determined. In some embodiments, the odometry algorithm use the last beacon measurements before a beacon coverage area is vacated to update the non-beacon speed. In some embodiments, the speed uncertainty is still determined in beacon coverage areas as the summation of the beacon speed precision (fixed value), the non-beacon speed precision and a certain margin. Additionally or alternatively, the non-beacon speed precision is determined based on error estimation techniques such as the covariance matrix of a Kalman Filter or equivalent. 
     In some embodiments, safety properties of the speed uncertainty in areas without beacon coverage is ensured by complementary measures such as determining that the non-beacon speed bias, in beacon coverage areas is consistent and contained within a certain envelop such as ±1 m/sec. Additionally or alternatively, consistency checks the calculated speed against the previous speed in consideration of the acceleration. In some embodiments, optimization of the beacon installation to maximize beacon coverage area with emphasis on areas where tighter speed uncertainty is needed. Additionally or alternatively, the beacon installation optimization is performed for both the positioning and odometry functions to find a solution that is good enough for both functions. 
     In some embodiments, in areas without beacon coverage the motion direction determined by the non-beacon speed function is checked for consistency with the motion direction previously determined in the beacon coverage area. Additionally or alternatively, the beacon coverage area motion direction is not expected to change as long as the vehicle is in motion and a stationary state is not determined. 
       FIG. 7  is a high level flow diagram of a method for determining position and odometry in accordance with some embodiments. In some embodiments, the processing circuitry determines a vehicle position on a guideway using range measurements between the vehicle and the guideway beacons configured to communicate with one or more vehicle beacons installed on an end of a vehicle that are configured to communicate with one or more guideway beacons on a guideway ( 702 ). For instance, in a cold start condition, the processing circuitry determines whether the vehicle is positioned on the correct tracks. 
     In some embodiments, the processing circuitry determines, using range measurements between the vehicle and the guideway beacons after the processing circuitry wakes from a sleep state (e.g., a cold start), any change in the vehicle position from before the processing circuitry entered the sleep state ( 704 ). For instance, cold motion detection determines whether the vehicle moved while the processing circuitry was shutoff. 
     In some embodiments, the processing circuitry determines, using the range measurements between the vehicle and the guideway beacons, whether the vehicle is stationary ( 706 ). For instance, if the vehicle&#39;s speed is consistently less than 0.5 kph or accumulative displacement is less than 3 cm. 
     In some embodiments, the processing circuitry determines, using range measurements between the vehicle and the guideway beacons, a vehicle speed and a vehicle direction of motion on the guideway ( 708 ). For instance, speed is determined using a change in position over time. In some embodiments, a direction of motion is determined by using the range measurements to determine if vehicle motion is moving from a first end to a second end or a second end to a first end. 
       FIG. 8  is a high-level functional block diagram of a processor-based system  800 , in accordance with some embodiments. In some embodiments, positioning and odometry system processing circuitry  800  is a general purpose computing device including a hardware processor  802  and a non-transitory, computer-readable storage medium  804 . Storage medium  804 , amongst other things, is encoded with, i.e., stores, computer program instructions  806 , i.e., a set of executable instructions such as a positioning and odometry algorithm. Execution of instructions  806  by hardware processor  802  represents (at least in part) a positioning and odometry tool which implements a portion or all of the methods described herein in accordance with one or more embodiments (hereinafter, the noted processes and/or methods). 
     Processor  802  is electrically coupled to a computer-readable storage medium  804  via a bus  808 . Processor  802  is also electrically coupled to an I/O interface  810  by bus  808 . A network interface  812  is also electrically connected to processor  802  via bus  808 . Network interface  812  is connected to a network  814 , so that processor  802  and computer-readable storage medium  804  are capable of connecting to external elements via network  814 . Processor  802  is configured to execute computer program instructions  806  encoded in computer-readable storage medium  804  in order to cause positioning and odometry processing circuitry  800  to be usable for performing a portion or all of the noted processes and/or methods. In one or more embodiments, processor  802  is a central processing unit (CPU), a multi-processor, a distributed processing system, an application specific integrated circuit (ASIC), and/or a suitable processing unit. 
     In one or more embodiments, computer-readable storage medium  804  is an electronic, magnetic, optical, electromagnetic, infrared, and/or a semiconductor system (or apparatus or device). For example, computer-readable storage medium  804  includes a semiconductor or solid-state memory, a magnetic tape, a removable computer diskette, a random access memory (RAM), a read-only memory (ROM), a rigid magnetic disk, and/or an optical disk. In one or more embodiments using optical disks, computer-readable storage medium  804  includes a compact disk-read only memory (CD-ROM), a compact disk-read/write (CD-R/W), and/or a digital video disc (DVD). 
     In one or more embodiments, storage medium  804  stores computer program instructions  806  configured to cause positioning and odometry system processing circuitry  800  to be usable for performing a portion or all of the noted processes and/or methods. In one or more embodiments, storage medium  804  also stores information, such as positioning and odometry algorithm which facilitates performing a portion or all of the noted processes and/or methods. In one or more embodiments, storage medium  804  stores parameters  807 . 
     Stationary resolution system processing circuitry  800  includes I/O interface  810 . I/O interface  810  is coupled to external circuitry. In one or more embodiments, I/O interface  810  includes a keyboard, keypad, mouse, trackball, trackpad, touchscreen, and/or cursor direction keys for communicating information and commands to processor  802 . 
     Stationary resolution system processing circuitry  800  also includes network interface  812  coupled to processor  802 . Network interface  812  allows stationary resolution system processing circuitry  800  to communicate with network  814 , to which one or more other computer systems are connected. Network interface  812  includes wireless network interfaces such as BLUETOOTH, WIFI, WIMAX, GPRS, or WCDMA; or wired network interfaces such as ETHERNET, USB, or IEEE-864. In one or more embodiments, a portion or all of noted processes and/or methods, is implemented in two or more stationary resolution system processing circuitries  800 . 
     Positioning and odometry processing circuitry  800  is configured to receive information through I/O interface  810 . The information received through I/O interface  810  includes one or more of instructions, data, design rules, and/or other parameters for processing by processor  802 . The information is transferred to processor  802  via bus  808 . Stationary resolution system processing circuitry  800  is configured to receive information related to a UI through I/O interface  810 . The information is stored in computer-readable medium  804  as user interface (UI)  842 . 
     In some embodiments, a portion or all of the noted processes and/or methods is implemented as a standalone software application for execution by a processor. In some embodiments, a portion or all of the noted processes and/or methods is implemented as a software application that is a part of an additional software application. In some embodiments, a portion or all of the noted processes and/or methods is implemented as a plug-in to a software application. 
     In some embodiments, the processes are realized as functions of a program stored in a non-transitory computer readable recording medium. Examples of a non-transitory computer-readable recording medium include, but are not limited to, external/removable and/or internal/built-in storage or memory unit, e.g., one or more of an optical disk, such as a DVD, a magnetic disk, such as a hard disk, a semiconductor memory, such as a ROM, a RAM, a memory card, and the like. 
     In some embodiments, a system of one or more computers are configured to perform particular operations or actions by virtue of having software, firmware, hardware, or a combination installed on the system that in operation causes or cause the system to perform the actions. One or more computer programs are configured to perform particular operations or actions by virtue of including instructions that, when executed by data processing apparatus, cause the apparatus to perform the actions. In some embodiments, a positioning and odometry system includes two or more vehicle beacons installed on an end of a vehicle and configured to communicate with one or more guideway beacons, the one or more guideway beacons installed along a guideway. The positioning and odometry system also includes processing circuitry configured to communicate with the one or more vehicle beacons, the processing circuitry configured to perform at least one of: determine, before the processing circuitry enters a sleep state, a first vehicle position on the guideway using range measurements between the vehicle beacons and the guideway beacons; determine, after the processing circuitry wakes from the sleep state, a second vehicle position on the guideway using range measurements between the vehicle beacons and the guideway beacons; determine, after the processing circuitry wakes from the sleep state, any difference between the first vehicle position on the guideway and the second vehicle position on the guideway; determine a third vehicle position on the guideway using range measurements between the vehicle and the guideway beacons taken at configurable time intervals; and determine a vehicle speed using range measurements between a single vehicle beacon and a single guideway beacon where speed is measured as a change in the third vehicle position over time. Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods. 
     In some embodiments, implementations include one or more of the following features. The system where the processing circuitry is further configured to determine motion of the vehicle using range measurements between the vehicle beacons and the guideway beacons. The processing circuitry is further configured to determine a stationary state of the vehicle using range measurements between the vehicle beacons and the guideway beacons. The processing circuitry is further configured to determine dead-reckoning positioning of the vehicle in areas where the guideway beacons are not available. The system includes a speed sensor to determine vehicle speed in areas where the guideway beacons are not available. The processing circuitry is further configured to determine a vehicle direction of travel on the guideway based on a comparison of one or more past range measurements between the vehicle beacons and the guideway and a most recent one or more range measurements between the vehicle beacons and the guideway beacons. The processing circuitry is further configured to determine a vehicle speed uncertainty. The guideway is a first guideway and the processing circuitry is further configured to determine whether the vehicle is positioned on the first guideway or a second guideway. The predetermined time period for range measurements between the vehicle and the guideway beacons is between 10 msec and 175 msec. At least one of the one or more guideway beacons is a temporary installation. Implementations of the described techniques include hardware, a method or process, or computer software on a computer-accessible medium. 
     In some embodiments, a method includes determining, with processing circuitry configured to communicate with one or more vehicle beacons installed on an end of a vehicle and configured to communicate with one or more guideway beacons positioned at predetermined locations along a guideway, a vehicle position on the guideway using range measurements between the vehicle and the guideway beacons; determining, with the processing circuitry using the range measurements between the vehicle and the guideway beacons, a vehicle speed and a vehicle direction of motion on the guideway. The method also includes determining, with the processing circuitry using the range measurements between the vehicle and the guideway beacons, whether the vehicle is stationary. The method also includes determining, with the processing circuitry using range measurements between the vehicle and the guideway beacons after the processing circuitry wakes from a sleep state, vehicle movement on the guideway and determine a change in the vehicle position from before the processing circuitry entering the sleep state. Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods. 
     In some embodiments, implementations include one or more of the following features. The method where the processing circuitry is a first processing circuitry, the method includes monitoring, with a second processing circuitry operatively coupled to the first processing circuitry, the first processing circuitry to prevent the processing circuitry from entering an unsafe state. The method includes determining, with the second processing circuitry, a safety bag for a dead reckoning positioning performed with the first processing circuitry. The method includes creating, with the second processing circuitry, a positioning uncertainty based on beacon positioning information from the first processing circuitry, dead reckoning positioning information from the first processing circuitry and a safety margin. The method includes issuing, with the second processing circuitry, an alarm when a difference between beacon positioning information and dead reckoning positioning information is outside bounds of an along guideways protection level. Implementations of the described techniques include hardware, a method or process, or computer software on a computer-accessible medium. 
     In some embodiments, a non-transitory computer-readable storage medium includes instructions to determine, with range measurements between one or more vehicle beacons installed on an end of a vehicle and configured to communicate with one or more guideway beacons positioned at predetermined locations along one or more guideways, after the processor wakes from a sleep state, vehicle position and guideway occupancy to determine a change in the vehicle position from before the processor entering the sleep state. The medium also includes instructions to determine, with the range measurements between the vehicle and the guideway beacons, a periodic vehicle position update. The medium also includes instructions to determine, with the range measurements between the vehicle and the guideway beacons, a vehicle speed and a vehicle direction of motion on the guideway. The medium also includes instructions to determine, with the range measurements between the vehicle and the guideway beacons, a vehicle stationary state. The medium also includes instructions to determine dead-reckoning positioning in guideway locations with no guideway beacons. The medium also includes instructions to determine the vehicle speed and the vehicle direction of motion in areas with no guideway beacons. Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods. 
     In some embodiments, implementations include one or more of the following features. The storage medium includes executable instructions that, when executed by a processor, cause the processor to determine a non-beacon speed bias compensation and uncertainty estimation. The storage medium includes executable instructions that, when executed by a processor, cause the processor to monitor the dead-reckoning positioning to determine a position uncertainty. The storage medium includes executable instructions that, when executed by a processor, cause the processor to determine a vehicle speed uncertainty. Implementations of the described techniques include hardware, a method or process, or computer software on a computer-accessible medium. 
     The foregoing outlines features of several embodiments so that those skilled in the art may better understand the aspects of the present disclosure. Those skilled in the art should appreciate that they may readily use the present disclosure as a basis for designing or modifying other processes and structures for carrying out the same purposes and/or achieving the same advantages of the embodiments introduced herein. Those skilled in the art should also realize that such equivalent constructions do not depart from the spirit and scope of the present disclosure, and that they may make various changes, substitutions, and alterations herein without departing from the spirit and scope of the present disclosure.