WO2017032978A1

WO2017032978A1 - Positioning system and method

Info

Publication number: WO2017032978A1
Application number: PCT/GB2016/052498
Authority: WO
Inventors: Brendan WATTS; Alexandre NAIRAC
Original assignee: Oxford Technical Solutions Limited
Priority date: 2015-08-25
Filing date: 2016-08-11
Publication date: 2017-03-02
Also published as: GB2541674B; GB2541674A; GB201515096D0

Abstract

The present invention provides a positioning system for determining the position of a moving object in a reference frame. The positioning system comprises a dead-reckoning unit (10) to calculate an estimated position (ŝ) of the object in the reference frame, a plurality of lines (31,32) on a surface across which the object moves, a detection unit (40) to detect if the moving object encounters one of the plurality of lines, an error correction unit (20), and an identification unit (50). The estimated position (ŝ) has an unknown, actual error (e (ŝ)) and an uncertainty (U (ŝ)) associated therewith. Each of the lines has a pre-measured mathematical description (m₁, m ₂, …, m_k, …, m_n ) in the reference frame, and the mathematical description of each line also has an uncertainty (U (m k )) associated therewith. The error correction unit (20) reduces the actual error and the uncertainty in the estimated position of the object by using these quantities to calculate an estimated error (ê (ŝ)) in the estimated position of the object, and by taking the uncertainty (U (ŝ)) in the estimated position of the object and the uncertainty (U (m_k )) in the mathematical description (m k ) of the detected one of said lines to calculate a new uncertainty (U' (ŝ)) in the estimated position of the object. The identification unit (50) identifies which one of the plurality of lines is most likely to have been detected by the detection unit based on the estimated position (ŝ) of the object, and supplies the pre-measured mathematical description (m_k) of the line thus identified to the error correction unit, to be used by the error correction unit as the mathematical description (m k ) of the detected one of said lines. The system may be used as part of a guidance, navigation and control (GNC) system further comprising a guidance and control system to guide and control the moving object on the basis of the position of the object determined by the positioning system. The invention also provides a corresponding method of determining the position of a moving object which may be used as part of a method for guidance, navigation and control (GNC) of the moving object.

Description

POSITIONING SYSTEM AND METHOD

The present invention concerns a positioning system and method. More particularly, it concerns a system for determining the position of a moving object within a reference frame, and a method of doing the same, which are particularly suitable for use in an indoor environment.

The position of a moving object in a reference frame can be estimated using dead reckoning. In general, dead reckoning takes one or more kinematic variables of an object, such as the object's orientation, position or velocity, and provides an updated estimate of the value of these variables at regular intervals by measuring a rate of change of the variables using one or more motion sensors. In one case, for example, the chosen kinematic variable of the object may be its position, and the velocity of the object, which provides the rate of change of its position, is measured. This measured velocity of the object is then used to calculate an updated estimate of the object's position. However, this updated estimate of the position is subject to an error because obtaining the updated position requires integrating the rate of change of the object's position. The error is the difference between the object's estimated position and its actual position. The cause of this error may arise from manufacturing tolerances and wear and tear within the motion sensors, for example. This generates an integration error, leading to an uncertainty in the estimated position. The uncertainty is the (mathematical) variance of the estimated position.

Updating the estimated position of the object can then be repeated at a predetermined frequency by performing successive dead reckoning calculations. However, each time that the estimated position is updated by dead reckoning, it is subject to cumulative errors arising from the uncertainty associated with the estimated position at each successive repetition of the updating process. If left uncorrected, therefore, the error will increase and the estimated value of the object's position will drift away from the actual position of the object. It is therefore very important to counteract this cumulative error by correcting the estimated position of the object with additional positional data derived from another source, other than from the motion sensors.

It is known, for example, to correct the position of a moving object estimated by dead reckoning by using positioning signals received from a satellite-based system, such as the global positioning system (GPS). These corrections can be performed using a process of linear quadratic estimation, also known as Kalman filtering. Such a technique works well in an outdoor environment. On the other hand, accurately determining the position of a moving object in an indoor environment is difficult. On the one hand, it would be highly desirable to be able to locate the position of a moving object to an accuracy of 1 cm or better. This would allow guidance, navigation and control (GNC) of moving objects, such as robots, indoors to an accuracy similar to that achieved by human beings. On the other hand, existing systems which seek to locate the position of a moving object indoors are only able to achieve accuracies much worse than this. For example, a nearfield wireless communication protocol such as Bluetooth™ is only able to locate the position of an object to an accuracy of about 1 to 5 m. Using sonar indoors produces too many multiple reflections from walls and other surfaces to be practicable. Wifi using specialist hardware to emit a train of 2.4 GHz pulses and measure the time of flight before reflections are received in order to calculate the position of a moving object can achieve an accuracy of about 20 cm, but this is still more than an order of magnitude less than is desirable. Satellite-based systems, such as GPS, can achieve the desired level of accuracy of about 1 cm, but only in an outdoor environment. In an indoor environment, both the accuracy and the reliability of such satellite-based systems is severely reduced. Accordingly, there is a much-felt want for a positioning system and method which can determine the position of a moving object in an indoor environment to an accuracy of 1 cm or better. Accordingly, in a first aspect, the present invention provides a positioning system for determining the position of a moving object in a reference frame. The system comprises a dead-reckoning unit to calculate an estimated position of the object in the reference frame, the estimated position having an unknown, actual error and an uncertainty associated therewith; a plurality of lines on a surface across which the object moves, each of said lines having a pre-measured mathematical description in the reference frame, the mathematical description of each line having an uncertainty associated therewith; a detection unit to detect if the moving object encounters one of the plurality of lines; an error correction unit to reduce the actual error and the uncertainty in the estimated position of the object by taking the estimated position of the object, the uncertainty in the estimated position of the object, the mathematical description of a detected one of said lines and the uncertainty in the mathematical description of the detected one of said lines to calculate an estimated error in the estimated position of the object, and by taking the uncertainty in the estimated position of the object and the uncertainty in the mathematical description of the detected one of said lines to calculate a new uncertainty in the estimated position of the object; and an identification unit to identify which one of the plurality of lines is most likely to have been detected by the detection unit based on the estimated position of the object, and to supply the pre-measured mathematical description of the line thus identified to the error correction unit, to be used by the error correction unit as the mathematical description of the detected one of said lines.

Since, in general, the moving object may be an extended body, the estimated position of the moving object may, for example, represent the centre of mass of the moving object in the reference frame. Alternatively, if, for example, the detection unit is mounted on the moving object, the estimated position of the moving object may instead represent an estimate of the location of the detection unit in the reference frame. The unknown, actual error associated with the estimated position of the object is the difference between the estimated position of the object and the actual position of the object, which, since the latter is unknown, causes the actual error to be unknown as well. As mentioned above, the uncertainty associated with the estimated position of the object is the variance of the estimated position.

As each of the plurality of lines is more than just a point, it cannot simply be described as having a particular position in the reference frame. It can, however, still be given a mathematical description. The mathematical description of each of the plurality of lines in the reference frame may, for example, be an equation of that line in the reference frame or it may be a table of splines representing that line in the reference frame. The mathematical description of each line is pre-measured. However, in practice, the lines may have a finite thickness (for example, if they are painted on the surface across which the object moves) and the measurement process for obtaining the mathematical description of each line may also involve some inaccuracy, so there is also an uncertainty associated with the mathematical description of each line. Although the identification unit can identify which one of the plurality of lines is most likely to have been detected by the detection unit based on the estimated position of the object, it may not be able to do so in all cases, for example if the detection unit detects an intersection of two or more of the plurality of lines. In such a case, the identification unit would determine that both or all of the lines meeting at the intersection were equally likely to have been detected by the detection unit, and therefore would not be able to supply the pre-measured mathematical description of just one of these lines to the error correction unit, to be used by the error correction unit as the mathematical description of a detected one of the lines. The error correction unit could then just await the supply of a pre-measured mathematical description of one of the plurality of lines when the detection unit next detects a line that the identification unit can uniquely identify as the one most likely to have been detected by the detection unit. The error correction unit is then able to reduce the actual error and the uncertainty in the estimated position of the object as specified above. With such a positioning system, therefore, if the mathematical descriptions of the plurality of lines are all pre-measured sufficiently accurately, then the position of the moving object can be determined to an accuracy of 1 cm or better, regardless of whether the object is moving in an indoor or an outdoor environment.

Preferably, the dead-reckoning unit comprises an inertial navigation system (INS) including an inertial measurement unit (IMU) and a strapdown navigator, and the inertial measurement unit (IMU) comprises a plurality of orthogonal accelerometers and a plurality of orthogonal angular rate sensors.

The error correction unit preferably comprises a Kalman filter.

The plurality of lines may be either curved or straight, or a combination of the two. In a preferred embodiment, the plurality of lines comprises a plurality of non-parallel, rectilinear lines. If so, the plurality of non-parallel, rectilinear lines may comprise a first set of parallel, rectilinear lines extending in a first direction and a second set of parallel, rectilinear lines extending in a second direction different from the first direction. In such a case, the first direction is preferably orthogonal to the second direction. Preferably, the first set of parallel, rectilinear lines may alternate with the second set of parallel, rectilinear lines. The first and second sets of parallel, rectilinear lines may also each comprise a plurality of groups of such lines. Alternatively or additionally, the plurality of lines may comprise one or more curved lines, such as an array of concentric circles centred on an origin of the reference frame or an array of arcs of different ellipses.

The plurality of lines may further comprise a third set of lines lying outside a surface defined by the first and second sets of lines. This allows the positioning system to determine the position of a moving object in three dimensions. At least one of the plurality of lines may be retroreflective, in which case, the detection unit may also comprise a source of electromagnetic radiation and a sensor of such electromagnetic radiation.

The plurality of lines may comprise a beam of electromagnetic radiation, in which case, the detection unit may also comprises a sensor of such electromagnetic radiation. At least one of the plurality of lines may be magnetic, in which case, the detection unit may comprise a Hall-effect sensor.

Preferably, the identification unit comprises a database of the pre-measured mathematical descriptions of the plurality of lines, and a probability calculator to compare respective ones of the pre-measured mathematical descriptions of the plurality of lines with the estimated position of the object calculated by the dead reckoning unit and to assign a probability to each one of the lines having been detected by the detection unit according to how close the estimated position of the object is to the respective ones of the pre-measured mathematical descriptions. In such a case, the database may contain mathematical descriptions of the plurality of lines in the form of, for example, a respective equation of each line in the reference frame or as a respective table of splines for each line in the reference frame.

The dead-reckoning unit is preferably operable to determine an additional kinematic variable of the moving object besides its position and/or a variable of the dead-reckoning unit using the reduced error and uncertainty in the estimated position of the object. The additional kinematic variable of the moving object may be any one of its heading, orientation, velocity and acceleration, but is not limited to the kinematic variables just mentioned. The variable of the dead-reckoning unit may, for example, be gyro bias.

In one preferred embodiment, the reference frame is a north-east-down (NED) reference frame fixed relative to the Earth.

In a preferred application, the positioning system may be used for determining the position of a robotically guided object, such as a robotically driven wheeled vehicle.

The positioning system may also form part of a guidance, navigation and control (GNC) system further comprising a guidance and control system to guide and control the moving object on the basis of the position of the object determined by the positioning system.

In a second aspect, the present invention also provides a method of determining the position of a moving object in a reference frame. The method comprises using dead reckoning to calculate an estimated position of the object in the reference frame, the estimated position having an unknown, actual error and an uncertainty associated therewith; providing a plurality of lines on a surface across which the object moves; measuring a mathematical description of each line in the reference frame, the mathematical description of each line having an uncertainty associated therewith; detecting if the moving object encounters one of the plurality of lines, and if so, identifying which one of the plurality of lines is most likely to have been detected based on the estimated position of the object, and reducing the actual error and the uncertainty in the estimated position of the object using the previously measured mathematical description of the line thus identified as the detected one of said lines by taking the estimated position of the object, the uncertainty in the estimated position of the object, the mathematical description of the detected one of said lines and the uncertainty in the mathematical description of the detected one of said lines to calculate an estimated error in the estimated position of the object, and by taking the uncertainty in the estimated position of the object and the uncertainty in the mathematical description of the detected one of said lines to calculate a new uncertainty in the estimated position of the object.

Thus, the estimated error in the estimated position of the object depends on both the estimated position of the object and the mathematical description of the detected one of the lines, as well as on the respective uncertainties associated with each of these two quantities. These four inputs to the calculation of the estimated error can be weighted according to a probability that can be attached to whichever one of the plurality of lines is most likely to have been detected. Similarly, the new uncertainty in the estimated position of the object depends on both the previous uncertainty in the estimated position of the object and the uncertainty in the mathematical description of the detected one of the lines. These two inputs to the calculation of the new uncertainty in the estimated position of the object can also be weighted according to the probability that can be attached to the one of the plurality of lines which is most likely to have been detected.

Preferably, using dead reckoning in this method of determining the position of a moving object comprises using inertial navigation.

It is also preferred that the error and the uncertainty in the estimated position of the object are reduced by Kalman filtering. Preferably, detecting if the object encounters one of the lines comprises emitting a beam of electromagnetic radiation, reflecting said beam from said one of the lines, and receiving the beam thus reflected. Detecting if the object encounters one of the lines may alternatively or additionally comprise receiving a beam of electromagnetic radiation emitted by said one of the lines. Furthermore, detecting if the object encounters one of the lines may alternatively or additionally comprise sensing a variation in a magnetic field of said one of the lines. Identifying which one of the plurality of lines is most likely to have been detected preferably comprises comparing respective ones of the mathematical descriptions of the plurality lines stored in a database with the estimated position of the object in the reference frame and assigning a probability to each one of the lines having been detected according to how close the estimated position of the object is to the respective ones of the pre-measured mathematical descriptions.

The method may further comprise determining an additional kinematic variable of the moving object besides its position and/or a variable of the dead reckoning process, using the reduced error and uncertainty in the estimated position of the object. The additional kinematic variable of the moving object may be any one of heading, orientation, velocity and acceleration, but is not limited to the kinematic variables just mentioned. The variable of the dead reckoning process may be due, for example, to gyro bias. The method of determining the position of a moving object may be part of a method for guidance, navigation and control (GNC) of a moving object which further comprises guiding and controlling the object on the basis of the position of the object thus determined.

Further features and advantages of the present invention will become apparent from the following detailed description, which is given by way of example and in association with the accompanying drawings, in which:

Fig. 1 is a schematic block diagram of a positioning system according to an embodiment of the invention;

Fig. 2 is a schematic block diagram of a dead-reckoning unit in the positioning system of Fig.

1 ;

Fig. 3 is a schematic block diagram of an identification unit in the positioning system of Fig. 1 ;

Figs. 4A and 4B show successive steps in an example of a moving object encountering a plurality of lines in the positioning system of Fig. 1 ;

Fig. 5A is a schematic diagram showing an example of a plurality of non-parallel, rectilinear lines; Fig. 5B is a schematic diagram showing another example of a plurality of non-parallel, rectilinear lines; and

Fig. 6 is a flow diagram showing the steps of a positioning method according to an embodiment of the invention.

Referring firstly to Fig. 1 , there is shown a schematic block diagram of a positioning system 1 according to an embodiment of the invention. The positioning system 1 is for determining the position of a moving object in a reference frame. It comprises a dead-reckoning unit 10, an error correction unit 20, a plurality of lines 31 , 32, a detection unit 40 and an identification unit 50. The dead-reckoning unit 10 calculates an estimated position s of the object in the reference frame. As used herein, the symbol ^Λ ("hat") written above a variable denotes an estimated value of that variable. In this embodiment, the dead-reckoning unit 10 comprises an inertial navigation system (INS) 12, although in other possible embodiments, the dead- reckoning unit 10 may use means other than inertial navigation to calculate an estimated position of the moving object by dead reckoning, such as, for example, an elapsed time.

In the embodiment of Fig. 1 , however, the INS 12, which is shown in greater detail in Fig. 2, includes an inertial measurement unit (IMU) 14 and a strapdown navigator 16. The IMU 14 comprises three orthogonal accelerometers 141a, 141 b, 141c and three orthogonal angular rate sensors 142a, 142b, 142c. These accelerometers and angular rate sensors respectively detect changes in the velocity and orientation of the moving object, and pass these detected changes to the strapdown navigator 16. The strapdown navigator 16 uses these detected changes to calculate the estimated position s of the moving object in the reference frame in a conventional manner. Since this position of the object is an estimate, it also has an unknown, actual error e (s) associated with it, as well as an uncertainty U (s). The unknown, actual error e (s) is equal to the difference between the estimated position s and the actual position s of the moving object. The uncertainty U (s) is the (mathematical) variance of the estimated position s. As shown in Fig. 1 , the error correction unit 20 reduces both the actual error e (s) and the uncertainty U (s) by calculating an estimated error e (s) and a new uncertainty U' (s) in the estimated position s of the object. As used herein, the superfix ' ("prime") written after a quantity denotes a revised or new value of a quantity. In this embodiment, the error correction unit 20 comprises a Kalman filter, which uses linear quadratic estimation to reduce both the actual error and the uncertainty in the estimated position based on a pre-measured mathematical description of a detected one of a plurality of lines, as will be described in greater detail below. The plurality of lines 31 , 32 in the positioning system 1 of Fig. 1 are provided on a surface across which the object moves. In this embodiment, the lines 31 , 32 are non-parallel, rectilinear lines, which are orthogonal to each other, although in other possible alternative embodiments, they could be curved lines, such as arcs of circles of different radii or ellipses of different eccentricity, for example. Each of the plurality of lines 31 , 32 has associated with it a pre-measured mathematical description of each line in the reference frame. Thus, in this example, the mathematical description of line 31 is mi and the mathematical description of line 32 is rri2. If there are n lines in total making up the plurality of lines, the nth line will therefore have a mathematical description m_n, and the mathematical description of a representative one, k, of the plurality of lines is denoted by rrik.

The mathematical description of each line in the reference frame can also be freely chosen. In polar co-ordinates, for example, the mathematical description of each line may include its distance from an origin of the reference frame and its angle from an axis passing through the origin. Thus, for example, in the positioning system 1 of Fig. 1 , the reference frame may be a rectangular Cartesian co-ordinate system with x and y axes, in which case, the rectilinear line 31 in Fig. 1 has a mathematical description mi which is an equation describing that line in the reference frame given by y = ax + b, where a is the gradient of line 31 and b is the value of the y-intercept of line 31 in the rectangular Cartesian co-ordinate system. Another line drawn parallel to line 31 but further to the left of Fig. 1 than line 31 would therefore have an equation with the same gradient a, but with a y-intercept having a value greater than b, and a third line drawn parallel to line 31 but further to the right of Fig. 1 than line 31 would also have an equation with the same gradient a, but with a y-intercept having a value less than b. Similarly, the line 32 in Fig. 1 has a different mathematical description rri2 which is an equation describing that line in the reference frame given by y = cx + d, where c is the gradient of line 32 and d is the value of the y-intercept of line 32 in the rectangular Cartesian co-ordinate system. Thus, a fifth line drawn parallel to line 32 but further to the right of Fig. 1 than line 32 would have an equation with the same gradient c, but with a y-intercept having a value greater than d, and a sixth line drawn parallel to line 32 but further to the left of Fig. 1 than line 32 would have an equation with the same gradient c, but with a y-intercept having a value less than d.

The detection unit 40 of the positioning system 1 detects if the moving object encounters one of the plurality of lines 31 , 32. At least one of the plurality of lines 31 , 32 may be retroreflective, in which case, the detection unit 40 comprises a source of electromagnetic radiation, such as a light and a sensor of such electromagnetic radiation, such as a photosensitive diode, to detect light emitted from the source and reflected by the line. The plurality of lines 31 , 32 may alternatively or additionally comprise a beam of electromagnetic radiation, such as an infrared laser beam, in which case, the detection unit 40 also comprises a sensor of such infrared light. Alternatively or additionally, at least one of the plurality of lines may be magnetic, for example a current-carrying wire embedded in the surface across which the object moves, in which case, the detection unit 40 also comprises a Hall-effect sensor to detect a magnetic field of the current-carrying wire. Typically, the detection unit 40 is mounted on the moving object, although this does not have to be so. Instead, the detection unit 40 could equally well detect if the moving object encounters one of the plurality of lines 31 , 32 by being mounted in a position other than on the moving object, with a mirror mounted on the moving object to provide a line of sight from the detection unit 40 to whichever one of the plurality of lines 31 , 32 the object encounters.

When the detection unit 40 detects that the moving object has encountered one of the plurality of lines 31 , 32, it outputs the fact that there has been a detection event to the identification unit 50. The identification unit 50 identifies which one of the plurality of lines 31 , 32 is most likely to have been detected by the detection unit 40 based on the estimated position s of the moving object. In the embodiment of Fig. 1 , the identification unit 50 comprises a database 51 and a probability calculator 52, as shown in greater detail in Fig. 3. The database 51 stores the pre-measured mathematical descriptions, mi , rri2, ... rrik, ... m_n of the plurality of lines. When the detection unit 40 notifies the identification unit 50 that a line has been detected, the probability calculator 52 calculates the probability that each one of the plurality of lines has been encountered by the moving object by comparing respective ones of these pre-measured mathematical descriptions mi , rri2, ... rrik, ... m_n with the estimated position s of the moving object and assigning a probability to each one of the lines according to how close the estimated position of the object is to the respective ones of the pre-measured mathematical descriptions. In this way, the identification unit 50 can then identify which one of the plurality of lines is most likely to have been detected by the detection unit 40 according to which one of the plurality of lines has had the highest probability assigned to it by the probability calculator 52.

Thus, suppose, for example, that the moving object has just encountered line 31 and that the estimated position of the moving object calculated by the dead-reckoning unit 10 at that time is s. The probability calculator 52 compares this value for the estimated position of the moving object with respective ones of the pre-measured mathematical descriptions mi , rri2, ... rrik, ... m_n of the plurality of lines 31 , 32 from the database 51 , and finds that s is closest to the pre- measured mathematical description mi for line 31. The probability calculator 52 therefore assigns a probability to line 31 which is greater than the probability it assigns to line 32, for example. The identification unit 50 therefore identifies that line 31 is the one of the plurality of lines most likely to have been detected by the detection unit 40 and supplies the pre-measured mathematical description mi of line 31 to the error correction unit 20 to be used by the error correction unit 20 as the mathematical description of the detected one of the lines.

Whereas in the embodiment just described, identification unit 50 comprises such a database 51 and a probability calculator 52 to identify which one of the plurality of lines 31 , 32 is most likely to have been detected by the detection unit 40 based on the estimated position of the moving object, in other possible alternative embodiments, the identification unit 50 could instead identify which one of the plurality of lines 31 , 32 is most likely to have been detected by the detection unit 40 by some other means, for example by monitoring an elapsed time and an estimated velocity of the moving object.

In any event, the error correction unit 20 receives the pre-measured mathematical description rrik of the one of the plurality of lines which the identification unit 50 has identified as being most likely to have been detected by the detection unit 40 and also receives the estimated position s of the object from the dead-reckoning unit 10, and uses these, together with the uncertainty U (s) in the estimated position s of the object and the uncertainty U (rrik) in the mathematical description rrik of the detected one of the lines, to calculate an estimated error e (s) in the estimated position s of the object. The error correction unit 20 may calculate the estimated error e (s) in one of several, different possible ways. For example, it may attach a weighting to each of the estimated position s of the object and the mathematical description rrik of the line most likely to have been detected by the detection unit 40, according to the probability of that line having been detected assigned to that particular line by the identification unit 50 for that detection event. The error correction unit 20 also takes the uncertainty U (rrik) in the mathematical description rrik of the detected one of the lines and the uncertainty U (s) in the estimated position s of the object, and uses these to calculate a new uncertainty U' (s) in the estimated position s of the object. Once again, the error correction unit 20 may achieve this in one of several ways, for example by attaching a weighting to each of the uncertainty U (s) in the estimated position s of the object and the uncertainty U (rrik) in the mathematical description rrik of the detected one of the lines, according to the probability of that line having been detected assigned to that particular line by the identification unit 50 for that detection event. In this way, the error correction unit 20 can reduce both the actual error and the uncertainty in the estimated position of the object.

Figs. 4A and 4B show successive steps in an example of a moving object encountering the plurality of lines 31 , 32 in the positioning system of Fig. 1 and how the error correction unit 20 reduces the uncertainty in the estimated position s of the moving object. In Figs. 4A and 4B, the arrow 60 represents how the unknown, actual position of the object changes over time, and the suffices i, i+1 , i+2 represent successive moments in time in the operation of the positioning system 1. Thus, in Fig. 4A, the moving object starts at time i with an estimated position s, which has an uncertainty U (§,) associated therewith. This uncertainty U (§,) is represented in Fig. 4A by a dashed circle around the estimated position At the next moment in time i+1 , if the moving object did not encounter a line, the estimated position would drift to Si+i which has a greater uncertainty U (§M) associated therewith. This uncertainty U (§M) is represented in Fig. 4A by a dashed circle around the estimated position §M which is larger than the dashed circle around the previous estimated position The unknown, actual error in the estimated position §M is represented by the distance of the estimated position §M from the arrow 60. However, when the object encounters line 31 , the error correction unit 20 reduces this actual error and the uncertainty U (§M), so that when the estimated position of the object is next calculated by the dead reckoning unit 10 to be S'M , the new uncertainty in the position of the object is calculated by the error correction unit 20 to be U' (S'M). This new uncertainty U' (S'M) is reduced in a direction orthogonal to line 31 , but remains unchanged in a direction parallel to line 31. This is therefore represented in Fig. 4A by a dashed ellipse having a major axis aligned with the direction in which the rectilinear line 31 extends and a minor axis orthogonal to the direction in which line 31 extends. It can also be seen in Fig. 4A how the actual error in the estimated position S'M represented by the distance of the estimated position S'M from the arrow 60 is also reduced.

Turning next to Fig. 4B, at the next moment in time i+2, if the moving object did not encounter another line, the estimated position would drift to s,+2 which has an uncertainty U (§,+2) associated therewith, which is greater than the uncertainty U' (S'M). This uncertainty U (§,+2) is therefore represented in Fig. 4B by a dashed ellipse around the estimated position ,+2 which is larger than the dashed ellipse around the previous estimated position S'M . The unknown, actual error in the estimated position ,+2 is again represented by the distance of the estimated position ,+2 from the arrow 60. However, when the moving object encounters line 32, the error correction unit 20 reduces this actual error and the uncertainty U (§,+2), so that when the estimated position of the object is next calculated by the dead reckoning unit 10 to be §',+2, the new uncertainty in the position of the object is recalculated by the error correction unit 20 to be U' (s'i+2). This new uncertainty U' (s'i+2) is reduced in a direction orthogonal to line 32, but remains unchanged in a direction parallel to line 32. This is therefore represented in Fig. 4B by a smaller dashed ellipse having a major axis aligned with the direction in which the rectilinear line 32 extends and a minor axis orthogonal to the direction in which line 32 extends. Thus the uncertainty in the estimated position of the moving object is reduced each time that the object encounters a line, and furthermore, if as in this example, the lines are non-parallel, the uncertainty can be reduced in different directions as well according to the respective mathematical descriptions of the plurality of lines. If, on the other hand, the object does not encounter a line before the estimated position of the object is next calculated by the dead reckoning unit 10, then the uncertainty in the estimated position will start to grow again as a result of errors introduced into the estimated position by the operation of the inertial measurement unit 14 and other uncertainties in the system.

As can be seen in both Figs. 4A and 4B, the estimated position of the moving object lies somewhere near the unknown, actual position of the object and becomes closer to the actual position as the uncertainty in the estimated position is reduced by the error correction unit 20 each time that the moving object crosses one of the plurality of lines. The actual error e (s) in the estimated position s, which is just the difference between the estimated position and the actual position of the object, is therefore also reduced as the uncertainty in the estimated position is reduced. In practice, in order for the error correction unit 20 to reduce the error and the uncertainty in the estimated position of the moving object in the reference frame more than just twice, the positioning system 1 comprises more than just the two lines 31 , 32 shown in Fig. 1. An example of such a greater plurality of lines 31 , 32 is shown in Fig. 5A. Here, the plurality of lines comprises a first set of parallel, rectilinear lines 31a, 31 b, 31c extending in a first direction and a second set of parallel, rectilinear lines 32a, 32b, 32c extending in a second direction different from the first direction. The first set of parallel, rectilinear lines 31a, 31 b, 31 c alternates with the second set of parallel, rectilinear lines 32a, 32b, 32c. Thus an object moving across Fig. 5A from left to right or from right to left will encounter one of the lines from each of the two sets of parallel, rectilinear lines in turn, and the uncertainty in the estimated position s of the moving object will be reduced alternately in different directions orthogonal to the first and second directions in which the two sets of lines extend.

Fig. 5B shows an alternative possible example of a plurality of lines. In this example, the first and second sets of parallel, rectilinear lines 31 a, 31 b, 31c; 32a, 32b, 32c each comprise a plurality of groups of such lines 311 a, 31 1 b; 322a, 322b. Thus the first set of lines 31a, 31 b, 31 c comprises the groups 31 1a, 31 1 b and the second set of lines 32a, 32b, 32c comprises the groups 322a, 322b. Such groups of lines can be used to provide additional information about kinematic variables of the object other than just its position, such as its heading or its velocity. For example, if the object is moving more rapidly, it will encounter the lines in one group in more rapid succession than if it is moving more slowly. Similarly, if the object is on a heading which crosses the lines in one group at a first angle, it will encounter the lines in that group at different locations from if the object were on a heading which crossed the lines in that group at a different, second angle. This additional information can then be used by the dead- reckoning unit 10 to determine an additional kinematic variable of the moving object besides its position using the reduced error and uncertainty in the estimated position of the object. Thus, for example, if the estimated heading or velocity of the object is different from its actual heading or velocity, the estimated positions of the lines in the group will be different from (i.e. in error with respect to) the measured positions of the lines in that group and the measured positions can be used to correct the estimated heading or velocity accordingly.

In another possible embodiment, the plurality of lines may comprise a third set of lines lying outside a surface defined by the first and second sets of lines. Thus, for example, if the first and second sets of lines lie in a plane across which the object moves, the third set of lines may be provided as a set of parallel lines at different heights above that plane. Thus if the object encounters one of the third set of lines, not only its two-dimensional position in the plane, but also its height about the plane can be determined by the positioning system. Thus the reference frame need not be just two-dimensional and the positioning system can determine the position of a moving object in three dimensions as well. An example of three- dimensional reference frame which the positioning system could use in such an embodiment is a north-east-down (NED) reference frame fixed relative to the Earth. The positioning system may be used to determine the position of a moving object which is a robotically guided object, such as a robotically driven wheeled vehicle. The positioning system can also be part of a guidance, navigation and control (GNC) system which further comprises a guidance and control system to guide and control the moving object on the basis of the position of the object determined by the positioning system. For example, if the moving object is a robotically driven wheeled vehicle which is to be subjected to a crash test, the plurality of lines of the positioning system can be provided along a target track of the vehicle from its starting position to the intended crash site. By guiding and controlling the movement of the vehicle along the target track on the basis of the position of the vehicle determined by the positioning system, the arrival of the vehicle at the intended crash site with the intended velocity and orientation of the vehicle can then be ensured to an accuracy of 1 cm or better provided that the mathematical descriptions of the plurality of lines are all pre-measured sufficiently accurately. This positioning system is particularly suited to such an application because such crash tests are generally carried out in an indoor environment, in order to ensure the accurate measurement of the final positions of all debris from the crash and the non- intervention in the crash test of such uncontrollable weather conditions as wind. Finally, Fig. 6 is a flow diagram showing steps in a method of determining the position of a moving object in a reference frame, according to an embodiment of the invention. In step 100, dead reckoning is used to calculate an estimated position s of the object in the reference frame. As can be seen, the estimated position s has an unknown, actual error e (s) and an uncertainty U (s) associated therewith. In step 300, a plurality of lines is provided on a surface across which the object moves. In step 350, a mathematical description mi , rri2, mk, m_n of each of these lines in the reference frame is measured, the mathematical description of each line having an uncertainty U (rrik) associated therewith. In step 400, whether the moving object encounters one of the plurality of lines is detected. If so, in step 500, which one of the plurality of lines is most likely to have been detected is identified, based on the estimated position s of the object. If not, the method returns to step 100 to calculate an estimated position s of the object using dead reckoning without any error correction. However, if it is detected that the moving object has encountered one of the plurality of lines, then in step 200, both the actual error e (s) and the uncertainty U (s) in the estimated position s of the object are reduced, using the previously measured mathematical description mk of the line which was identified in step 500 as being the detected one of the plurality of lines. This is done by taking the estimated position s of the object, the uncertainty U (s) in the estimated position s of the object, the mathematical description mk of the detected one of the lines and the uncertainty U (rrik) in the mathematical description mk of the detected one of the lines to calculate an estimated error e (s) in the estimated position of the object, and by taking the uncertainty U (s) in the estimated position of the object and the uncertainty U (rrik) in the mathematical description mk of the detected one of the lines to calculate a new uncertainty U' (s) in the estimated position of the object. In this embodiment, the dead reckoning step 100 comprises using inertial navigation, and the step 200 of reducing the actual error and the uncertainty in the estimated position of the object comprises Kalman filtering. In this example, the step 300 of providing a plurality of lines on the surface across which the object moves is carried out by painting the plurality of lines onto the surface, although it could also be carried out by transmitting lines of laser light across the surface and/or by embedding current-carrying wires into the surface, for example. In this embodiment, the step 350 of then measuring a mathematical description mi , rri2, mk, m_n of each of the plurality of lines in the reference frame is carried out by carefully surveying the disposition of each of the plurality of lines on the surface using a computerised theodolite, the position of which is itself accurately known relative to a north-east-down reference frame fixed relative to the Earth, whilst taking account of any uncertainties in these mathematical descriptions, such as are due to the thickness of the lines themselves and any inaccuracies in the measurement process. In this embodiment, the step 400 of detecting whether the moving object encounters one of the plurality of lines comprises emitting a beam of electromagnetic radiation, reflecting the beam from one of the lines, and receiving the beam thus reflected, although it may alternatively or additionally comprise receiving a beam of electromagnetic radiation emitted by one of the lines and/or sensing a variation in a magnetic field of one of the lines using the Hall effect, according to how in step 300 the lines were provided on the surface across which the object moves. Finally, the step 500 of identifying which one of the plurality of lines is most likely to have been detected comprises comparing respective ones mi , rri2, rrik, m_n of the mathematical descriptions of the plurality lines stored in a database with the estimated position of the object in the reference frame and assigning a probability to each one of the lines according to how close the estimated position of the object is to the respective ones of the pre-measured mathematical descriptions.

The method shown in Fig. 6 and described above may further comprise determining an additional kinematic variable of the moving object besides its position and/or a variable of the dead reckoning step 100, using the reduced error and uncertainty in the estimated position of the object calculated in step 200. Moreover, this method may also be used as part of a method for guidance, navigation and control (GNC) of a moving object which further comprises guiding and controlling the object on the basis of the position of the object thus determined. Whereas various optional features of the invention have been described above in particular combinations by way of example only, such optional features may be combined in other ways without restriction to the scope of the invention, which is defined by the appended claims.

Claims

A positioning system for determining the position of a moving object in a reference frame, the system comprising:

a dead-reckoning unit (10) to calculate an estimated position (s) of the object in the reference frame, the estimated position having an unknown, actual error (e (§)) and an uncertainty (U (§)) associated therewith;

a plurality of lines (31 , 32) on a surface across which the object moves, each of said lines having a pre-measured mathematical description (mi , rri2, rrik, m_n) in the reference frame, the mathematical description of each line having an uncertainty (U (rrik)) associated therewith;

a detection unit (40) to detect if the moving object encounters one of the plurality of lines;

an error correction unit (20) to reduce the actual error and the uncertainty in the estimated position of the object by taking the estimated position (s) of the object, the uncertainty (U (§)) in the estimated position of the object, the mathematical description (rrik) of a detected one of said lines and the uncertainty (U (rrik)) in the mathematical description of the detected one of said lines to calculate an estimated error (e (§)) in the estimated position of the object, and by taking the uncertainty (U (§)) in the estimated position of the object and the uncertainty (U (rrik)) in the mathematical description (rrik) of the detected one of said lines to calculate a new uncertainty (U' (§)) in the estimated position of the object; and

an identification unit (50) to identify which one of the plurality of lines is most likely to have been detected by the detection unit based on the estimated position (s) of the object, and to supply the pre-measured mathematical description (rrik) of the line thus identified to the error correction unit, to be used by the error correction unit as the mathematical description (rrik) of the detected one of said lines.

A positioning system according to any one of the preceding claims, wherein the dead- reckoning unit (10) comprises an inertial navigation system (INS) (12) including an inertial measurement unit (IMU) (14) and a strapdown navigator (16), and wherein the inertial measurement unit (IMU) (14) comprises a plurality of orthogonal

accelerometers (141 a, 141 b, 141c) and a plurality of orthogonal angular rate sensors (142a, 142b, 142c).

3. A positioning system according to any one of the preceding claims, wherein the error correction unit (20) comprises a Kalman filter.

4. A positioning system according to any one of the preceding claims, wherein the

plurality of lines (31 , 32) comprises a plurality of non-parallel, rectilinear lines.

5. A positioning system according to claim 4, wherein the plurality of non-parallel,

rectilinear lines comprises a first set of parallel, rectilinear lines (31a, 31 b, 31 c) extending in a first direction and a second set of parallel, rectilinear lines (32a, 32b, 32c) extending in a second direction different from the first direction.

6. A positioning system according to claim 5, wherein the first direction is orthogonal to the second direction. 7. A positioning system according to claim 5 or claim 6, wherein the first set of parallel, rectilinear lines alternates with the second set of parallel, rectilinear lines.

8. A positioning system according to any one of claims 5 to 7, wherein the first and

second sets of parallel, rectilinear lines (31a, 31 b, 31 c; 32a, 32b, 32c) each comprise a plurality of groups of such lines (311 a, 311 b; 322a, 322b).

9. A positioning system according to any one of the preceding claims, wherein the

plurality of lines (31 , 32) comprises one or more curved lines. 10. A positioning system according to any one of the preceding claims, wherein the

plurality of lines further comprises a third set of lines lying outside a surface defined by the first and second sets of lines.

1 1. A positioning system according to any one of the preceding claims, wherein at least one of the plurality of lines is retroreflective, and wherein the detection unit comprises a source of electromagnetic radiation and a sensor of such electromagnetic radiation.

12. A positioning system according to any one of the preceding claims, wherein the

plurality of lines comprises a beam of electromagnetic radiation, and wherein the detection unit comprises a sensor of such electromagnetic radiation.

13. A positioning system according to any one of the preceding claims, wherein at least one of the plurality of lines is magnetic, and wherein the detection unit comprises a Hall-effect sensor.

14. A positioning system according to any one of the preceding claims, wherein the

identification unit (50) comprises:

a database (51) of the pre-measured mathematical descriptions of the plurality of lines; and

a probability calculator (52) to compare respective ones (mi , rri2, rrik, m_n) of the pre-measured mathematical descriptions of the plurality of lines with the estimated position (s) of the object calculated by the dead reckoning unit and to assign a probability to each one of the lines having been detected by the detection unit (40) according to how close the estimated position (s) of the object is to the respective ones (mi , rri2, rrik, m_n) of the pre-measured mathematical descriptions of the plurality of lines.

15. A positioning system according to any one the preceding claims, wherein the dead- reckoning unit is operable to determine at least one of an additional kinematic variable of the moving object besides its position and a variable of the dead-reckoning unit, using the reduced error and uncertainty in the estimated position of the object.

16. A positioning system according to any one of the preceding claims, wherein the

reference frame is a north-east-down (NED) reference frame fixed relative to the Earth.

17. A positioning system according to any one of the preceding claims, wherein the

moving object is a robotically guided object.

18. A positioning system according to claim 17, wherein the moving object is a robotically driven wheeled vehicle.

19. A guidance, navigation and control (GNC) system comprising a positioning system according to any one of the preceding claims, and further comprising a guidance and control system to guide and control the moving object on the basis of the position of the object determined by the positioning system.

20. A method of determining the position of a moving object in a reference frame, the

method comprising: using dead reckoning (100) to calculate an estimated position (s) of the object in the reference frame, the estimated position having an unknown, actual error (e (§)) and an uncertainty (U (§)) associated therewith;

providing (300) a plurality of lines on a surface across which the object moves;

measuring (350) a mathematical description (mi , rri2, mk, m_n) of each line in the reference frame, the mathematical description of each line having an uncertainty (U (mk)) associated therewith;

detecting (400) if the moving object encounters one of the plurality of lines, and if so: identifying (500) which one of the plurality of lines is most likely to have been detected based on the estimated position (s) of the object; and

reducing (200) the actual error (e (§)) and the uncertainty (U (§)) in the estimated position of the object using the previously measured mathematical description (rrik) of the line thus identified as the detected one of said lines by taking the estimated position (s) of the object, the uncertainty (U (§)) in the estimated position of the object, the mathematical description (rrik) of the detected one of said lines and the uncertainty

(U (mk)) in the mathematical description of the detected one of said lines to calculate an estimated error (e (§)) in the estimated position of the object, and by taking the uncertainty (U (§)) in the estimated position of the object and the uncertainty (U (rrik)) in the mathematical description (rrik) of the detected one of said lines to calculate a new uncertainty (U' (§)) in the estimated position of the object.

21. A method according to claim 20, wherein using dead reckoning comprises using

inertial navigation. 22. A method according to claim 20 or claim 21 , wherein reducing the actual error and the uncertainty in the estimated position of the object comprises Kalman filtering.

23. A method according to any one of claims 20 to 22, wherein detecting if the object encounters one of the lines comprises emitting a beam of electromagnetic radiation, reflecting said beam from said one of the lines, and receiving the beam thus reflected.

24. A method according to any one of claims 20 to 23, wherein detecting if the object encounters one of the lines comprises receiving a beam of electromagnetic radiation emitted by said one of the lines.

25. A method according to any one of claims 20 to 24, wherein detecting if the object encounters one of the lines comprises sensing a variation in a magnetic field of said one of the lines.

26. A method according to any one of claims 20 to 25, wherein identifying which one of the plurality of lines is most likely to have been detected comprises comparing respective ones (mi , rri2, ... , rrik, ... , m_n) of the mathematical descriptions of the plurality of lines stored in a database with the estimated position of the object in the reference frame and assigning a probability to each one of the lines having been detected according to how close the estimated position of the object is to the respective ones of the pre- measured mathematical descriptions.

27. A method according to any one of claims 20 to 26, further comprising determining at least one of an additional kinematic variable of the moving object besides its position and a variable of the dead reckoning, using the reduced error and uncertainty in the estimated position of the object.

28. A method for guidance, navigation and control (GNC) of a moving object comprising a method of determining the position of the object according to any one of claims 20 to 27, and further comprising guiding and controlling the object on the basis of the position of the object thus determined.