Apparatus and methods for assessing vehicles straddled between lanes

Abstract

A method of assessing whether a vehicle is straddled between lanes (12,14) on a multi-lane carriageway, the method comprising the steps of: a) measuring inductance change values from two adjacent inductive loops (22a, 20b) situated at a loop site, as the vehicle traverses the loop site; b) summing separate logarithms of the inductance change values, or taking a logarithm of the product of the inductance change values, to obtain a value; and c) comparing the value from step (b) against a predetermined threshold value to make a determination as to whether: i) a single vehicle is straddling multiple lanes (12,14), where the value from step (b) is on one side of the predetermined threshold value, or ii) two vehicles are present in adjacent lanes (12,14), where the value from step (b) is on the other side of the predetermined threshold value.

Claims

1. A method of assessing whether a vehicle is straddled between lanes on a multi-lane carriageway, the method comprising the steps of a) measuring inductance change values from two adjacent inductive loops situated at a loop site, as the vehicle traverses the loop site; b) summing separate logarithms of the inductance change values, or taking a logarithm of the product of the inductance change values, to obtain a value; and c) comparing the value from step (b) against a predetermined threshold value to make a determination as to whether: i) a single vehicle is straddling multiple lanes, where the value from step (b) is on one side of the predetermined threshold value, or ii) two vehicles are present in adjacent lanes, where the value from step (b) is on the other side of the predetermined threshold value.

2. The method of claim 1, wherein steps (b) and (c) involve using a calculation, the calculation being substantially equivalent to $\mathrm{straddling}\mathrm{value}=\log \left(\mathrm{ampl}1\right)+\log \left(\mathrm{ampl}2\right)$ $\mathrm{or}$ $\mathrm{straddling}\mathrm{value}=\log \left(\mathrm{ampl}1\right)+\log \left(\mathrm{ampl}2\right)+\mathrm{correction}$ where ampl1 and ampl2 are measured inductance change values, and a magnitude of the straddling value is an indicator of whether the vehicle is straddling lanes, and correction is a correction term which may be calculated using a calculation substantially equivalent to $\mathrm{correction}=\frac{\log \left(\frac{\mathrm{ampl}1}{\mathrm{ampl}2}\right)}{\mathrm{factor}}$ $\mathrm{or}$ $\mathrm{correction}=\frac{\log \left(\frac{\max \left(\mathrm{ampl}1,\mathrm{ampl}2\right)}{\min \left(\mathrm{ampl}1,\mathrm{ampl}2\right)}\right)}{\mathrm{factor}}$ where factor is a scaling term.

3. The method of claim 1, further including the step of modifying the calculated logarithm or logarithms of step (b) with at least one correction term, in which the correction term is derived by: I) obtaining a ratio of i) the inductance change value of one inductive loop relative to the inductance change value of the other inductive loop, or ii) the greater inductance change value to the lesser inductance change value; II) calculating a logarithm of the ratio; and III) using a further term to modify the calculated logarithm of step (II).

4. A vehicle detection apparatus for assessing whether a vehicle is straddled between lanes on a multi-lane carriageway, the apparatus comprising a loop site including two inductive loops, provided on or in adjacent lanes of the carriageway, a loop controller associated with each inductive loop, each loop controller energising its associated loop, and measuring inductance change values in that loop when the vehicle traverses the loop site; and processing means for receiving the inductance change values from the loop controllers, and adapted to establish a calculated value by: a) taking logarithms of each inductance change value, and summing the logarithms; or b) taking a product of the inductance change values, and taking the logarithm of that product; the processing means being further adapted to compare the calculated value against a predetermined threshold value, and make a determination as to whether the inductance change values relate to: i) a single vehicle straddling multiple lanes, where the calculated value is on one side of the predetermined threshold value; or ii) two vehicles present in adjacent lanes, where the calculated value is on the other side of the predetermined threshold value.

5. A method of estimating the lateral position of a vehicle substantially straddled between lanes on a multi-lane carriageway, the method comprising the steps of: a) measuring inductance change values from two adjacent inductive loops situated at a loop site, as a vehicle traverses the loop site; b) establishing logarithms of the inductance change values; c) taking the difference between the logarithms of step (b); thereby obtaining an estimate related to the lateral position of the vehicle on the carriageway.

6. The method of claim 5, wherein steps (b) and (c) involve using a relationship substantially equivalent to
location∝(log(ampl1)−log(ampl2)) where ampl1 and ampl2 are measured inductance change values, and location relates to the lateral position of the vehicle on the carriageway.

7. The method of claim 5, further including the steps of: d) combining the logarithms of step (b) to establish a combined value; e) establishing a ratio of the difference of step (c) to the combined value of step (d).

8. The method of claim 7, wherein steps (b) to (e) involve using a calculation substantially equivalent to $\mathrm{location}=\frac{\log \left(\mathrm{ampl}1\right)-\log \left(\mathrm{ampl}2\right)}{\log \left(\mathrm{ampl}1\right)+\log \left(\mathrm{ampl}2\right)}$ where ampl1 and ampl2 are measured inductance change values, and location relates to the lateral position of the vehicle on the carriageway.

9. The method of claim 5, wherein the difference of the logarithms in step (c) is modified by one or more correction terms, and the relationship is substantially equivalent to
location=(log(ampl1)−log(ampl2))*width.sub.factor*vehicle_type.sub.factor where width.sub.factor and vehicle_type.sub.factor are correction terms.

10. The method of claim 5, wherein the difference of the logarithms in step (c) is modified by one or more correction terms, and the calculation is substantially equivalent to one of equations (A) to (F): $\begin{array}{cc}\mathrm{location}=\frac{\begin{array}{c}\left(\log \left(\mathrm{ampl}1\right)-\log \left(\mathrm{ampl}2\right)\right)*\\ \mathrm{lane\_width}\mathrm{\_multiplier}\end{array}}{\log \left(\mathrm{ampl}1\right)+\log \left(\mathrm{ampl}2\right)}& A)\end{array}$ where lane_width_multiplier is one of the correction terms; $\begin{array}{cc}\mathrm{location}=\frac{\begin{array}{c}\left(\log \left(\mathrm{ampl}1\right)-\log \left(\mathrm{ampl}2\right)\right)*\\ \mathrm{lane\_width}\mathrm{\_multiplier}\end{array}}{\begin{array}{c}\log \left(\mathrm{ampl}1\right)+\log \left(\mathrm{ampl}2\right)+\\ \left(\mathrm{correction}*\mathrm{multiplier}\right)\end{array}}& B)\end{array}$ where correction, lane_width_multiplier and multiplier are correction terms; $\begin{array}{cc}\mathrm{location}=\frac{\log \left(\mathrm{ampl}1\right)-\log \left(\mathrm{ampl}2\right)+\mathrm{correction}}{\log \left(\mathrm{ampl}1\right)+\log \left(\mathrm{ampl}2\right)+\mathrm{correction}}& C)\end{array}$ where correction is one of the correction terms; $\begin{array}{cc}\mathrm{location}=\left[\frac{\begin{array}{c}\log \left(\mathrm{ampl}1\right)-\log \left(\mathrm{ampl}2\right)+\\ \left(P*\mathrm{correction}\right)\end{array}}{\begin{array}{c}\log \left(\mathrm{ampl}1\right)+\log \left(\mathrm{ampl}2\right)+\\ \mathrm{correction}\end{array}}\right]*\mathrm{lane\_width}\mathrm{\_multiplier}& D)\end{array}$ where P, correction and lane_width_multiplier are correction terms; $\begin{array}{cc}\mathrm{location}=\frac{\log \left(\mathrm{ampl}1\right)-\log \left(\mathrm{ampl}2\right)}{\frac{1}{\mathrm{scale}}{\log }^{-1}\left[\frac{1}{2}\left(\log \left(\mathrm{ampl}1\right)+\log \left(\mathrm{ampl}2\right)\right)\right]}& E)\end{array}$ where scale is one of the correction terms; or $\begin{array}{cc}\mathrm{location}=\frac{\log \left(\mathrm{ampl}1\right)-\log \left(\mathrm{ampl}2\right)}{\frac{1}{\mathrm{scale}}{\log }^{-1}\left[\frac{1}{2}\left(\log \left(\mathrm{ampl}1\right)+\log \left(\mathrm{ampl}2\right)\right)+\mathrm{correction}\right]}& F)\end{array}$ where scale and correction are correction terms.

11. The method of claim 10, wherein one of the correction terms, such as correction, is derived by: I) obtaining a ratio of i) the inductance change value of one inductive loop relative to the inductance change value of the other inductive loop, or ii) the greater inductance change value to the lesser inductance change value; II) calculating a logarithm of the ratio; and III) using a further term, such as a scaling term, to modify the calculated logarithm.

12. A vehicle detection apparatus for estimating the lateral position of a vehicle substantially straddled between lanes on a multi-lane carriageway, the apparatus comprising a loop site including two inductive loops provided adjacent to one another on or in the carriageway, a loop controller associated with each inductive loop, each loop controller energising its associated loop, and measuring inductance change values in that loop when the vehicle traverses the loop site; and processing means for receiving the inductance change values from the loop controllers, and adapted to establish an estimate of the lateral position of the vehicle on the carriageway by: a) taking logarithms of the inductance change values, and taking a difference of those logarithms; or b) establishing a ratio of the inductance change values, and taking a logarithm of the ratio.

13. The apparatus of claim 12, wherein the processing means is further adapted to modify the output from (a) or (b), and/or (c), with at least one correction term when establishing the estimate of lateral position, and the correction term or terms are based on one or more of the following: a logarithm of the ratio of the inductance change values; the distance between the inductive loops; the distance between centres of the inductive loops; lane widths on the carriageway; materials that form part of the carriageway at the loop site; vehicle type.

14. A method of estimating an inductance change value that would arise for a vehicle travelling centrally over a given inductive loop in a carriageway, the method comprising the steps of: a) measuring inductance change values from two adjacent inductive loops situated at a loop site, as the vehicle traverses the loop site; b) establishing one or more logarithms of the inductance change values; c) applying first and second correction terms to the one or more logarithms to establish an estimated inductance change value that would have arisen in one of the inductive loops if the vehicle had travelled substantially centrally over that loop.

15. The method of claim 14, wherein steps (b) and (c) involve using a calculation substantially equivalent to ${\mathrm{ampl}}_{\mathrm{inline}}=\frac{\log \left(\mathrm{ampl}1\right)+\log \left(\mathrm{ampl}2\right)-\mathrm{factor}1}{\mathrm{factor}2}$ $\mathrm{or}$ ${\mathrm{ampl}}_{\mathrm{inline}}=\frac{\log \left(\mathrm{ampl}1\right)+\log \left(\mathrm{ampl}2\right)+\mathrm{correction}-\mathrm{factor}1}{\mathrm{factor}2}$ where ampl1 and ampl2 are measured inductance change values, factor1 and factor2 are correction terms, and ampl.sub.inline is an estimated theoretical inductance change value, and correction is a further correction term which may be calculated by using a calculation substantially equivalent to $\mathrm{correction}=\frac{\log \left(\frac{\mathrm{ampl}1}{\mathrm{ampl}2}\right)}{\mathrm{factor}}$ $\mathrm{or}$ $\mathrm{correction}=\frac{\log \left(\frac{\max \left(\mathrm{ampl}1,\mathrm{ampl}2\right)}{\min \left(\mathrm{ampl}1,\mathrm{ampl}2\right)}\right)}{\mathrm{factor}}$ where factor is scaling term.

16. The method of claim 14, wherein a further correction term is applied to the one or more logarithms, the further correction term being derived by: I) obtaining a ratio of i) the inductance change value of one inductive loop relative to the inductance change value of the other inductive loop, or ii) the greater inductance change value to the lesser inductance change value; II) calculating a logarithm of the ratio; III) applying a correction to the calculated logarithm.

17. The method of claim 15, further including the step of determining factor2 by i) collecting sets of inductance change values for the vehicles travelling substantially in lane during normal traffic conditions on the carriageway; ii) collecting further sets of inductance change values for vehicles straddled between lanes during normal traffic conditions on the carriageway; iii) setting an initial value for factor2, and calculating an ampl.sub.inline value for each further set of inductance change values; and iv) using the initial value of factor2 to derive a refined value of factor2 via a calculation substantially equivalent to $\mathrm{factor}{2}_{n+1}=\frac{s{d}_{\mathrm{calc}}}{s{d}_{\mathrm{inlane}}}*\mathrm{factor}{2}_n$ where factor2.sub.n is the initial value of factor2 from (iii), sd.sub.inlane is the standard deviation of the values in the sets of inductance change values in (i), sd.sub.calc is the standard deviation of the ampl.sub.inline values from (iii), and factor2.sub.n+1 is the refined value of factor2.

18. The method of claim 17, further including the step of determining factor1 by v) calculating logarithms for each set and further set of inductance change values; vi) using one or more correction terms to modify the logarithms of each set of inductance change values; and vii) using an initial value of factor1 to derive a refined value of factor1 via a calculation substantially equivalent to $\mathrm{factor}{1}_{n+1}=\frac{mea{n}_{\mathrm{strad}}-\left(\left(mea{n}_{\mathrm{strad}}-\mathrm{factor}{1}_n\right)*\mathrm{factor}2\right)}{\mathrm{factor}{1}_n*\frac{mea{n}_{\mathrm{calc}}}{mea{n}_{\mathrm{inlane}}}}$ where factor1.sub.n is the initial value of factor1, mean.sub.strad is the mean of the values of the modified logarithms in (vi), mean.sub.calc is the mean of the ampl.sub.inline values from (iii), mean.sub.inlane is the mean of the values in the sets of inductance change values in (i), and factor1.sub.n+1 is the refined value of factor1.

19. A vehicle detection apparatus for estimating an inductance change value that would arise for a vehicle travelling centrally over a given inductive loop in a carriageway, the apparatus comprising: a loop site including at least two inductive loops provided adjacent to one another on or in the carriageway, a loop controller associated with each inductive loop, each loop controller energising its associated loop, and measuring inductance change values in that loop when the vehicle traverses the loop site; and processing means for receiving the inductance change values from the loop controllers, and adapted to establish an estimate of the inductance change value that would have arisen for one of those inductive loops had the vehicle travelled centrally over that loop by: summing logarithms of the inductance change values, and applying one or more correction terms to the summed logarithms to establish the estimate.

20. The apparatus of claim 19, wherein the processing means is further adapted to use statistics related to the inductance change values to refine the values of the first and/or second correction factors, before applying the correction factors to the logarithms.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) For a better understanding of the present invention, and to show more clearly how it may be carried into effect, reference will now be made by way of example only to the accompanying drawings, in which:

(2) FIG. 1 is a schematic showing the layout of an apparatus having inductive loops for detecting vehicles on a carriageway according to the method of the present invention;

(3) FIG. 2 shows the change in inductance measured in two adjacent inductive loops of the apparatus in FIG. 1, when a vehicle passes substantially centrally between the two loops, that is, straddled between lanes;

(4) FIG. 3 shows the change in inductance measured in two adjacent inductive loops of the apparatus in FIG. 1, when a vehicle passes somewhat off-centre over the two loops, partially straddled between lanes; and

(5) FIG. 4 shows the change in inductance measured in two adjacent inductive loops of the apparatus in FIG. 1, when a vehicle passes over substantially only one of the two loops, and is straddled yet further away from the centre line between lanes.

DESCRIPTION OF PREFERRED EMBODIMENTS

(6) Referring firstly to FIG. 1, a three-lane carriageway is shown. Each lane 12, 14, 16 is for vehicles travelling in the same direction indicated by arrows A. In the following description, references to “length” or “along” the lane refer to the direction indicated by arrows A, and references to “width” or “across” the lane refer to a direction substantially perpendicular to arrows A.

(7) An inductive loop apparatus is provided across the carriageway. The apparatus includes three inductive loops 18a, 18b, 18c. The loops 18a, 18b, 18c are arranged in a row in the respective lanes 12, 14, 16. The stretch of carriageway containing the loops may be considered to form a loop site. It will be appreciated that alternative embodiments may include any number of such rows of loops arranged along the carriageway. It will also be appreciated that the calculations described herein could be applied on all of or any combination of the rows of loops in such an embodiment.

(8) Each loop is energised with alternating current at a selected frequency, allowing the inductance of the loop to be measured. Measurements are taken at a rate which enables accurate vehicle detection taking account of loop length and the speed of vehicles passing over the loops. The frequencies selected for each loop may differ to avoid coupling between loops, or the inductance of each loop may be sampled independently for the same reason.

(9) When a vehicle passes over a loop, the inductance in the loop is generally reduced due to the effect of the conducting materials in the vehicle chassis. The magnitude of the change in inductance (i.e. the inductance change value) depends on the height of the bulk of the vehicle above the loop, and the amount of the loop covered by the vehicle when passing. Vehicles with a high chassis tend to cause a lower drop in inductance as they pass over the loop as compared with vehicles which travel low to the ground. A vehicle which only partially passes over a loop will cause less of a drop in inductance than a vehicle which passes over the full width of the loop.

(10) Each inductive loop 18a, 18b, 18c is positioned substantially centrally in its lane. Each inductive loop 18a, 18b, 18c is substantially square in shape. Each inductive loop 18a, 18b, 18c has a width substantially less than the width of its lane, so that the edges of the loop are spaced from the boundaries of the lane. In other words, each inductive loop 18a, 18b, 18c is positioned with a substantial lateral gap between it and the adjacent loop. The lateral gap is typically 1.6 m. It will be appreciated that other shapes of inductive loop can be used, such as round or rectangular inductive loops, for example.

(11) FIGS. 2, 3, and 4 are illustrative examples of plots of the simultaneous measured inductance of two inductive loops 18a, 18b whilst vehicles pass over the respective loops 18a, 18b at various positions.

(12) In FIG. 2, the vehicle is travelling along and straddled between two lanes 12, 14 substantially centrally, and therefore the pattern of the change in inductance in each loop is substantially similar. It is clear from the measurements that only a single vehicle is passing over the loops 18a, 18b, since the plots are substantially the same shape.

(13) In FIG. 3, a vehicle is again travelling along and straddled between two lanes 12, 14. The shape of the plot from the loops 18a, 18b is substantially identical, but the magnitude is different, indicating the vehicle is partially (or asymmetrically) straddling lanes 12 and 14, i.e. the majority of the vehicle is offset to one lane.

(14) FIG. 4 shows the measured inductance in the loops 18a, 18b of a different type of vehicle passing over them, indicated by the different shape of plot. The vehicle is substantially offset into one lane 12, because there is a much greater inductance drop measured in one loop 18a than in the other loop 18b. This indicates that the vehicle is straddled even more asymmetrically between lanes.

(15) The inductance change value will vary depending on whether or not a vehicle is straddled between lanes, giving a reliable detection means.

(16) Determining Whether a Vehicle is Straddled Between Lanes

(17) It is possible to determine using the inductive loop apparatus whether a vehicle is straddled between lanes 12, 14, 16 using the following equation (1):
straddling value=log(ampl1)+log(ampl2)+correction  (1)

(18) The value of the correction term above is determined by the following equation (2):

(19) $\begin{array}{cc}\mathrm{correction}=\frac{\log (\frac{\max \left(ampl1,ampl2\right)}{\min \left(ampl1,ampl2\right)})}{factor}& \left(2\right)\end{array}$ ampl1 is the magnitude (or amplitude) of the inductance change value measured as a vehicle passes over a loop in a lane. ampl2 is the magnitude (or amplitude) of the inductance change value measured as the same vehicle also passes over a loop adjacent to the loop of ampl1 in an adjacent lane. factor is a value used take account of the width of lanes on a carriageway. A typical value of factor is around 3 for calculating straddling value, but depends on the loop site configuration. Other values greater or lesser than 3 may be used. A good value for factor can be determined experimentally for a particular site geometry by taking measurements with vehicles passing over the loops in varied lateral positions and selecting a value that produces the best correspondence between the physical positions and calculated positions. straddling value is a value derived from ampl1, ampl2 and correction. It is used for comparison against a predetermined threshold value, in order to determine whether a vehicle is straddled between lanes.

(20) In most cases, ampl1 and ampl2 can be the peak or maximum amplitudes measured in each inductive loop for a given plot (i.e. corresponding to a given inductance change event as one or more vehicles pass over the loops, within a given time frame).

(21) If straddling value is equal to or greater than the predetermined threshold value, then two vehicles are determined as being present in adjacent lanes. If straddling value is less than the predetermined threshold value, then a single vehicle is determined to be straddling two lanes. The threshold value depends on the base of the logarithm used.

(22) For example, the threshold value may be set at 5.1 when using logarithms in base 10. In one scenario, the peak inductance drop over loop 18a in lane 12 is measured as 168. Meanwhile, the peak inductance drop over loop 18b in lane 14 is measured as 110. The value of factor is 3, for example. Therefore, in this case, straddling value is:
log(168)+log(110)+([log(168/110)]/3)=4.33 (3 s.f.)
which is below the threshold value, indicating that a single vehicle is straddled between lanes. A different threshold value may be used for logarithms in base 2, for example.

(23) Although ampl1 and ampl2 may be the overall peak values of inductance change as the vehicle passes over the loops, there are advantages in using the peak value generated by the tractor unit of a semi trailer, for example, rather than later portions of the vehicle. This avoids using an unnecessarily high straddle threshold to deal with low-slung trailers, such as low-loaders and car transporters, which may give rise to very high amplitude inductance changes. The peak value induced by the tractor unit can be selected by picking a peak early in the overall signature, for example the highest level before there is significant activation on a subsequent loop along the carriageway (where a series of inductive loops are present). Alternatively, selection of the first peak that has around a 20% to 40% retracement of the inductance change plot after the peak (of the type seen in FIGS. 2 to 4) may be used to determine a notional peak value.

(24) Additional means specific to motorcycles can be used when these are travelling adjacent to heavy goods vehicles, for example, since motorcycles give rise to anomalously low inductance change values. Motorcycles can be detected independently based on characteristics such as calculated length (due to time delay in passing over pairs of loops) and other measures.

(25) In this embodiment, inductive loops are provided wholly within a lane, and processing measurements of inductance changes caused by a passing vehicle gives an indication of whether the vehicle was straddled between lanes at the loop site. In this case, a vehicle is deemed to be straddling if the sum of the logarithms is below a threshold values, and a non-straddling vehicle will have a sum above the threshold.

(26) However, it will be appreciated that the loops could themselves be provided substantially straddled across lanes. In this case there would need to be a translation between the lateral space reference frame for the loops and the corresponding locations for the physical lanes.

(27) Determining the Lateral Position of a Vehicle Straddling Lanes on the Carriageway

(28) If the vehicle had been determined not to be straddled between lanes, then the vehicle would be detected and counted as normal. If needed, a camera in the respective lane, such as those used for ANPR (automatic number plate recognition), can capture an image of a vehicle in order to obtain the license plate number.

(29) However, if a vehicle is straddled between lanes as in the present scenario, it is necessary to determine which lane camera to use in order to capture an image of the vehicle. The lateral position of the vehicle in the lane affects this, and may be calculated based on the measured inductance change values using the following equation (3):

(30) $\begin{array}{cc}\mathrm{location}=\frac{\left(\log \left(ampl1\right)-\log \left(ampl2\right)\right)*\mathrm{lane\_width}\mathrm{\_multiplier}}{\log \left(ampl1\right)+\log \left(ampl2\right)+\mathrm{correction}*\mathrm{multiplier}}& \left(3\right)\end{array}$

(31) The value of the correction term above is determined using equation (2), and ampl1 and ampl2 are as defined above. lane_width_multiplier is a value used to take account of the lateral spacing (i.e. distance) between centres of the adjacent loops used to measure inductance. The value can be approximately the same as the lane width. multiplier The value of multiplier is chosen based on the value of factor used in calculating correction to provide a good correspondence between physical vehicle position and calculated position. For example, a value of multiplier 2.5 times greater than factor can work well in a standard site with 3.6 m to 3.75 m lane widths, e.g. a multiplier value of 7.5. location is the approximate lateral position of a vehicle between two lanes, derived from equation (3). It is equivalent to the distance between a central plane of the vehicle (the plane running parallel with and along the lane) and the mid-line between two lanes.

(32) The value of location can then be used, for example, to determine which camera in an array of cameras (focused on different lanes) should be used to capture a license plate picture of the vehicle.

(33) Based on the above, and using the same inductance change values as in the earlier scenario, the value of location can be calculated as follows. In this case, lane_width_multiplier (the spacing between loop centres) is 3.6 metres, i.e. the full width of the lane, factor is 10, and multiplier is 25. Therefore:

(34) $\mathrm{location}=\frac{\left(\log \left(ampl1\right)-\log \left(ampl2\right)\right)*\mathrm{lane\_width}\mathrm{\_multiplier}}{\log \left(ampl1\right)+\log \left(ampl2\right)+\left(\mathrm{correction}*\mathrm{multiplier}\right)}$$\mathrm{location}=\frac{\left(\log \left(168\right)-\log \left(110\right)\right)*3.6m}{\log \left(168\right)+\log \left(110\right)+(\frac{\log \left(\frac{168}{110}\right)}{10}*25)}$$\mathrm{location}=0.140m\left(3s.f.\right)$

(35) This means that the centre of the vehicle is offset from the mid-line dividing the two lanes by around 14 cm, towards the lane with the larger inductance change value. Note that the width of the vehicle does not need to be known or estimated as it is not a factor in this equation.

(36) The value of location can also be calculated in other ways, for example, using one of equations (3a) to (3c) below. Note that in (3a) width.sub.factor has a value of 0.6 m in this instance, having units of distance:

(37) $\begin{array}{cc}\mathrm{location}=\left(\log \left(ampl1\right)-\log \left(ampl2\right)\right)*{\mathrm{width}}_{\mathrm{factor}}*{\mathrm{vehicle\_type}}_{\mathrm{factor}}\mathrm{location}=\left(\log \left(168\right)-\log \left(110\right)\right)*0.6m*1\mathrm{location}=0.110m& \left(3a\right)\end{array}$

(38) $\begin{array}{cc}\mathrm{location}=\left[\frac{\log \left(ampl1\right)-\log \left(ampl2\right)*\left(P*\mathrm{correction}\right)}{\log \left(ampl1\right)+\log \left(ampl2\right)+\mathrm{correction}}\right]+\mathrm{lane\_width}\mathrm{\_multiplier}\mathrm{location}=\left[\frac{\log \left(168\right)-\log \left(110\right)*\left(0.5*\frac{\log \left(\frac{168}{110}\right)}{10}\right)}{\log \left(168\right)+\log \left(110\right)+\frac{\log \left(\frac{168}{110}\right)}{10}}\right]*1.8m\mathrm{location}=0.081m\left(3s.f.\right)& \left(3b\right)\end{array}$

(39) 0$\begin{array}{cc}\mathrm{location}=\frac{\left(\log \left(ampl1\right)-\log \left(ampl2\right)\right)*}{\frac{1}{\mathrm{scale}}{\log }^{-1}\left[\frac{1}{2}\left(\log \left(ampl1\right)+\log \left(ampl2\right)+\mathrm{correction}\right)\right]}\mathrm{location}=\frac{\log \left(168\right)-\log \left(110\right)}{\frac{1}{25}{\log }^{-1}\left[\frac{1}{2}\left(\log \left(168\right)+\log \left(110\right)+\frac{\log \left(\frac{168}{110}\right)}{10}\right)\right]}\mathrm{location}=3.28\%& \left(3c\right)\end{array}$

(40) Equation (3c) produces a proportional value for location, rather than an absolute distance. In this case, for a vehicle straddled between lanes, its position is offset towards the loop where ampl1 was measured by around 3.3% of the lane width (3.6 m), which is around 0.12 metres.

(41) The values selected for the various correction terms are exemplary only, and other values for the terms would lead to a more harmonised set of values for location. For example, P may take a value other than 0.5 in other embodiments. In any case, a variation of around 0.06 metres in location across the different calculations in equations (3) to (3c) demonstrates good agreement between the different approaches, and high accuracy relative to the size of the lanes and vehicles involved, particularly given that the values for the correction terms are only examples, and have not been refined.

(42) Estimating a Theoretical In-Lane Inductance Change for a Vehicle

(43) Where inductance change values are known for a vehicle straddled between two lanes, it is possible to subsequently determine an estimate for the inductance change value that would have been measured if the vehicle had instead been travelling centrally within a lane using the following equation (4):

(44) $amp{l}_{inline}=\frac{\log \left(ampl1\right)+\log \left(ampl2\right)+\mathrm{correction}-\mathrm{factor}1}{factor2}$

(45) The value of the correction term above is determined using equation (2), and ampl1 and ampl2 are as defined above. factor1 is a value which may take account of lane width and/or vehicle characteristics such as vehicle width. The value of factor1 may correspond to the y-intercept of equation (4) when plotted graphically, due to the linear relationship between the sum of the logarithms of ampl1 and ampl2 and in lane amplitude. Typical values of factor1 are between 3.3 and 3.8, with wider vehicles (such as heavy goods vehicles or buses) at the same site using a value typically 0.2 or 0.3 less than this, to mitigate over-estimation of ampl.sub.inline for these vehicles. Changing the value of factor1 is not required for some purposes, for example where over-estimation of in-lane amplitude for heavy vehicles does not adversely impact performance. The values given are those used where a carriageway has standard lane widths. factor2 is a value which scales the sum of the logarithms of ampl1 and ampl2 to typical vehicle detection amplitudes. For example, it may typically increase the output value by a factor of around 1000 to 2000. The value of factor2 affects the gradient of equation (4) when plotted graphically. Typical values of factor2 are between 0.0005 and 0.001, although other values may be used depending on loop site configuration. ampl.sub.inline is an inductance change value corresponding to the vehicle for which values of ampl1 and ampl2 were measured. The value of ampl.sub.inline is an estimation of the inductance change value that would be measured if that vehicle were to traverse the loop centrally, i.e. the centre of the vehicle passing over the centre of the inductive loop in question.

(46) Values for factor1 and factor2 can be determined in various ways. One approach is to collect statistical data on the road in which an inductive loop apparatus is installed, using initial or default values for factor1 and factor2. The initial/default values may be represented as f1.sub.deflt and f2.sub.deflt respectively, although other notation can be used. For example, f1.sub.deflt might be set to 3.6 and f2.sub.deflt might be set to 0.0007. The values chosen for this step are not especially critical.

(47) Using these default values, data can be collected for a sample of vehicles in normal traffic conditions, and used to derive means and standard deviations. For example, mean and standard deviation values for the following can be derived: a) The amplitudes of vehicles travelling substantially in lane, i.e. not straddled between lanes (deriving mean.sub.inlane, sd.sub.inlane); b) Values for [log(ampl1)+log(ampl2)+correction] for straddling vehicles as calculated using equation (1) (deriving mean.sub.strad); c) The calculated in lane amplitudes for vehicles straddled between lanes, calculated in accordance with equation (4), using the default values chosen for factor1 and factor2 (deriving mean.sub.calc, strad.sub.calc).

(48) The values of factor2 and factor1 can be calculated as:

(49) $\begin{array}{cc}\mathrm{factor}2=\frac{{\mathrm{sd}}_{\mathrm{calc}}}{{\mathrm{sd}}_{\mathrm{inlane}}}*f{2}_{\mathrm{deflt}}& \left(5\right)\\ \mathrm{factor}1=\frac{{\mathrm{mean}}_{\mathrm{strad}}-\left(\left({\mathrm{mean}}_{\mathrm{strad}}-f{1}_{\mathrm{deflt}}\right)*\mathrm{factor}2\right)}{f{1}_{\mathrm{deflt}}*\frac{{\mathrm{mean}}_{\mathrm{calc}}}{{\mathrm{mean}}_{\mathrm{inlane}}}}& \left(6\right)\end{array}$

(50) In this embodiment, for equation (6) factor2 takes the value calculated in equation (5).

(51) Processing the default values of factor1 and factor2 using the above calculations refines each value for that particular loop site, improving the accuracy of the calculated theoretical inductance change value ampl.sub.inline. For example, if f2.sub.deflt is 0.0007, factor2 may end up being around 0.00057.

(52) Although means and standard deviations of inductance change values are used to calculate factor1 and factor2, these are not the only statistics which may be used. It will be appreciated that substantially equivalent calculations could be performed utilising values for medians and interquartile ranges of the data, instead of means and standard deviations.

(53) Sufficient vehicles should be included in the data collection so that the confidence limits for the statistics are adequately small to produce good estimates for factor1 and factor2.

(54) In most sites installed with a loop apparatus, all of the lanes in a roadway which may have vehicles straddled between them are of substantially uniform width and construction. In these cases, the data for all straddling events collected can be aggregated to produce overall statistics and calculate a single pair of factor1 and factor2 values which can then be used for all straddling vehicles. This applies irrespective of the lanes that the vehicles are straddled across.

(55) In cases where there are substantial differences in lane widths across the roadway, or in loop widths or lateral loop separation distances, it may be appropriate to calculate separate factor1 and factor2 values for each pair of adjacent lanes.

(56) This method of determining factor1 and factor2 relies on the number and type of vehicles straddling lanes being substantially similar to the number and type of vehicles travelling in lane, which is generally true. However, in some situations, vans or trucks may be filtering into a particular lane, for example, which can bias the statistical data. Therefore, the vehicle samples should be checked to assess whether the resulting values for factor1 and factor2 are likely to be reliable. It may be necessary to adjust the samples of vehicles to avoid a substantial mismatch, which could otherwise significantly alter the in lane statistics.

(57) The standard deviation for amplitudes of vehicles travelling in lane may be increased by vehicles travelling slightly offset to one side or the other of the loops, but not sufficiently offset for adjacent loop activation. Using a value for sd.sub.inlane slightly less than that derived from the data may lead to slightly more accurate calculated in lane values. A reduction of between 10% and 20% may be used depending on the level of lane discipline observed for the sample.

(58) Alternatively, values for factor1 and factor2 can be obtained in a test configuration by running a sample of vehicles fully over the loops and straddling between them, and measuring the in-lane amplitudes. The corresponding straddling logarithm values (and correction, where used) can then be calculated. Plotting the in-lane amplitudes against the logarithm sums allows a value for the slope (for factor2) and intercept value (for factor1) to be obtained from the plot by inspection, or by application of a suitable regression calculation.

(59) The values of factor1 and factor2 may be determined experimentally for a given site, particularly where the lanes and/or inductive loops of a carriageway differ significantly. For example, if there are different lane widths, or significant rebar effects, the values may differ from those given above. Vehicles with different chassis heights can be used to gather inductance change value data and select optimal values for factor1 and factor2 in such cases.

(60) Note that wide vehicles can be identified with sufficient accuracy from the structure of the inductance change value over time as the vehicle passes over an inductive loop. They can also be identified via axle detectors, where these are used, since heavier vehicles produce higher axle detection amplitudes for most forms of axle detector.

(61) For example, using the same inductance change values as in the earlier scenario, the value of ampl.sub.inline can be calculated as follows. In this case, factor1 is 3.76 and factor2 is 0.000568, and factor (for calculating correction) is 10. Therefore:

(62) $\frac{\begin{array}{c}\log \left(168\right)+\log \left(110\right)+\\ \left[\left(\log \left(168/110\right)\right)/10\right]-3.76\end{array}}{0.000568}=924\left(3s.f\right)$

(63) Note that the outputs from the inductive loops for a particular vehicle type can vary in amplitude in response to such factors as loop sensitivity, loop size, the presence and proximity of ferrous or conducting reinforcing materials in the pavement, and the length of lead-ins, amongst other factors. The described calculations work best when the vehicle detection amplitudes are standardised. It is common practice to standardise detection amplitudes to values of around 1300 for a typical sedan car, and the figures may be based around that standard response.

(64) The skilled person will appreciate that it is assumed that the loops in the system are all of the same size and are situated in magnetically uniform pavement. In the unusual event that the site is significantly laterally non-uniform, adjustments may be needed to some of the parameters if very accurate lateral locations are required. Further, it is assumed that the activations for all loops are scaled before use in any of the methods so that they would be the same for any given vehicle travelling over them.

(65) The skilled person will also appreciate that mathematical rearrangement and/or redistribution of terms in the above equations would give rise to substantially equivalent equations within the scope of the claims. In particular, rearrangement of the logarithms to combine or expand them—for subsequent factorisation of other terms, for example—is considered to give rise to substantially equivalent equations. Similarly, including, altering or omitting terms of negligible magnitude, factors which have minimal effect on the resulting value, and/or selected mathematical sign inversions would also give substantially equivalent equations. Where standard deviations are used, using a value derived from the variance of the sample is an alternative.

(66) Any combination of correction terms, such as those presented above, may be applied to the numerator and/or the denominator, in calculations where these are present. Correction terms may be applied as operators involving addition, subtraction, multiplication, or division, amongst others.

(67) Although the invention is described in terms of lanes on a carriageway, the apparatus of the invention is applicable in any system where the lateral position of a vehicle needs to be determined as it moves along a road, irrespective of lane markings. It will be appreciated that the calculations described may be modified to take into account inductive loops of different lengths and/or widths.

(68) The embodiments described above are provided by way of example only, and various changes and modifications will be apparent to persons skilled in the art without departing from the scope of the present invention as defined by the appended claims.