GB2472618A

GB2472618A - Range-finding

Info

Publication number: GB2472618A
Application number: GB0914085A
Authority: GB
Inventors: David Gunn; Said Assous; Clare Hopper
Original assignee: University of Leicester; Natural Environmental Research Council
Current assignee: University of Leicester; Natural Environmental Research Council
Priority date: 2009-08-12
Filing date: 2009-08-12
Publication date: 2011-02-16
Also published as: GB0914085D0

Abstract

A method of measuring the length D of a path between two points comprises transmitting first and second waves of acoustic or other radiation at frequencies f1 and f2 between the points along the path, where f2 - f1 < c/D. The difference in the residual phases of the two waves at the second position provides a first, unambiguous, measure of the path length D. By transmitting a third wave of frequency f3 from the first position to the second position along the path, where f3 — f1 > c/D, and finding the difference in the residual phases of the third and first waves at the second position, a second measurement of D may be made with increased resolution. The invention provides a measurement method that does not require the tuning of a transmitted frequency, and does not require measurement of the total phase difference of wave between the first and second positions. The path may be straight, or may be a return path to and from a reflector (sonar).

Description

RANGE-FINDING METHOD AND APPARATUS

The invention relates to methods and apparatus for measuring the length of a path between two points and to methods and apparatus for range-finding, i.e. measuring the range of a remote target.

The use of waves of various kinds, such as sound waves, light waves etc, to measure distance by various techniques is known. For example in one technique, disclosed in published patent application GB 2 188 420 A, the range of a remote target is found by reflecting ultrasonic waves from the remote target and adjusting the frequency of the waves until the round-trip distance to the remote target contains an integer number n of cycles of the wave; that is until the phase of the wave on transmission is the same as its phase on reception. The frequency of the ultrasonic wave is then increased until the round-trip distance to the remote target contains n+ 1 cycles of the wave. The frequency difference Af between the two frequencies then provides a measurement c/Af of the range of the remote target, where c is the velocity of the wave. In other techniques, such as that disclosed in US patent number 4 905 207, distance is measured by finding the total phase difference between two points along a wave, the separation of the two points corresponding to the distance to be measured.

One aspect of the present invention provides a method of measuring the length D of a path between a first position and a second position, the method comprising the steps of: (a) transmitting first and second waves of frequency f1 and f2 respectively from the first position to the second position along the path, where f2 > f1 and f2 -f1 < cID and c is the velocity of the waves; and (b) finding the difference A4i2i between the residual phases of the first and second waves at the second position to obtain a measure of the length D. The total difference between the phase of a wave at the second position and its phase at the first position is 2ltm+4), where m is a positive integer and 4) is the residual phase, which is in the range 0 4) < 2it. Since f2 -f1 < cID, the difference between the residual phases of the first and second wave at the second position is unique (unambiguous), and can be taken as a measure of the path length D for given frequencies f1, f2. The method of the invention only requires the difference between the residual phases of the waves at the second position to be found: there is no requirement to find the total phase difference of either wave between the first and second positions. Prior art techniques relying on the measurement of such a total phase difference, such as that disclosed in US 4 905 207, require a timing reference or a reference wave to be transmitted in order to measure total phase difference, and are therefore more complex and difficult to implement. The need for a reference wave or a timing reference also makes such techniques unsuitable for passive distance measurement, i.e. measurement of path length between two positions in which transmission of waves at the first position cannot be controlled from the second position. The invention relies on the fact that whilst the individual phases of the first and second waves at the second position are not unique, the difference in phase between the two waves at the second position is unique. If the first and second waves have a common phase at the first position, measuring their phases at the second position and taking the difference between these measured phases leads directly to the required difference in residual phases. However, if the respective phases of the two waves at the first position are different, then the difference in measured phase at the second position must be corrected to give the residual phase difference.

Although the method disclosed in GB 2 188 420 A provides an unambiguous measurement of distance, it has the disadvantage that frequency tuning is required, which makes the method slow to carry out and apparatus is needed for performing the complex method. The frequency of a transmitted wave has to be adjusted so that the phase of the wave is the same at the ends of a path for two adjacent frequency values. The method of the present invention provides an unambiguous measurement of a path length without the need for frequency-tuning, and path length is measured using the difference in the residual phases of two waves at the second position. The speed at which a path length can be measured by the present method (and hence the calculation time) thus depends largely on the speed at which phase information is extracted, which is typically faster than the speed at which two frequencies can be found satisfying the condition that the path length to be measured is equivalent to exactly n and n+ 1 cycles of two waves. It is noted that the present method is applicable to any system involving wave propagation and therefore the invention has a potentially wide range of application.

The first and second positions may be different points in space, the path either directly connecting the two points, or involving reflection of the waves at one or more intermediate positions for example. The two points could alternatively be one and the same position, the waves being transmitted from the point and then reflected from an object or target back to the same position. The method of the invention may be applied to measurement of path lengths on the order of microns to kilometres for example, using waves of suitable frequency or wavelength. For example, when using sound for unambiguous sonar distance ranging, path lengths of a few microns may be measured unambiguously using GHz frequency-differences and path lengths of a few kilometres may be measured unambiguously using Hz frequency-differences.

The difference A421 in the residual phases of the waves at the second position may be taken directly as a measure of the path length D, since cI((f2-f1)) is a constant for two given frequencies f1, f2. To provide a measurement of the path length D in units of length, the method further comprises the step of evaluating the quantity (cI(f2-f1))(n21 + (A421/2it)), where n21 = 0 if A4i2i > 0 and n21 = 1 if A4i2i < 0 to obtain a first measurement of D in units of length.

In order to measure the path length D with greater resolution, preferably the method further comprises transmitting a third wave of frequency f3 from the first position to the second position along the path, wherein (f3 -f1) > (f2 -f1) and f3 -f1 > cID, finding the difference A4i31 between the residual phases of the third wave and the first wave at the second position, and evaluating the quantity (cI(f3-f1))(n31 + (A43iI2it)) to obtain a second measurement of D, where n31 is a positive integer selected such that the second measurement of D in units of length corresponds to the first such measurement. Measurement of D using the frequencies f3, f1 results in several possible values of D, depending on the integer n31, but the value selected as a final measured value is the one that corresponds most closely to the value obtained using the frequencies f1, f2. Using a pair of waves with a higher frequency-difference Af leads to greater resolution in the measurement of D because the factor c/Af is decreased.

The increased in resolution is akin to use of a Vernier slide rule.

It is also possible to use the frequencies f2 and f3 (instead of f1 and f3) to provide measurement of D with improved resolution, provided f3 -f2 > f2 -f1.

To measure D with even greater resolution, a fourth frequency f4 may be transmitted from the first position to the second position along the path, and the difference z4 in residual phase at the second position between the fourth wave and one of the other three waves (say the ith wave of frequency f where i = 1, 2 or 3) used to provide a third measurement of the path length D. This requires f4-f to be greater than f3-f1 (or f3-f2 as the case may be) and greater than cID. The difference A4 between the residual phases of the fourth wave and the ith wave at the second position provides a value for D of (cI(f4-f)(n4+A44) where n4 is an integer, i.e. there are multiple possible values of D depending on the value of n4. The value selected as the actual measured value of D is that which corresponds most closely to the second value of D found using the frequencies f1, f3 (or f2, f3 as the case may be).

The resolution with which the path length D can be measured depends on the greatest frequency difference amongst the transmitted waves. By using appropriate combinations of frequencies, a long path length can be measured very accurately. For example in the case of marine sonar distance ranging, sub-metric resolution is possible using tens of kHz frequencies over a range of kilometres if two frequency components differ by 1 Hz.

Preferably the waves are transmitted simultaneously as a pulse directed along the path between the first and second positions. Transmission of the waves in a pulse provides an energy saving compared to the case where the waves are transmitted continuously. The invention allows for the waves to be transmitted as a pulse as a result of the fact that only the difference in phase between two frequency components at the second position is required to be found, and not the total phase difference of a wave between the first and second positions. A series of pulses may be transmitted to monitor changes of the path length D over time. For example the range of a remote target may be monitored by reflecting a series of pulses from the remote target, each pulse containing two or more frequency components, and finding the phase differences between pairs of frequency components on reception of the pulses after reflection from the remote target. Preferably the waves in the pulse have a common phase at the start of the pulse. This allows the phases of a pair of waves at the second position to be measured and their difference taken in order to arrive directly at the difference in their residual phases at the second position. Otherwise the measured phase difference of a pair of waves at the second position has to be corrected for the difference in their phases at the first position in order to arrive at their residual phase difference at the second position.

The phase difference of two waves (i.e. two frequency components) in a pulse is preferably found on reception of the pulse at the second position by the steps of: (i) receiving the pulse at the second position; (ii) sampling a portion of the pulse within a time window having a duration of at least 1/f1 to produce a pulse sample; (iii) measuring the phases of each of the pair of waves at a time which is delayed from the beginning of the time window by a time delay which is at least 1/f1 and which is equal to respective integer multiples of the periods of all frequency components in the pulse; and (iv) calculating the difference in the phases of each of the pair of waves at the said time.

This approach provides a phase difference value (and hence a value for the path length D) which is not dependent on the frequency at which the pulse is sampled, as is the case with other techniques such as cross- correlation. The additional processing requirements associated with over- sampling and signal interpolation, which are often necessary in cross-correlation, are avoided by the present approach to finding phase differences.

Conveniently the phase difference is found by applying a discrete Fourier transform to the pulse sample.

In order to correct for errors in the measurement of phases of frequency components at the second position, the method may be initially used to measure a known path length, and the result of the measurement compared to the known path length for find the errors. When measuring an unknown path length, phase measurements may then be corrected to provide enhanced accuracy in the measurement of the unknown path length.

The waves may be acoustic waves, e.g. ultrasonic waves, or radio waves, microwaves, or light waves or some other type of wave, depending on the circumstances.

The range of a remote target may be found using the invention to measure the length of a path between a first position and a second position via the remote target.

A second aspect of the invention provides apparatus for measuring the length D of a path between a first position and a second position, the apparatus comprising: (a) transmitting means arranged to transmit first and second waves of frequency f1 and f2 respectively from the first position to the second position along the path, wherein f2 > f1 and f2 -f1 < cID; and (b) means arranged to find the difference A4i2i between the residual phases of the first and second waves at the second position to obtain a measure of the length D. In order to provide a measurement of D in units of the length, the apparatus may further comprise means arranged to evaluate the quantity (cI(f2-f1))(n21 + (A421/2it)), where n21=O if A4i2i >0 and n21=1 if A4i2i <0.

Embodiments of the invention are described below with reference to the accompanying drawings in which: Figure 1 illustrates the principle of the invention; Figure 2 shows an apparatus of the invention; Figure 3 shows the form of signals transmitted and received by the Figure 1 apparatus; Figure 4 illustrates the repeatability of path length measurements obtained using the Figure 1 apparatus and; Figure 5 shows an apparatus of the invention for measuring the range of a remote target.

In Figure 1, a path length D to be measured is defined by positions A and B. A first wave of frequency f1 transmitted from A to B has a phase 2itm1 + 4 at B relative to its phase at A, where m1 is a positive integer and 4 is the residual phase of the first wave at B (4i < 2it). A second wave of frequency f2( > f) has a phase 2itm2 + 42 at B relative to its phase at A, where m2 is another positive integer and the residual phase of the second wave at B is 42 (42 < 2it). In terms of the wavelengths of the waves, the distance D is D = m1X1 + (4112it)X1 = m2X2 + (2/2it)X2, i.e. D = (cI(f2-f1))(n21 + ((4i2-4i1)/2it)), where n21 = m2 -m1.

If f2-f1 < cID, then the difference 42-4 in the residual phases at B is unique, even though the phases of the individual waves are not unique, and D is given unambiguously by D = (cI(f2-f1))(n21 + ((4i2-4i1)I2it)). Measurement of the residual phase difference 42-4 at the second position B therefore allows D to be found unambiguously. If the first and second waves have a common phase at A, then the phases of the waves at B (in the range 0 to 2it) may be directly measured and their difference taken in order to arrive at the difference in their residual phases at B. Having obtained an unambiguous value for D (a first measurement of D), D may be measured with greater resolution by transmitting a third wave of frequency f3 between A and B, where f3 > f1 and f3 -f1 > cID. In this case D = m3X3 + (4)312it)X3, 4) < 2it.

Using the residual phase difference 4)-4 between the residual phases of the third wave and of the first wave at the second position B, D is given by D = (cI(f3-f1))(n31 + where n31 is an unknown positive integer greater than 1. That value of n31 which gives a value of D which corresponds to (i.e. is closest to) the unambiguous value of D given by the first measurement provides a second measurement of D, this second measurement of D having greater resolution than the first due to the higher frequency difference f3-f1 compared to f2-f1.

Alternatively, the difference 4)3-4)2 between the residual phases of the third wave and the second wave at the second position B may be used to provide the second measurement of D with improved resolution, if f3-f2 > f2-f1 and f3-f2 > cID.

Further frequencies of higher frequency may be transmitted between A and B and their residual phases at B found to provide further measurements of D with even greater resolution.

If two waves have a common phase at A, then the respective phases of the two waves at B may be measured directly to obtain their residual phase difference; otherwise the difference in the phases of the waves at B will need to be corrected by their respective phases at A in order to obtain their residual phase difference at B. As an example, consider a distance D = 1000.1234 mm which is to be measured accurately (but which is initially unknown) by use of acoustic waves in water. Assuming the velocity of sound c in water is 1500 ms', an acoustic wave of frequency f1 = 200 kHz has a wavelength X = 7.5 mm, and an acoustic wave of frequency f2 = 201 kHz has a wavelength X2 = 7.4627 mm. The maximum unambiguous range that may be measured using f1 and f2 is 1.5 m. For waves of frequency f1 the distance D corresponds to 133 full cycles (266it) plus a residual phase 4 of 125.923°. For waves of frequency f2 the distance D corresponds to 134 full cycles (268it) plus a residual phase 42 of 5.953°. In this case n21 = 1 and D is given unambiguously as D = (1500/1000)(1 + (-119.97°1360°)) = 1000.125 mm.

This value of D may be taken as a first measurement of D. For a third wave of frequency f3 = 210 kHz, the distance D corresponds to 140 full cycles plus a residual phase 4 of 6.219°. Thus -4 equals -119.704°. In this case D = (1500/10000)(n31 + (-119.704°1360°)) where n31 is a positive integer. The value of n31 which gives a value of D that corresponds to the first measurement is n31 =7, which gives a second, higher resolution measurement of D of 1000.1233 mm.

An even more precise value for D may be obtained by measuring the residual phase of a fourth wave having a frequency higher than that of the third. For example, for a fourth wave of frequency f4 = 300 kHz, the residual phase over the distance D is 8.8848°. In this case, using the residual phase difference of the fourth and first wave gives D = (1500/100000)(n41 + (-117.038°1360°)).

With n41 = 67 this provides a third measurement of D of 1000.1234 mm.

In certain situations, the measurement of residual phases may involve systematic errors. By applying the above method to the unambiguous measurement of an accurately known distance, the error in residual phase difference associated with a particular measurement apparatus may be determined from the error found in the measurement of the accurately known distance. This error may then be used to correct residual phases in subsequent measurements of unknown distances or path lengths. An error ii\4 in residual phase difference results in an error SD in measured distance of (cl2itAf) SA4. So for example if an accurately known distance of 0.1 m is (unambiguously) measured using frequencies of 200 kHz and 201 kHz as 0.1833 m, then this implies an error SD of 0.0833 m in D and a corresponding error of 2itAThDIc, or +20° in the residual phase difference. In measuring subsequent unknown distances using the same frequencies the residual phases may be corrected by +200 to provide more accurate distance or path length measurements.

Referring to Figure 2, an apparatus of the invention for measuring a distance D by use of pulsed ultrasonic waves in water is indicated generally by 100. The apparatus 100 comprises two ultrasonic broadband transducers 102, 104 operating as a transmitter and a receiver respectively. The transducers 102, 104 have a beam width of approximately 10° at their centre frequency and a -6dB bandwidth of 99 kHz (from 72 kHz to 171 kHz). The transmitter 102 is driven directly by a 20 V peak-to-peak waveform consisting of four sine waves added together, the sine waves having zero phase-offset (i.e. a common initial phase at the start of each pulse) and frequencies f1, f2, f3, f4 of 70, 71, 80 and 170 kHz respectively. Transmission and reception of signals is carried out and monitored by a modular unit 108 comprising a 16-bit arbitrary waveform generator (Ztec ZT53OPXI) and a digital storage oscilloscope (Ztec ZT41OPXI), a second oscilloscope 106 and a PC 110 coupled to the modular unit 108. The PC 110 is programmed in C + + to control signal transmission and acquisition.

In operation of the apparatus 100, three ultrasonic pulses each of 2 ms duration, and each containing the frequencies 70, 71, 80 and 170 kHz, are transmitted from the transmitter 102 and to the receiver 104. At the receiver 104 the pulses are sampled at a frequency of 10 MHz, providing 20,000 samples per pulse. The PC 110 is arranged to apply a discrete Fourier transform (DFT) to the received pulses using a window of [(N12) + 1: NI to obtain magnitude and phase information for each of the four frequency components. This provides a resolution of 1 kHz which is consistent with the smallest frequency difference between any two frequency components in a pulse.

Figure 3 shows typical forms for the transmitted and received signals when the separation D of the transmitter 102 and receiver 104 is 305.8 mm.

The PC 110 extracts residual phase differences A421, A4i31, A4i41, A432, A442, for the pairs of frequencies f2f1, f3f1, f4f1, f3f2, ff2 and f4f3 respectively. (A4 = -4). An unambiguous estimate D21 of the range D is obtained using the frequencies f1 and f2. Accurate values of D are then computed by the PC 110 using the method described above, the most accurate being D41 = (cI(f4-f1))(n41+(A44112it)) where n41 is a positive integer. Figure 3 shows values of D obtained using the frequencies f1 and f4 over 60 measurements using the Figure 1 apparatus. The measurements are consistent to within 30 pm.

Figure 5 shows another apparatus of the invention indicated generally by 200 and comprising an ultrasonic transmitter 202, sensors 204...204N, a receiver unit 207 and a PC 210 comprising a signal processor. The principle of operation of the apparatus 200 the same as that of the apparatus 100 of Figure 1. However the apparatus 200 is arranged to measure the length of a path from the transmitter 202 to one of the receiver 204 via a remote target and hence to determine the range of the remote target from the apparatus 200.