GB2446941A - Determining the direction of arrival of an acoustic pulse using spectral decomposition of signals from a plurality of sensors - Google Patents
Determining the direction of arrival of an acoustic pulse using spectral decomposition of signals from a plurality of sensors Download PDFInfo
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- GB2446941A GB2446941A GB0803007A GB0803007A GB2446941A GB 2446941 A GB2446941 A GB 2446941A GB 0803007 A GB0803007 A GB 0803007A GB 0803007 A GB0803007 A GB 0803007A GB 2446941 A GB2446941 A GB 2446941A
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/80—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using ultrasonic, sonic or infrasonic waves
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/80—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using ultrasonic, sonic or infrasonic waves
- G01S3/802—Systems for determining direction or deviation from predetermined direction
- G01S3/808—Systems for determining direction or deviation from predetermined direction using transducers spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems
- G01S3/8083—Systems for determining direction or deviation from predetermined direction using transducers spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems determining direction of source
Abstract
A method of estimating the direction of arrival of an acoustic pulse comprises: detecting the pulse with a plurality of sensors so as to generate a plurality of sensor signals; spectrally decomposing each sensor signal so as to generate one or more spectral components for each signal; and processing the spectral components to estimate the direction of arrival of the acoustic pulse. The plurality of sensors may comprise a volumetric array comprising two microphones on each of three orthogonal axes. The direction of arrival may be calculated from phase delays between pairs of spectral components, or by performing a power versus bearing scan. The method may be used to estimate the direction of a target and/or to estimate the trajectory of a projectile. The sensors may be mounted on a weapon (e.g. rifle), and an indicator may be provided when the weapon is aligned with the estimated direction. The sensor signals may be sampled at a rate as low as the Nyquist rate whilst maintaining an accurate estimate.
Description
I
ACOUSTIC PULSE ANALYSIS
The present invention relates to a method and apparatus for estimating the direction of arrival of an acoustic pulse. The method may be employed typically, although not exclusively, in a system for identifying the direction and/or range of a sniper and/or determining the trajectory of a bullet fired by the sniper.
US6178141 describes a system for determining the trajectory of a supersonic bullet by observing the shock wave from the bullet. Muzzle blast observations may also be used to estimate the exact sniper location along the trajectory. The sensors are helmet-mounted, and each helmet is supported by wireless communications, GPS and a backpack or otherwise mounted computer system that computes and displays the solutions.
In US6178141, fine resolution time difference of arrivals, for the shock wave arrivals, are determined via cross-correlation between the channels. The data are interpolated eight times during the cross-correlation process.
The invention provides a method of estimating the direction of arrival of an acoustic pulse, the method comprising: a. detecting the pulse with a plurality of sensors so as to generate a plurality of sensor signals; b. spectrally decomposing each sensor signal so as to generate one or more spectral components for each signal; and c. processing the spectral components to estimate the direction of arrival of the acoustic pulse.
The invention also provides apparatus for detecting the direction of arrival of an acoustic pulse by the above method, the apparatus comprising an array of sensors; and a processor programmed to perform steps b and c.
The invention provides a processing method which enables the sensor signals to be sampled at a low rate (which may be as low as the Nyquist rate), whilst maintaining an accurate estimate. ft'
Spectrally decomposing the sensor signal reduces the effects of noise, compared with a conventional time-of-arrival method in which a threshold crossing point is detected for each sensor. The invention is particularly suited to use in a volumetric sensor with a small baseline.
In one example of the invention, the direction of arrival is calculated by performing a power versus bearing scan. This provides improved accuracy through "bearing coherent" averaging of noise, However for some applications this method may be overcomplicated. Therefore in a preferred embodiment the pulse is detected with a volumetric array of three or more pairs of sensors in step a. so as to generate three or more pairs of sensor signals; a plurality of pairs of spectral components are generated for each pair of sensor signals in step b; and step c. includes calculating a phase delay between each pair of spectral components, and determining the direction of arrival of the acoustic pulse in accordance with the calculated phase delays. The preferred embodiment is computationally simpler than a power versus bearing scan, and also provides improved accuracy through "bearing coherent" averaging of noise.
The method may be used in any suitable application, but in preferred examples it is used to estimate the direction of a target and/or to estimate the trajectory of a projectile.
Preferably the invention is used as part of a method of providing an indication of the direction of a target, the method comprising the steps of detecting an acoustic signal originating from the target; processing the signal to estimate the direction of the target relative to a weapon; and providing an indication when the weapon is aligned with the estimated direction of the target.
In this case, the apparatus typically comprises a sensor for detecting an acoustic signal originating from the target; a processor for processing the signal to estimate the direction of the target relative to a weapon; and a direction indicator for providing an indication when the weapon is aligned with the estimated direction of the target.
By providing a user with an indication when a weapon (typically held or controlled by the user) is aligned with the estimated direction of a target such as a sniper, the user can quickly and accurately return fire.
The acoustic signal may comprise, for example, a muzzle blast or projectile shock wave.
I
The signal may be detected by helmet-mounted sensors as in US6 178141. However in some situations it may be preferable for the user to be operating in a "helmets off' environment.
Also, if the sensors are helmet-mounted then a complex system must be provided to estimate the target direction relative to the weapon. Therefore preferably the signal is detected by one or more sensors mounted on the weapon.
Preferably the indication is also provided by an indicator mounted on the weapon.
Preferably the sensor, indicator and processor are mounted in a common housing.
In a preferred embodiment an indication is provided when the weapon is aligned with a vertical and/or horizontal plane containing the estimated target direction.
The indication may be visual or audible. In a preferred example the colour of a visual indicator is changed when the weapon is aligned with the estimated direction of the target.
The signal is typically detected by a plurality of sensors which may be arranged in a planar array, or in a volumetric array. Preferably the spacing (or baseline) between the sensors is small, in order to reduce the size of the apparatus. Small spacing does however make it difficult to accurately estimate the target direction.
The weapon may be a tank or helicopter, but preferably the weapon is a hand-held weapon such as a rifle.
Preferably the (or each) sensor is mounted on the sight of the weapon. This automatically aligns the sensors with the sight and enables more accurate targeting.
The direction and/or range indicators may also be mounted on the sight to provide a compact integrated system.
Various embodiments of the present invention will now be described with reference to the accompanying drawings, in which: Figure 1 is a perspective view of part of a rifle incorporating an acoustic sensor device; Figure 2 is an exploded view of the acoustic sensor device, with some parts omitted; Figure 3 is a schematic view of the components of the acoustic sensor device; Figure 3a is a schematic view of the rifle in combination with a PDA and communication device; Figure 4 is a schematic view of a bullet trajectory, as viewed in a plane containing the trajectory and receiver; Figure 5 is a graph showing a pulse waveform x, a pulse with uniform noise spread over the bandwidth of the pulse, and a spectral analysis window function, all used in a simulation of method a; Figure 6 is a graph showing spectra for the pulse and noise used in the simulation of method a; Figure 7 is a graph shows a pulse waveform, noise waveform, and threshold level used in the simulation of method a; Figure 8 is a graph showing bearing errors calculated in the simulation of method a; Figure 9 is a graph shows a pulse waveform and noise waveform used in the simulation of method b; Figure 10 is a graph showing bearing errors calculated in the simulation of method b; Figure 11 is a graph shows a pulse waveform and noise waveform used in the simulation of method C; Figure 12 is a graph showing pulse waveforms from two sensors cO and c2; Figure 13 is a graph showing bulk delays for microphone pairs c20 and c3 1; and Figure 14 is a graph showing bearing errors calculated in the simulation of method c.
Figure 1 shows a rifle I with a sight 2, and an acoustic sensor device 3. The device 3 is shown in further detail in Figure 2. The device 3 has a pair of mounting legs 4 which are screwed in place onto the sight 3 and a housing comprising upper and lower hemispheres 5,6. A digital range display 7 is mounted on the lower hemisphere 5, in this case showing a range of 800m.
A support plate 8 is screwed onto the lower hemisphere 5. Three light emitting diodes (LEDs) 9 are mounted in the lower hemisphere 5 and one in the upper hemisphere 6 Figure 3 is a schematic view showing various component parts of the device 3, some of which are omitted from Figure 1 for clarity. A volumetric array 20 of six miniature microphones is mounted to the support plate 8. The microphones are arranged in orthogonal positions around a sphere, with a diameter of between about 4 and 6 cm. The microphones are digitally sampled by an analogue to digital converter 21 and processed by an embedded digital signal processor (DSP) 22. A pseudo-omni output is formed for automatic detection of impulsive noise. The relative phases of all six microphones are then used to estimate the 3-dimensional direction of arrival of the detected sound. Systematic errors associated with the construction or mounting of the device (e.g. due to resonance, coupling or shading) can be precalibrated. Adaptive processing can be used to reject noise and interference.
The DSP 22 controls the LEDs 9, and range display 7, and also outputs data to a Bluetooth antenna 24.
As shown in Figure 3a, the Bluetooth antenna communicates with a personal digital assistant (PDA) 23 which is carried by the soldier. The PDA 23 also receives GPS data 24, and displays range and direction information in a map-based format. The PDA 23 is connected to a radio communication device 25 via an RS232 link.
The DSP 22 estimates the direction of the muzzle blast pulse, and the direction of the shock wave pulse. The range is then estimated by the DSP 22 using the method illustrated in Figure 4. The shot is fired from the left hand corner, and is detected at the right hand corner. The muzzle blast travels directly between the target and the receiver. The shock wave from the passing bullet arrives from a different angle. By measuring the included angle, and the time delay between the two events, and making assumptions about the speed and deceleration of the bullet, a range estimate can be computed.
Extraction of direction involves two essential steps: (i) measure the propagation delay across the array, and (ii) infer the direction of arrival.
A feature of the sensor array is that it includes three orthogonal axes each with two microphones.
Therefore, direction can simply be extracted by computing the time delay component along each axis, and resolving them to form a direction vector. This direct form of direction estimation is simpler than say a full maximum-likelihood power vs bearing scan of the array, with almost as good results for high SNR pulses.
The preferred method of calculating direction will now be contrasted with other methods which may also be performed by the DSP 22. Three candidate methods are considered in detail: a) Measure the time of arrival of the pulse at each microphone using a threshold crossing technique. Form the direction vector from the three component delays.
b) Cross-correlate each pair of microphones in the time domain, to estimate the delay based on the whole pulse shape. Form the direction vector from the three component delays.
c) The preferred method: decompose the pulse into its spectral components; compute the phase delay for each component along each axis; hence create a direction spectrum (ie. power-weighted direction vector vs frequency); and sum the weighted direction vectors, to obtain the overall direction vector.
The relative advantages and disadvantages of each technique are discussed below.
Method a' The array is small in terms of wavelengths (less than two wavelengths across) which means that if using a direct time-domain measurement method the signals must be sampled at a much higher rate (e.g. 400 kl-Iz vs 20 kHz). This will increase power drain and increase the size of the electronics.
Method b' The use of correlation-based time measurement means that the necessary high sample rate can be obtained post-correlation, by interpolation. Method b' also has the advantage over method a' that using the whole pulse shape provides averaging of the effects of noise, whereas using a threshold-crossing method yields just one time sample per event. However, for sensible length interpolation filters the basic sample rate would have to exceed the Nyquist rate by a factor.
Method Method c' retains the advantage of method b' by using the whole pulse shape, but avoids the need to interpolate the correlation output to a very high effective sample rate, so allowing' sampling at the Nyquist rate. The phase domain method also provides slightly improved accuracy through bearing coherent' averaging of noise, rather than just temporal averaging of noise.
Some more explanation of method c. will now be given. An alternative method of using phase in the direction estimation (employing a power vs bearing scan) will also be described.
The signal vector, across all six microphones, for a signal at elevation 9 and azimuth 8 is as follows: j.2.1.L.cos(w).cos(e) e A r J it-. sin( 9$ ). cos(O) e -j2it.-.cos(9$ )cos(e) e = -j.2 it *--. sin( si). cos( )
C eJ20
e 2it--.cos(9) So the received signal, at true direction ( 00 w o), in the presence of noise, is no ni x(X)= s(900,X) + n4 n5 The optimal method of estimating the signal direction, assuming uncorrelated background noise would be to do a power vs bearing scan. ie. for beamweights w given by: w(oiA.)=(wx))T we find the 0 and w that maximise the following expression
-T
P= w*Xw where x=(.).x(x) However this is overcomplicated for the preferred application.
Let us consider a modified signal vector, in which opposite microphones along each axis are cross-correlated (or equivalently, the complex frequency-domain signals are multiplied in conjugate).
E.g. taking microphones 0 and 2 we have our correlated x-axis sensor: r r r J2'71cos(p).cos(O) -J21r---.cos().cos(e) j4.1t.-.cos(I).cos(9) a=s0.s2e *e =e -ç Therefore a(O,p,)= e8"'' where cos (v,) cos (e) 4(8,v,X) = 4.ir-.sin(w).cos(e) 4.ir.-.cos(8) But the direction vector of the true signal (in x y z coordinates) is as follows: cos (i).co (e) d(O,,) = sin(ip).cos(e) cos(O) Therefore we see the following relationship, from which signal direction is obtained directly: = 4.it.L.d(O,w) Therefore, in words, the phase of the cross-correlated microphone pairs, directly yields the signal direction vector, to within a frequency-dependent scale factor. Therefore by analysing the phase of the received pulse, we can estimate the bearing of each spectral component. We can then produce an overall bearing estimate from the power-weighted sum of the component direction vectors. This is not quite optimal (compared to a power bearing scan) but is simpler.
Also it does not require any of the microphones to be matched in gain, and only requires them to be phase-matched in pairs, which simplifies construction or calibration of the array.
Example calculations
Maximum frequency fmax 10000 Hz -ç Speed of sound in air c:= 344 mIs Acoustic radius of array r 0.025 m Acoustic wavelength)umn -s---Amin = 0.0344 m fmax Acoustic diameter in wavelengths = 1.4535 .nhin Time delay across array t -t. = 145.35 J.LS Time delay for I degree bearing c.sin(1.__) 106 2.536687.LS Sample rate for Nyquist sampling fSNyq:= 2*fmax fSNyq*103 20 kHz Sample rate to resolve 1 degree change fsldeg fS1deg10 = 394.21 kHz Three algorithms compared The three algorithms are compared using a simple simulation.
A band-limited pulse is constructed.
An uncorrelateci noise background is obtained by phase-randomising band-limited pulses, to ensure simulation consistency regardless of sample rate.
The scenario is run 100 times, with a different true pulse bearing each time, and the resulting accuracy is compared for the three methods.
Sample rates and data collection block lengths for the three methods: TbIock TbIock.103 = 1.6 fSa:= 32*fmax fsb:= 4*fmax fs:= 2*fmax fsa 10 = 320 Ii fsb.103 =40 fs.I03=2o Na:= round (TbIOCk fsa) Nb round (TbIOCk. fsb) N round(TbIOCk.fsC) Na = 512 Nb = N = 32 Nominal pulse, and (approximately) equal energy flat-spectrum pulse used to generate noise.
We assume that the pulse is windowed or gated, so as to exclude extraneous noise. fmax
f0:= 2 sync(x) if(x= 0,1 sin(x)) ( __ T) win(t) sin1 p(t) 0 ( -Tblock' 2 ] sin[2 it t: ( Tbjock'\ i1 t-1 2.1t.-.t 2 2, 2,, 4] q(t) := sYnc[2.ir.fo{t -TbiockjJ [2f( -TbiockJ] n:= 0.. Na -C1 x:=p n*-fsa) X:= FFT(x) y:= Y:= FFT(y) stdev(x)') SNRdjusldB SNRadjust = 1.4118 Common simulation parameters and functions 1000 k:=0..K-I 0k 2t.!
K
SNRdB 16 getpulse(N,fs,dejay) := for n EU.. N-I x P(fl._--deIaY}win(--.TbIOCk) getnoise(N,fs,sJ..&j8) := for n EU.. N-I x -w wj.TblOCk) X <-CFF1x) 4±runit(N,-7r,7t) for nEO..N-1 J. 4,n Y -X *e n n -SNRdB_SNRadjustdB y -Re(ICFFgY)).1o 20 -p (y. w) Method a' Generate pulses for each of 100 bearings, for 4 microphones (0=north, I =east, 2=south, 3=west) puIseaO:= getpulse Na, _! . cos (Ok)) pulsea getpuise (Nat fSa, _.! .sin(Ok)) pulsea2:= getpulse (Na, fsa, -. (Ok)) pulse a3:= getpulse (Nat fsa, Sth(0k)) Generate noise waveforms * (k) nolseaO getnolse(Na,fsa,s1.JB) * (k) nolseal:= getnoIse(N,fs,stsm) noise a2 getnoise (Na, fsa, SNRj) (k) nolsea3 getnoIse(N,fs,sN1) Pulse detection threshold (say set at 4 sigma wrt noise, or 1/4 of the peak, whichever is greater) Thresh a:= ma{4. stdev (noise aO)' -! ma,(pulse aO)) Thresha 0.2392 Compute times of arrival for each pulse getTOA(x,T) := n -0 while (x <T).(n < Na -n 4-n + I n TOAa0:= getTOA (pulse aO + noise aO,Thresh a) TOAai k:= getTOA (puiseai + flOSCa,Thresh a) TOA getTOA (puise a2 + noise,Thresh a) TOA:= getTOA(pulse + noisea3,Thresha) compute bearing error for each pulse a arjj(TOAa2 -TOAaOk) + *(TOAa3 -TOAalk)].e Method b' Generate pulses for each of 100 bearings, for 4 microphones (Onorth, 1 =east, 2=south, 3=west) pulsebO:= getpulse (Nba fsb, .COS (eiJ) pulsebi getpulse (Nba fsb._Lsin(ek)J puIseb2:= getPuIse(Nbfsb.cos(Ok)) pulseb3 getpulse (Nb fsb, ;sln(ek)) Generate noise waveforms noisebo getnoise (Nb, fsb, SNRJB) * (k) .1 nolsebi getnoIseN, fsb, SNRJB * (k) nolseb2:= getnoise Nb, fsb, SNRdB * (k) .1 nolseb3 getnoise Nb, fsb, SNRdB 0.. Nb -I Compute time delays for each axis by circular correlation and interpolation getDT(x,y) := X 4-CFFT(x) Y*-CFF1y) z -(x for n E 0.. Na -1 zintpn +. 0 Nb for fl E 1.. -I z. *-z Intpn n Na_n 4-ZNfl zintp 4--ICFFT(Z1,) for fl e 0.. Na -I sortarray <-n 4-Na Na modcsort(sortarray,1)NIO + _NaJ -T I () . (i) (k) DTb2O:=getDTpuIse2 + nolseb2,pulsebO + flolsebO I () () (i) . () DTb3I:=getDTpuIse3 + nolseb3,puIsebI + nolsebi Compute each bearing error for each pulse argftDTb2O + j DT,3 1k) 9k] Method c' Generate pulses for each of 100 bearings, for 4 microphones (0=north, I =east, 2=south, 3 =west) puIse getpulse fs, -! *cos (eiJ) puIse1 getpulse fs, _-.sin(eiJ) puIse02 getpuise fs0, -.cos(6iJ) puIse3 etPu1se(NCfsC).sin(9k)) Generate noise waveforms * (k) noise cO getnoise (Ne, fs0, SNRdB) noisecj getnoise (N0, fs0, sNRdB) * (k) noise02 getnoise (N0, fs0 sNRJB) * (k) noise3 getnoIseNC,fsC,SNRdB Compute spectra for each microphone (k) .J (k) * (k) X00:=Fripu1se00 + noise00 (k.1 (k) * () X1:=FFlLpuIsecI + noise01 (k) ,.,.J (k) * () X2:=Fripu1se02 + noise02 (k) ..J (k) * () X3:=FripuIse03 + noise03 Compute bulk delays (by circular correlation, without interpolation) to a resolution of I sample (ie. half wavelength max) to eliminate phase ambiguity.
getBulkDT(x,y) X -CFFT(x) Y-CFFT(y) 24-ICFF1Z) for n E 0.. N -I sortarray -n sortarray -z n,I n
N N
mod(csort(sortay, N_I,0 + NC) -BuIkDT2:= getBuIkDT(puIse2 + noise2,pu1se0 + noisecü) Bu1kDT3 getBulkDT(puIse3 + noisec3, puise1 (I + noiseci) Compute direction vector spectrum, accounting for bulk delay phase ambiguity.
frequency resolution: N = 32 fs
C N
of=625 ( ( N N'fs freq(n) := mod(n + -arrgh(x) := if(x 0,0, arg(x))
N
getDvecspect (X0, X1,X2, X3, DT2O DT3I) := for n E 0.. -i -f *-freq(n) z02.E-XO.X2 n n z13-X1 *X3 n n f adj20 2it*DT2c-fs 4adj31 2.n.DT3I.._!-. fs
802 f-arrgh(z adj2O' 02e I + 4'adj2o e13 _arrgii(z Jl)adj3l') 13e. + 4adj31 m 4-'/z02.z13r n
N
for n E 0.. _E -Dvec *-rn (802 + i813) n n Dvec (k) () (i) (k) Dvec:=getDvecspect,X1,X3 BuIkDTc;BuIkDTc3i) Compute weighted sum direction vector
N
Dvecsumk:= Dvec n,k n =0 Compute bearing error for each pulse arg(Dvecsum.e_19'o) Now compare the three results: stdev (Oerr) med ian( eerr f) ma( 9err a a a (0.6928 0.4886 2.2567 stdev(Oerrb) median(J9errbl) ma)(jeerrbr) *--= 0.5096 0.3562 1.4211 0.3638 0.2388 1.2215 stdev (8err) median( eerrf) ma( I oerrcr) So typically method c wins, whether compared in terms of standard deviation, median, or maximum error. However, the advantage is not overwhelming, so the main advantage is that we can use a lower sample rate (and hence use less standby power).
Note that this analysis does not account for frequency-dependent bearing distortion (e.g. short multipath reception), and so there may be further, possibly more significant, advantages in bearing coherent processing when more complex environments are considered.
Claims (6)
- A method of estimating the direction of arrival of an acoustic pulse, the method comprising: a. detecting the pulse with a plurality of sensors so as to generate a plurality of sensor signals; b. spectraily decomposing each sensor signal so as to generate one or more spectral components for each signal; and c. processing the spectral components to estimate the direction of arrival of the acoustic pulse.
- 2. A method according to claim 1 wherein the pulse is detected with a volumetric array of three or more pairs of sensors in step a. so as to generate three or more pairs of sensor signals; wherein a plurality of pairs of spectral components are generated in step b. for each pair of sensor signals; and wherein step c. includes calculating a phase delay between each pair of spectral components, and estimating the direction of arrival of the acoustic pulse in accordance with the calculated phase delays.
- 3. A method according to claim I wherein the direction of arrival is estimated in step c.by performing a power versus bearing scan.
- 4. A method of detecting the direction of a target, the method comprising detecting the direction of arrival of an acoustic pulse from the target by a method according to any preceding claim, and inferring the direction of the target from the estimated direction of arrival.
- 5. A method of detecting the trajectory of a projectile, the method comprising detecting the direction of arrival of an acoustic pulse from the projectile by a method according to any of claims I to 3, and inferring the trajectory of the projectile from the estimated direction of arrival.
- 6. Apparatus for detecting the direction of arrival of an acoustic pulse by a method according to any of claims 1 to 3, the apparatus comprising a plurality of sensors; and a processor programmed to perform steps b and c.
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| Application Number | Priority Date | Filing Date | Title |
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| GB0803007A GB2446941B (en) | 2005-02-15 | 2006-01-30 | Acoustic pulse analysis |
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| Application Number | Priority Date | Filing Date | Title |
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| GBGB0503212.3A GB0503212D0 (en) | 2005-02-15 | 2005-02-15 | Improvements relating to target direction indication and acoustic pulse analysis |
| GB0601843A GB2423140B8 (en) | 2005-02-15 | 2006-01-30 | Improvements relating to target direction indication and accoustic pulse analysis |
| GB0803007A GB2446941B (en) | 2005-02-15 | 2006-01-30 | Acoustic pulse analysis |
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| GB0803007D0 GB0803007D0 (en) | 2008-03-26 |
| GB2446941A true GB2446941A (en) | 2008-08-27 |
| GB2446941B GB2446941B (en) | 2008-10-29 |
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| US20230150690A1 (en) * | 2021-11-15 | 2023-05-18 | Honeywell International Inc. | Systems and methods for providing safe landing assistance for a vehicle |
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| GB0803007D0 (en) | 2008-03-26 |
| GB2446941B (en) | 2008-10-29 |
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