Detecting a distance and a relative velocity of a target using a frequency-modulated continuous wave laser device

A method for detecting a distance and a relative velocity of a target using a frequency-modulated continuous wave ( FMCW) laser device and a device for detecting a distance and a relative velocity of a target are provided .

For detecting a distance and a relative velocity of a target with an FMCW laser device , the laser device emits laser radiation with a varying frequency . In most cases it is desired that the frequency varies linearly . However, in reality the change of the emitted frequency is not linear . This leads to di f ficulties in analyzing the detected data . Furthermore , unwanted noise can disturb the measurement .

It is an obj ective to provide a method for detecting a distance and a relative velocity of a target using an FMCW laser device with an improved accuracy . It is further an obj ective to provide a device for detecting a distance and a relative velocity of a target with an improved accuracy .

These obj ectives are achieved by the subj ect matter of the independent claims . Further developments and embodiments are described in dependent claims .

According to at least one embodiment of the method for detecting a distance and a relative velocity of a target using an FMCW laser device , the method comprises transmitting FMCW laser radiation by the laser device . This can mean, that the laser device emits continuous laser radiation . The frequency of the emitted laser radiation changes with time . Thus , the laser radiation is frequency-modulated . The laser device can transmit the FMCW laser radiation to a region outside of the laser device . For example , the laser device transmits the FMCW laser radiation in the direction of the target . The laser device can comprise a laser source . The laser device can have a cavity . In the cavity laser radiation can be generated . The laser device can comprise any type of laser source , for example a vertical-cavity surface-emitting laser (VCSEL ) . The target can be arranged at a particular distance to the laser device . The target and the laser device can move relative to each other . Thus , seen from the laser device , the target can have a relative velocity .

The method further comprises receiving a reflection signal comprising FMCW laser radiation reflected at the target . The reflection signal can comprise FMCW laser radiation emitted by the laser device and reflected at the target . The reflection signal can be received by the cavity of the laser device . It is also possible that the reflection signal is received by a component outside of the laser device , for example a receiving device .

The method further comprises mixing the reflection signal with FMCW laser radiation to a mixed signal . That the reflection signal is mixed with FMCW laser radiation can mean, that the reflection signal is superimposed with FMCW laser radiation to a mixed signal . For obtaining the mixed signal , the reflection signal can be mixed with FMCW laser radiation emitted by the laser device . For obtaining the mixed signal the reflection signal can be mixed with FMCW laser radiation emitted by the laser device and not reflected at the target . The reflection signal can be mixed with FMCW laser radiation within the cavity of the laser device . It is also possible that the reflection signal is mixed with FMCW laser radiation outside of the laser device , for example in a receiving device .

The method further comprises detecting the mixed signal , wherein the mixed signal has a time scale . That the mixed signal is detected can for example mean that it is recorded and/or stored . The mixed signal can be detected with an optical detector . That the mixed signal has a time scale can mean that the mixed signal has a time axis . The mixed signal can be detected at di f ferent points in time . In this way, the mixed signal has a time scale . The mixed signal can vary with time . That the mixed signal is detected at di f ferent points in time can mean that the mixed signal is sampled .

The method further comprises resampling the time scale of the mixed signal by time warping . That the time scale of the mixed signal is resampled by time warping can mean, that the detected mixed signal is further processed . During this further processing the time scale of the mixed signal is changed by time warping . Time warping can mean that the time scale of the mixed signal is realigned . This can mean, that data points of the time-warped mixed signal are assigned to di f ferent points in time than in the mixed signal . Thus , the time scale of the mixed signal can be changed . Time warping is a known way in adj usting a time scale for the case that two signals of di f ferent measurement speeds are present . Time warping can be achieved in di f ferent ways . The method described herein is not limited to any of these ways .

In many cases , laser devices that emit FMCW laser radiation, can only emit laser radiation with a frequency varying in a nonlinear way . This means , for most laser devices the frequency of emitted laser radiation does not change in a linear way . Thus , in the mixed signal laser radiation with its frequency varying at at least two di f ferent speeds is mixed . The laser radiation of the reflection signal travels along a longer path before being mixed with FMCW laser radiation than the FMCW laser radiation with which it is mixed . Therefore , the frequency of the laser radiation of the reflection signal changes with a di f ferent speed than the frequency of the FMCW laser radiation with which the reflection signal is mixed . These two di f ferent speeds of the change in the frequency of the laser radiation leads to inaccuracies in determining the distance and the relative velocity of the target .

In order to prevent these inaccuracies , in the method described herein time warping is employed . Time warping allows to reduce the ef fect that two di f ferent speeds of changing frequencies can have on the distance and relative velocity measurement . For determining the distance and the relative velocity of the target the mixed signal is analyzed . According to the method described herein, before analyzing the mixed signal in order to determine the distance and the relative velocity of the target , the time scale of the mixed signal is resampled by time warping .

With the time warping it is not only possible to change the time scale of the mixed signal which leads to an improved accuracy in determining the distance and the relative velocity of the target . The time warping also leads to a reduced relative amplitude of noise in the mixed signal . This leads to a more precise measurement of the distance and the relative velocity of the target and the signal-to-noise ratio is improved .

Employing time warping further has the advantage that it is achieved easier than for example adj usting the current for driving the laser device for achieving a more linear change in the frequency . The time warping can easily be implemented in the processing of the mixed signal and no elaborate processing or additional recording of data is required . Thus , a method for improving the accuracy of determining the distance and the relative velocity of a target is provided .

The laser device can be arranged within a vehicle . The target can be another vehicle or any other obj ect in the vicinity of the vehicle with the laser device . Moreover, the method can also be employed in other fields of surveillance , robotics or augmented and virtual reality . The method described herein is not limited to any of these examples .

According to at least one embodiment of the method the frequency of the FMCW laser radiation varies with time . This can mean, that the frequency of the FMCW laser radiation emitted by the laser device varies with time . In this way, a modulation of the emitted laser radiation is achieved .

According to at least one embodiment of the method the frequency of the FMCW laser radiation increases with time and subsequently decreases with time . This can mean, that the frequency of the FMCW laser radiation emitted by the laser device increases with time during a first time frame . The frequency of the FMCW laser radiation emitted by the laser device can decrease with time during a second time frame . The second time frame can follow immediately after the first time frame . The first timeframe and the second time frame can alternate . This can mean, that after the frequency decreased with time , the frequency increases again with time . During the first timeframe the frequency can increase with time according to the shape of a ramp . During the second time frame the frequency can decrease with time according to the shape of a ramp . During the first timeframe the frequency can be modulated upwards . During the second time frame the frequency can be modulated downwards . The modulation of the frequency of the emitted laser radiation enables to determine the distance and the relative velocity of the target from the mixed signal .

According to at least one embodiment of the method a number of fringes in the mixed signal is determined for one whole period of time during which the frequency of the FMCW laser radiation changes either upwards or downwards . This can mean, that a number of fringes in the mixed signal is determined during the first timeframe . It is also possible that a number of fringes in the mixed signal is determined during the second time frame . The fringes can be interferometric fringes . The number of fringes in the mixed signal during a particular timeframe divided by the length of this timeframe gives a parameter referred to as beat frequency . From the beat frequency the distance and the relative velocity of the target can be determined . How the distance and the relative velocity of the target can be determined from the beat frequency is for example described in : Mengkoung Veng : Sel fmixing interferometry for absolute distance measurement : modelling and experimental demonstration of intrinsic limitation . Micro and nanotechnologies/Microelectronics . Institut national polytechnique de Toulouse ( INPT ) , 2020 . In the method described herein a full modulation length, this means either the whole first timeframe or the whole second timeframe , can be employed to determine the beat frequency . This enables to determine the beat frequency with an improved accuracy .

According to at least one embodiment of the method in a calibration phase the steps of the method are carried out for a constant distance to the target . This can mean, that the laser device is arranged at a constant distance to the target . In the calibration phase the steps of the method can be carried out for a constant distance to the target several times . The calibration phase enables to characteri ze parameters of the laser device . These parameters can advantageously be employed later for processing detected data .

According to at least one embodiment of the method during the calibration phase the change of the frequency of the FMCW laser radiation with time is determined and deviations from a linear change of the frequency of the FMCW laser radiation are stored in a database . This can mean, that the change of the frequency of FMCW laser radiation with time emitted by the laser device is determined and deviations from a linear change of the frequency of FMCW laser radiation emitted by the laser device are stored in a database . For example , deviations from a linear change of the frequency of the FMCW laser radiation within the first timeframe and or within the second timeframe are stored in the database . Deviations from a linear change of the frequency of FMCW laser radiation can be a nonlinear change of the frequency of FMCW laser radiation . The calibration phase can thus be employed to characteri ze the laser device and how its emission of laser radiation deviates from a linear change of the frequency of the emitted radiation . This information can advantageously be employed for the time warping .

According to at least one embodiment of the method the stored deviations are employed for the time warping . This can mean that the time warping is based on the particular characteristics of the laser device . In particular, the time warping can be based on the determined deviations from a linear change of the frequency of emitted laser radiation . Since the deviations from a linear change of the frequency of laser radiation emitted by the laser device only depend on speci fic features of the laser device , the deviations can be determined during the calibration phase and they can later be employed for the measurement of the distance and the relative velocity of the target . Thus , the parameters required for the time warping only need to be determined once . Therefore , the method enables to improve the accuracy of determining the distance and the relative velocity of the target in a simple way .

According to at least one embodiment of the method the mixed signal is formed within the cavity of the laser device by mixing the reflection signal with FMCW laser radiation generated in the cavity . This means , the method can be employed for sel f mixing interferometry . In this case , FMCW laser radiation emitted by the laser device and reflected at the target returns into the cavity of the laser device . In the cavity, the reflection signal and FMCW laser radiation generated in the cavity can be mixed with each other . In this way, the mixed signal is formed . Employing sel f mixing interferometry has the advantage that the distance and the relative velocity of the target can be determined from the mixed signal .

According to at least one embodiment of the method the mixed signal is formed outside of the cavity of the laser device by mixing the reflection signal and FMCW laser radiation that propagated along a shorter pathway than the laser radiation of the reflection signal . This can be achieved by splitting FMCW laser radiation emitted by the laser device into at least first laser radiation and second laser radiation . The first laser radiation can be transmitted towards the target and reflected at the target . The second laser radiation can be transmitted to a receiving device . The part of the first laser radiation being reflected at the target and returning to the receiving device can be the reflection signal . In the receiving device the mixed signal can be formed . From the mixed signal advantageously the distance and the relative velocity of the target can be determined .

According to at least one embodiment of the method the mixed signal is detected with a photodetector . The photodetector can be a photodiode . The photodetector can be arranged adj acent to the cavity of the laser device or the photodetector can be arranged within the receiving device . Detecting the mixed signal enables to analyze the mixed signal so that the distance and relative velocity of the target can be determined .

According to at least one embodiment of the method the time warping is based on a Bezier curve with at least three control points . The Bezier curve can be a convex Bezier curve . The three control points can be fixed as follows . A first control point can be fixed at the beginning of a first timeframe or the beginning of a second timeframe . The second control point can be anywhere in the plane , as long as it is between the first and third control point . The third control point can be fixed at the end of the respective timeframe . In order to determine the positions of the second control point and the third control point a minimi zation routine can be employed . The minimi zation routine can be chosen to optimi ze at least one parameter, for example to reduce the hori zontal standard deviation of the estimated beat frequency, to maximi ze the height of the beat frequency peak, or to optimi ze the prominence of the beat frequency peak .

The time warping uses an interpolation approach to resample the mixed signal to a new time scale . This interpolation can be done with a linear or cubic signal interpolation . In the mixed signal before time warping, the time is linearly increasing, this means the di f ference between time points of the time scale is constant . In the time warped mixed signal the di f ference between time points of the time scale is not constant , this can mean that the di f ference between time points of the time scale changes along the time scale . For example , at first the di f ference between time points of the time scale is smaller than for the mixed signal before time warping and at a later time point along the time scale of the mixed signal the di f ference between time points of the time scale is larger than for the mixed signal before time warping . Thus , the time scale can be squeezed at the beginning and stretched at the end . It is however also possible that the time scale is stretched first and then squeezed . Therefore , using a signal interpolation approach, the mixed signal that initially had constant distances between time points along its time scale is resampled to a signal that has this warped time scale . With this , a time warping leading to an improved accuracy of determining the distance and the relative velocity of the target can be determined .

According to at least one embodiment of the method the time warping is based on a parameteri zed log-trans formation . The interpolation via log-trans formation follows the same mechanic as the time warping based on a Bezier curve . Just the estimation of the line of the new time scale is done via a log function, and not via the Bezier curve with three control points . However, the Bezier control points can be chosen in such a way that they follow exactly the logtrans formation . Therefore , the log-trans formation could be considered as a sub-category of the time warping based on a Bezier curve . The advantage of the log-trans formation is that only one parameter needs to be estimated in order to determine the new time scale .

According to at least one embodiment of the method the distance and the relative velocity of the target are determined from a frequency of fringes in the mixed signal . It is necessary to determine the number of fringes in the mixed signal for one whole period of time during which the frequency of the FMCW laser radiation changes upwards and for one whole period of time during which the frequency of the FMCW laser radiation changes downwards .

Furthermore , a device for detecting a distance and a relative velocity of a target is provided . The device for detecting a distance and a relative velocity of a target can preferably be employed for the method described herein . This means all features disclosed for the method for detecting a distance and a relative velocity of a target using an FMCW laser device are also disclosed for the device for detecting a distance and a relative velocity of a target and vice-versa .

According to at least one embodiment of the device for detecting a distance and a relative velocity of a target , the device comprises an FMCW laser device that is configured to transmit FMCW laser radiation .

The device further comprises a mixing region, wherein the mixing region is configured to receive a reflection signal comprising FMCW laser radiation reflected at the target . The mixing region can be arranged within the cavity of the FMCW laser device . It is also possible that the mixing region is arranged outside of the cavity of the FMCW laser device , for example in a receiving device .

The device further comprises a detection unit that is configured to detect a mixed signal formed in the mixing region by mixing the reflection signal with FMCW laser radiation, wherein the mixed signal has a time scale . The detection unit can be comprised by the receiving device .

The device further comprises a processing unit that is configured to resample the time scale of the mixed signal by time warping .

With the device the method described herein can be carried out . Therefore , the device has the same advantages as described with the method .

The following description of figures may further illustrate and explain exemplary embodiments . Components that are functionally identical or have an identical ef fect are denoted by identical references . Identical or ef fectively identical components might be described only with respect to the figures where they occur first . Their description is not necessarily repeated in successive figures .

With figure 1 an exemplary embodiment of the method for detecting a distance and a relative velocity of a target using an FMCW laser device is described .

In figure 2 a mixed signal is plotted .

Figure 3 shows the power spectral density of a mixed signal .

Figure 4 shows the short time Fourier trans form of a mixed signal .

With figure 5 the resampling of the time scale is described .

Figure 6 shows the short time Fourier trans form of several mixed signals .

Figure 7 shows the power spectral density of a mixed signal as shown in figure 6 .

Figure 8 shows the short time Fourier trans form of several mixed signals after time warping.

Figure 9 shows the power spectral density of a mixed signal as shown in figure 8 after time warping . Figure 10 shows an exemplary embodiment of the device for detecting a distance and a relative velocity of a target .

With figure 1 an exemplary embodiment of the method for detecting a distance and a relative velocity of a target 21 using an FMCW laser device 20 is described . In a first step S I of the method FMCW laser radiation LR is transmitted by the laser device 20 . The frequency f of the FMCW laser radiation LR increases with time and subsequently decreases with time .

In a second step S2 of the method a reflection signal RS comprising FMCW laser radiation LR reflected at the target 21 is received .

In a third step S3 of the method the reflection signal RS is mixed with FMCW laser radiation LR to a mixed signal MS . The mixed signal MS can be formed within the cavity 22 of the laser device 20 by mixing the reflection signal RS with FMCW laser radiation LR generated in the cavity 22 or the mixed signal MS can be formed outside of the cavity 22 of the laser device 20 by mixing the reflection signal RS and FMCW laser radiation LR that propagated along a shorter pathway than the laser radiation of the reflection signal RS .

In a fourth step S4 of the method the mixed signal MS is detected, wherein the mixed signal MS has a time scale . The mixed signal MS can be detected with a photodetector .

In a fi fth step S5 of the method the time scale of the mixed signal MS is resampled by time warping . For example , the time warping can be based on a Bezier curve with at least three control points or the time warping can be based on a parameteri zed log- trans format ion .

In a calibration phase before the first step S I is carried out , the steps of the method can be carried out for a constant distance to the target 21 . During the calibration phase the change of the frequency f of the FMCW laser radiation LR with time is determined and deviations from a linear change of the frequency f of the FMCW laser radiation LR are stored in a database . The stored deviations can be employed for the time warping in the fi fth step S5 of the method .

The distance and the relative velocity of the target 21 are determined from a frequency f of fringes in the mixed signal MS , namely from the frequency for an upwards modulation and the frequency of a downwards modulation of the FMCW laser radiation . Advantageously, with the method a number of fringes in the mixed signal MS can be determined for one whole period of time during which the frequency f of the FMCW laser radiation LR changes either upwards or downwards .

In figure 2 a mixed signal MS is plotted . The mixed signal MS can be detected with the method described herein . The mixed signal MS is obtained by sel f mixing interferometry . On the x-axis the time is plotted . On the y-axis the power emitted by the laser device 20 is plotted . Figure 2 shows that at first the power increases with time . During this period, the frequency f of emitted FMCW laser radiation LR increases . Afterwards , the power decreases with time . During this period, the frequency f of emitted FMCW laser radiation LR decreases . Over both periods the mixed signal MS shows interference fringes . These fringes occur due to the interference of the reflection signal RS and FMCW laser radiation LR generated within the cavity 22 .

Figure 3 shows the power spectral density of a mixed signal MS . In particular, figure 3 shows the power spectral density of that part of the mixed signal MS shown in figure 2 where the frequency f of emitted FMCW laser radiation LR increases , thus of the first period of the mixed signal MS of figure 2 . On the x-axis the frequency f is plotted . On the y-axis the amplitude is plotted . At several frequencies f peaks larger than the noise level are visible . From figure 3 it is not straightforward to distinguish the peak relating to a beat frequency BF from peaks relating to noise .

Figure 4 shows the short time Fourier trans form of the first period of the mixed signal MS of figure 2 . This means , during this first period, the frequency f of emitted FMCW laser radiation LR increases with time . On the x-axis the frequency f is plotted . On the y-axis the time is plotted . The amplitude is depicted on a bright to dark scale . Thus , regions that appear darker have a higher amplitude . The peak on the very left shows a change in frequency f with time . This peak relates to the beat frequency BF . Thus , the beat frequency BF changes with time . A beat frequency BF changing with time leads to the measurement of the distance and the relative velocity of the target 21 being less accurate . The frequency f of the other peaks on the right side does not change with time . Therefore , these peaks relate to noise .

With figure 5 the resampling of the time scale is described . On the x-axis a reference time is plotted . On the y-axis a warped time is plotted . The straight line is the time scale before the time warping . Thus , before time warping, the time scale linearly increases with time . The bent line is the time scale after time warping . The time scale after time warping follows a Bezier curve defined by the three control points that are marked by stars .

Figure 6 shows the short time Fourier trans form of several mixed signals MS without time warping . On the x-axis the frequency f is plotted . On the y-axis the time is plotted . The amplitude is plotted in the third dimension . Thus , regions that appear brighter have a higher amplitude . In figure 6 several of the first periods shown in figure 4 follow after one another . Therefore , the peak on the very left has several regions where the beat frequency BF increases with time . These di f ferent regions follow after one another with time . As in figure 4 , on the right side noise peaks are visible whose frequency f does not change with time .

Figure 7 shows the power spectral density of one of the mixed signals MS of figure 6 . On the x-axis the frequency f is plotted . On the y-axis the amplitude is plotted . As in figure 3 , at several frequencies f peaks larger than the noise level are visible . The peak relating to the beat frequency BF on the very left is broader than the noise peaks .

Figure 8 shows the short time Fourier trans form of several mixed signals MS after time warping. This means , before carrying out the Fourier trans formation, the time scale of the mixed signal MS is resampled by time warping . On the x- axis the frequency f is plotted . On the y-axis the time is plotted . The amplitude is plotted in the third dimension . Thus , regions that appear brighter have a higher amplitude . As in figure 6 , several of the first periods shown in figure 4 follow after one another in figure 8 . However, because of the time warping the beat frequency BF does not change with time . Thus , the peak relating to the beat frequency BF is more narrow or more coherent .

Another ef fect of the time warping is that for the peaks relating to noise , the time scale is changed as well . This leads to a broadening of these peaks . The peaks relating to noise are less coherent . Therefore , in figure 8 the peaks relating to noise are less visible than for example in figures 6 . The method described herein thus also has the advantage that the signal-to-noise ratio is improved .

Figure 9 shows the power spectral density of one of the mixed signals MS of figure 8 . On the x-axis the frequency f is plotted . On the y-axis the amplitude is plotted . After time warping the amplitude of the peak relating to the beat frequency BF is signi ficantly increased in comparison to the rest of the signal . The noise peaks cannot be di f ferentiated from the noise level anymore . Therefore , after time warping the peak relating to the beat frequency BF can easily be identi fied in the power spectral density plot . In this way, less errors are introduced in the measurements and outliers can be identi fied more easily . Therefore , the accuracy of determining the distance and the relative velocity of the target 21 is increased .

Due to the broadening of the noise peaks , the noise level of the power spectral density is increased in the region of the noise peaks . To counter this unwanted ef fect , the power spectral density can be detrended . This detrending can for example be done with a low degree polynomial . Figure 10 shows an exemplary embodiment of the device 24 for detecting a distance and a relative velocity of a target 21 . The device 24 comprises an FMCW laser device 20 that is configured to transmit FMCW laser radiation LR . The FMCW laser radiation LR is transmitted towards the target 21 which is arranged outside of the device 24 . The device 24 further comprises a mixing region 23 , wherein the mixing region 23 is configured to receive a reflection signal RS comprising FMCW laser radiation LR reflected at the target 21 . In this embodiment the mixing region 23 is arranged within the cavity 22 of the FMCW laser device 20 . The device 24 further comprises a detection unit 25 that is configured to detect a mixed signal MS formed in the mixing region 23 by mixing the reflection signal RS with FMCW laser radiation LR, wherein the mixed signal MS has a time scale . The mixed signal MS can be transmitted by the FMCW laser device 20 to the detection unit 25 . The device 24 further comprises a processing unit 26 that is configured to resample the time scale of the mixed signal MS by time warping . The processing unit 26 is connected with the detection unit 25 .

It will be appreciated that the disclosure is not limited to the disclosed embodiments and to what has been particularly shown and described hereinabove . Rather, features recited in separate dependent claims or in the description may advantageously be combined . Furthermore , the scope of the disclosure includes those variations and modi fications , which will be apparent to those skilled in the art . The term " comprising" , insofar it was used in the claims or in the description, does not exclude other elements or steps of a corresponding feature or procedure . In case that the terms " a" or " an" were used in conj unction with features , they do not exclude a plurality of such features . Moreover, any reference signs in the claims should not be construed as limiting the scope .

This patent application claims the priority of German patent application 102022127898 . 0 , the disclosure content of which is hereby incorporated by reference .

References

20 laser device

21 target 22 cavity

23 mixing region

24 device

25 detection unit

26 processing unit BF beat frequency f frequency

LR FMCW laser radiation

MS mixed signal

RS reflection signal S 1-S5 steps