SE545475C2 - A method, computer program product, system and radar arrangement for resolving range and velocity information - Google Patents
A method, computer program product, system and radar arrangement for resolving range and velocity informationInfo
- Publication number
- SE545475C2 SE545475C2 SE2000074A SE2000074A SE545475C2 SE 545475 C2 SE545475 C2 SE 545475C2 SE 2000074 A SE2000074 A SE 2000074A SE 2000074 A SE2000074 A SE 2000074A SE 545475 C2 SE545475 C2 SE 545475C2
- Authority
- SE
- Sweden
- Prior art keywords
- velocity
- baseband signal
- quotient
- time intervals
- target
- Prior art date
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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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/06—Systems determining position data of a target
- G01S13/08—Systems for measuring distance only
- G01S13/32—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated
- G01S13/34—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated using transmission of continuous, frequency-modulated waves while heterodyning the received signal, or a signal derived therefrom, with a locally-generated signal related to the contemporaneously transmitted signal
- G01S13/343—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated using transmission of continuous, frequency-modulated waves while heterodyning the received signal, or a signal derived therefrom, with a locally-generated signal related to the contemporaneously transmitted signal using sawtooth modulation
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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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/50—Systems of measurement based on relative movement of target
- G01S13/58—Velocity or trajectory determination systems; Sense-of-movement determination systems
- G01S13/583—Velocity or trajectory determination systems; Sense-of-movement determination systems using transmission of continuous unmodulated waves, amplitude-, frequency-, or phase-modulated waves and based upon the Doppler effect resulting from movement of targets
- G01S13/584—Velocity or trajectory determination systems; Sense-of-movement determination systems using transmission of continuous unmodulated waves, amplitude-, frequency-, or phase-modulated waves and based upon the Doppler effect resulting from movement of targets adapted for simultaneous range and velocity measurements
-
- 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
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/023—Interference mitigation, e.g. reducing or avoiding non-intentional interference with other HF-transmitters, base station transmitters for mobile communication or other radar systems, e.g. using electro-magnetic interference [EMI] reduction techniques
-
- 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
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/35—Details of non-pulse systems
- G01S7/352—Receivers
- G01S7/354—Extracting wanted echo-signals
-
- 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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/93—Radar or analogous systems specially adapted for specific applications for anti-collision purposes
- G01S13/931—Radar or analogous systems specially adapted for specific applications for anti-collision purposes of land vehicles
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- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Computer Networks & Wireless Communication (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
The present disclosure relates to a chirp Doppler processing method for resolving range and velocity information, the method (100) comprising the steps of determining (160) an angular beat frequency based on a Fourier transform of a formed (130) baseband signal, and determining (170) a velocity of a target based on the determined angular beat frequency. Determining (170) target velocity comprises:- forming a first quotient between complex amplitudes for a first set of time intervals and a second set of time intervals and the determined angular beat frequency, said complex amplitudes numerically calculated based on an analytical expression for the Fourier transformed baseband signal.- forming a second quotient between the analytical expression for the Fourier transformed baseband signal at the angular beat frequency for said time intervals, and- determining the target velocity by finding the velocity (v) for which the complex distance between the first quotient and the second quotient is minimized.
Description
TECHNICAL FIELD
The present disclosure relates to a method and system for resolving range and velocity information. The disclosure also relates to a computer program product to perform the method and to a radar
arrangement comprising such a system.
BACKGROUND
Doppler radar is a specialized radar that uses the Doppler effect to produce velocity data about objects at a distance. Doppler radar does this by bouncing an electromagnetic waveform off a desired target and analysing how the object's motion has altered the frequency of the returned signal. During the 19405 continuous-wave Doppler radar systems arranged to transmit continuously were developed. These continuous-wave Doppler radars generate signal information indicative of the target's velocity, however, the signal information characteristically comprises a velocity-range ambiguity making it problematic to determine both target range and velocity. Pulse-wave Doppler radar combines the features of pulse radars and continuous-wave radars, which were historically separated due to the complexity of the electronics required. Pulse-wave Doppler radar determines the range to a target using pulse-timing techniques and determines the target object's velocity using
the Doppler effect of the returned signal.
Frequency-modulated continuous wave radar is a special type of radar that transmits continuous transmission power like a continuous wave radar. In contrast to the typical continuous wave radar, the frequency-modulated continuous wave radar can change its operating frequency during the measurement. The frequency-modulated continuous wave radar may be arranged to sweep the transmitted frequency across a frequency band, such a signal with constantly decreasing or
constantly increasing frequency is called a chirp or sweep signal.
With an increased prevalence of radar systems able to resolve velocity and range in vehicles, interference between radar systems becomes an increasing concern. A goal in a scenario with multiple radar systems is to maximize the number of radar systems of the same type that may be able operate in the same frequency band with minimizing interferences. The currently dominant
automotive radar method utilizes fast chirp modulation for which the number of radar systems able
to share a frequency band may become a limiting factor for practical use. There is a demand for methods and systems for resolving velocity and range information with improved frequency band
cohabitation.
SUMMARY
An object of the present disclosure is to provide a solution for resolving range and velocity information from a single frequency moduiated chirp wherein some of the problems with prior art
technologies are mitigated or at least alleviated.
The disclosure proposes a chirp Doppler processing method for resolving range and velocity information, the method comprising the steps of transmitting an electromagnetic
waveform comprising at least one frequency moduiated chirp, obtaining a time domain signal (sn) indicative of a received electromagnetic waveform reflected off a target, and forming a baseband
signal (sß) based on the obtained signal (sR).
A time interval of the baseband signal (sß) is selected, wherein said time interval corresponds to at least a part of one chirp, an angular beat frequency (Ohm) of the baseband signal (sß) in said time interval is determined based on a Fourier transform of the baseband signal (sa) in said time interval, a velocity (vestimate) of the target is determined, and a range (ro) to the target may be determined based
on the determined angular beat frequency (Qbeat) and the determined target velocity (vestimate).
The determination of the velocity (vestimate) of the target comprises:
- forming a first set of time intervals and a second set of time intervals within the selected time interval,
- calculating the complex amplitude of the Fourier transformed baseband signal (sBFT(Q)) at the determined angular beat frequency (Qbeat) for each time interval of the first and the second set of time intervals, wherein the complex amplitude is calculated based on a complex-valued function of angular frequency, said complex valued function corresponding to an analytical expression for the Fourier transformed baseband signal (sJT(Q)),
- forming a first quotient between the calculated complex amplitudes for the first set of time intervals and the second set of time intervals,
- forming a second quotient between the analytical expression for the Fourier transformed baseband signal at the angular beat frequency (sBFWQbeaJ) corresponding to the first set of time intervals and
the second set of time intervals, wherein the second quotient is a function of velocity (v), and
- determining the target velocity (vestimate) by finding the velocity (v) for which the complex distance
between the first quotient and the second quotient is minimized.
This has the advantage of allowing target velocity and target range to be resolved from a single frequency modulated chirp. This further has the advantage of allowing the use of slow chirps whereby the number of cohabitating systems transmitting and receiving chirps may be increased
without causing interference between systems. A set of time intervals may consist of a single time interval.
According to some aspects, calculating the complex amplitude utilizes a discrete Fourier transform
corresponding to the analytical expression for the Fourier transformed baseband signal (sBFT(Q)).
This has the advantage of allowing the analytical expression comprising an integral to be estimated
based on the finite sequence of equally-spaced samples of the baseband signal.
According to some aspects, forming a baseband signal comprises forming at least two velocity channels each with a different digital frequency offset of the signal. For each velocity channel,
determine angular beat frequency, determine target velocity, and determine target range.
This has the advantage of allowing a baseband signal for which range and velocity information may be accurately resolved within a first range of velocities to accurately determined range and velocity within additional ranges of velocities by forming offset baseband signals. ln some embodiments a baseband signal would be suitable for velocities 120 m/s, forming three velocity channels may
accurately estimate velocities 160 m/s (-60 to -20, -20 to 20, and 20 to 60 m/s).
The present disclosure also relates to a computer program product comprising a non-transitory computer-readable storage medium having thereon a computer program comprising program instructions. The computer program being loadable into a processor and configured to cause the
processor to perform the method according to what is presented herein.
The computer program corresponds to the steps performed by the method discussed above and
have all the associated effects and advantages of the disclosed method.
The present disclosure also relates to a system for resolving range and velocity information, the system comprising control circuitry comprising a computer. The control circuitry is arranged to communicate with a frequency-modulated continuous-wave radar providing a signal indicative of a
received electromagnetic waveform comprising at least one chirp. The computer is arranged to
obtain a time domain signal (sk) indicative of a received electromagnetic waveform reflected off a
target, and form a baseband signal (sß) based on the obtained signal (sR).
The computer is arranged to select a time interval of the baseband signal (sB), wherein said time interval corresponds to at least a part of one chirp, determine an angular beat frequency (Ohm) of the baseband signal (sa) in said time interval based on a Fourier transform of the baseband signal (sß) in said time interval, determine a velocity (vestimate) of the target (380), and may determine a
range (ro) to the target based on the determined angular beat frequency (Qbeat) and the determined
target velocity (vesfimate).
Determining the velocity (vestimm) of the target comprises:
- forming a first set of time intervals and a second set of time intervals within the selected time interval,
- calculating the complex amplitude of the Fourier transformed baseband signal (sBFT(Q)) at the determined angular beat frequency (Ohm) for each time interval of the first and the second set of time intervals, wherein the complex amplitude is calculated based on a complex-valued function of angular frequency, said complex valued function corresponding to an analytical expression for the Fourier transformed baseband signal (sBFT(Q)),
- forming a first quotient between the calculated complex amplitudes for the first set of time intervals and the second set of time intervals,
- forming a second quotient between the analytical expression for the Fourier transformed baseband signal at the angular beat frequency (sBWQbeaJ) corresponding to the first set of time intervals and the second set of time intervals, wherein the second quotient is a function of velocity (v), and
- determining the target velocity (vestimate) by finding the velocity (v) for which the complex distance
between the first quotient and the second quotient is minimized. The system corresponds to the steps performed by the method discussed above.
The present disclosure also relates to a radar arrangement comprising a frequency modulated radar
and a system for resolving range and velocity information according to what is presented herein.
BRIEF DESCRIPTION OF THE DRAWINGS
Fig. 1 shows schematically a method for method for resolving range and velocity information from a
chirp.
Fig. 2 depicts schematically a system for resolving range and velocity information from a chirp.
Fig. 3 depicts schematically a radar arrangement comprising a system for resolving range and velocity
information.
Fig. 4 depicts schematically a data processing unit comprising a computer program product.
DETAILED DESCRIPTION
Throughout the figures, same reference numerals refer to same parts, concepts, and/or elements. Consequently, what will be said regarding a reference numeral in one figure applies equally well to
the same reference numeral in other figures unless not explicitly stated otherwise.
Throughout the description angular frequency is used in equations describing the signals and the functions derived thereof. lt is to be understood that the equations herein may be modified to use temporal frequencies (f) by substituting angular frequencies with Zn times the corresponding
temporal frequencies (f), according to w = 2nf.
Fig. 1 shows schematically a method for method for resolving range and velocity information from a chirp. The method 100 comprises the steps of transmitting 110 an electromagnetic
waveform comprising at least one frequency-modulated chirp, obtaining 120 a time domain
signal (sk) indicative of a received electromagnetic waveform reflected off a target, and forminga baseband signal (sß) based on the obtained signal (sk).
The method further selecting 150 a time interval of the baseband signal (sß), wherein said time interval corresponds to at least a part of one chirp, determining 160 an angular beat frequency (Qbeat) of the baseband signal (sß) in said time interval based on a Fourier transform of the baseband signal (sß) in said time interval, and determining 170 a velocity (Vest-unite) of the target. The method may further comprise determining 190 a range (remmate) to the target based on the determined angular
beat frequency (Qbeat) and the determined target velocity (vesflmate).
The determination 170 of the velocity (vestimate) of the target comprises:
- forming a first set of time intervals and a second set of time intervals within the selected time interval,
- calculating the complex amplitude of the Fourier transformed baseband signal (sB"(Q)) at the determined angular beat frequency (Ohm) for each time interval of the first and the second set of time intervals, wherein the complex amplitude is calculated based on a complex-valued function of angular frequency, said complex valued function corresponding to an analytical expression for the
Fourier transformed baseband signal (sßFT(Q)),
- forming a first quotient between the calculated complex amplitudes for the first set of time intervals and the second set of time intervals,
- forming a second quotient between the analytical expression for the Fourier transformed baseband signal at the angular beat frequency (sBWQbeaJ) corresponding to the first set of time intervals and the second set of time intervals, wherein the second quotient is a function of velocity (v), and
- determining the target velocity (vesflmate) by finding the velocity (v) for which the complex distance
between the first quotient and the second quotient is minimized. A set of time intervals may consist of a single time interval.
The term baseband signal is the resulting signal of down converting the received signal by the transmitted signal. Down conversion corresponds mathematically to multiplying a signal with the
complex conjugate of the down conversion signal.
Transmitting 110 the electromagnetic waveform may comprise transmitting a single frequency
modulated chirp.
Transmitting 110 the electromagnetic waveform comprises transmitting at least one linear
frequency-modulated chirp.
ln some examples, the transmitted electromagnetic waveform is a single frequency modulated chirp,
and the selected interval corresponds to the single frequency modulated chirp.
ln some examples the baseband signal corresponds to a single linear frequency modulated chirp. The baseband signal may then be described according to Eq. 1, wherein ro is range, vis velocity, B is bandwidth, T is sweep time, wc is angular centre frequency, c is the speed of light, and C(r0,v) is a
function relating to target scattering amplitude.
4112811; 411811;
. B SBU) = C(r0,v)e-i[4ïT-'c'c2+( T cnwcäc-gír C zwg] (Eq 1)
ln these examples the Fourier transform of the baseband signal is defined according to Eq. 2, wherein a range function il: is described according to Eq. 3, and wherein angular frequency 0 is described
according to Eq.
.41rBv_ 1 T/z _- c( ,) _- r/z SÉTGI) = ;f_T/2 sB(t)e 'mdt = _TT°3-e ”f” LT/ze' T ct dt (Eq. 2) w Éfïßrå- Zwc) (Eqßl 41rB ro Z .Q-T:+2 CC (Eq.4)
The complex amplitude may be calculated based on a discrete Fourier transform corresponding to
the analytical expression for the Fourier transformed baseband signal (sßn(Q)).
ln some examples, calculating the complex amplitude of the Fourier transformed baseband
signal (sBFT(Q)) at the determined angular beat frequency (Ohm) utilizes an estimation according to Eq. 5, wherein AT is sample interval. ln these examples, the complex amplitudes of the analytical expression in Eq. 2 may be estimated from the baseband signal based on a finite sequence of equally-
spaced samples.
SB (mAT) e -iQmAT
SETUI) E Éfm siflfleflmdr ~ ”Em” (Eqß)
-T/z ? m=-T/2AT
The first quotient may be formed by dividing the sum of the complex amplitudes for the first set of time intervals with the corresponding sum for the second set of time intervals. ln the examples relating to Eq. 6 the first set of time intervals comprise the interval -T/2 to -T/4 and the interval
T/4 to T/
For each formed time interval, a complex amplitude may be calculated for the determined angular beat frequency. At least some calculated complex amplitudes may be used to form the first quotient. ln a preferred embodiment the first set of time intervals and the second set of time intervals are of substantially equal length, and the second set of time intervals consists of a time interval of half the selected time interval length centred around zero (t =0), and the first set of time intervals
corresponds to the time remaining edge intervals furthest from zero.
ln some examples, the first quotient is formed according to Eq. 6, wherein the first quotient is constant for a specific angular beat frequency and measured baseband signal. ln these examples, the selected time interval corresponds to the whole chirp with the sweep time T. The four complex amplitudes in Eq. 6 each correspond to an interval covering a fourth of the selected interval (-T/2 to T/2), wherein the sum of the complex amplitudes for the intervals furthest from zero, -T/2 to -T/4 and T/4 to T/2, are divided by the corresponding sum for the intervals closest to zero, -T/4 to 0 and
0 to T/4. ln this example, each complex amplitude is estimated according to Eq.
AT -T/4AT _- AT T :AT _- TXm:_T/ZATSB(mAT)e *ÛmAT+-,I-,-XTn/=T/4ATSB(mAT)e mmm'
AT _- AT 'r AT _- ?Z$n=_T/4ATs3(mAT)e ÜWÅT+?Z /4 sB(mAT)e *ÛTMT
Qdata _ (Eq- 6)
1I1=Forming the second quotient of the expression on the right hand side of Eq. 2 that describes the Fourier transform of the baseband signal, eliminates the functions relating to target scattering
amplitude C(r0,v) and the range function LI).
ln these examples, the corresponding second quotient may be described according to Eq. 7, wherein the second quotient is a function of velocity. ln Eq. 7 the integration of the interval furthest from zero, T/4 to T/2, is divided by the integration of the interval closest to zero, 0 to T/
.IT/z íÅ-flBVtZ
e T C dt Q(v) = ï/Ä .Mtßvtz fo ä? c a:
(Eq- 7)
ln a preferred embodiment, the first set of time intervals and the second set of time intervals of the second quotient correspond to the interval furthest from zero and the interval closest from zero respectively, and the sets of time intervals each cover substantially half the selected interval. The sets of time intervals of the preferred embodiment are due to the Fresnel integrals in Eq. 7 that for an integration interval concentrated around zero have a slow dependence on v, while the dependence on v increases as the integration interval is pushed outwards from zero. Thus with denominator integration interval at the edge and numerator integration interval closest to zero, the quotient becomes a good measure of velocity. A further aspect of the preferred embodiment is that the first and second set of time intervals should be substantially equally long to represent a similar spectral resolution, and the intervals should together cover the selected time interval for maximum
suppression of additive noise.
The velocity value minimizing the complex distance between the first and second quotient is
determined as the target velocity (vestimate), according to Eq.
'Qdata " = min => V = Vestimate (Eq- 8)
The method may determine 170 target velocity by finding the velocity value minimizing the phase
difference between the first and the second quotient.
Determining 190 target range (restimate) based on angular beat frequency and target velocity may
utilize Eq.
T restimate = Lä; (CO-beat _ zwcvestímate) (Eq- 9)
Forming 130 the baseband signal (sß) may comprise forming at least two velocity channels each with a different digital frequency offset of the signal, and wherein the method 100 for each velocity channel, determine 160 angular beat frequency, determine target velocity, and determine target range. ln some examples the method, provided a specific baseband signal is able to accurately resolve range and velocity information from -30 to 30 m/s from one chirp for one velocity channel.
By forming three velocity channels of said chirp with an offset corresponding to -60, 0, and 60 m/s (-
90 to -30, -30 to 30, and 30 to 90 m/s), whereby relative speeds from -90 to 90 m/s may be
accurately determined.
ln a preferred embodiment the step of selecting 150 the time interval of the baseband signal (sß)
comprises selecting the time interval corresponding to one whole chirp.
Determining 160 an angular beat frequency (Qbeat) may further comprise zero padding the baseband signal, and determining 160 the angular beat frequency is based on the zero-padded baseband signal. ln some examples, the baseband signal is zero-padded to at least twice the initial number of
points.
By zero padding is meant adding additional sample points to a signal, wherein the additional sample points have zero value. Zero padding a signal may relate to increasing the resolution of a direct
Fourier transform of said signal.
ln a preferred embodiment the selected interval has a bandwidth value and interval duration value, wherein the product of the bandwidth value, the interval duration value and a minimum detectable
target velocity divided by the speed of light is of unity order or larger, BTv/c >
In some examples, the selected interval has a bandwidth value and interval duration value, wherein the product of the bandwidth value, the interval duration value and the minimum detectable target
velocity divided by the speed of light is at least two, at least five, or at least ten.
Eq. 1 describes the baseband signal wherein a product of bandwidth, sweep time and velocity is in the exponent in a term corresponding to the Fresnel integral in Eq. 2, said the Fresnel integrals forming the second quotient used to determine the target velocity. lf said product divided by the speed of light is significantly below one then resolving the phase for the corresponding term in Eq.may be unachievable, thereby reducing the reliability of the method.
ln some examples, the selected interval duration is at least 5 milliseconds. ln some examples, the
selected interval duration is at least 10 milliseconds, or at least 20 milliseconds.
The angular beat frequency of the baseband signal in the selected interval may be determinedbased on a fast Fourier transform for an initial assessment of the angular beat frequency.
The determination 160 of the angular beat frequency may comprise identifying local modulus maxima by interpolation of the Fourier transform of the baseband signal. ln some examples, the
interpolation is based on a second order Taylor expansion.
Determining 160 an angular beat frequency (Qbeat) of the baseband signal (sB) in the selected time interval based on the Fourier transform of the baseband signal (sB) in said time interval may determining at least two angular beat frequency (Ohm) each corresponding to a local amplitude maxima in said Fourier transform, wherein each determined angular beat frequency (Ohm) may be used to determine a velocity and a range. ln some examples each determined angular beat
frequency (Qnear) may relate to a target that reflected the transmitted waveform.
The first quotient may be formed by at least three calculated complex amplitudes corresponding to the first and second set of time intervals. ln the examples relating to Eq. 6, the first quotient comprises four calculated complex amplitudes each corresponding to a formed time interval within the selected time interval -T/2 to T/2. ln these examples, the first set of time intervals comprises two time intervals at the edges of the selected time interval -T/2 to -T/4 and T/4 to T/2, and the second set of time intervals comprises two time intervals closest to zero -T/4 to 0 and 0 to T/4. ln these examples, the integral intervals, 0 to T/4 and T/4 to T/2, in the second quotient described in Eq.correspond to the first and second set of time intervals.
Determining 170 a velocity of the target may be based on forming a first quotient comprising
fractional Fourier integrals.
Determining 170 the velocity of the target may be based on forming the second quotient comprising
Fresnel integrals, wherein said Fresnel integrals are functions of velocity (v).
Fig. 2 depicts schematically a system for resolving range and velocity information from a chirp. The example system 200 comprises control circuitry 210 comprising a computer 220. The control circuitry 210 is arranged to communicate with a frequency-modulated continuous-wave radar 230 providing a signal indicative of a received electromagnetic waveform comprising at least one
frequency-modulated chirp.
The computer 220 is arranged to obtain a time domain signal (sn) indicative of a received electromagnetic waveform reflected off a target, and form 130 a baseband signal (sn) based on the
obtained signal (sn).
The computer 220 is arranged to select a time interval of the baseband signal (SB), wherein said time interval corresponds to at least a part of one chirp, determine an angular beat frequency (Qbeat) of the baseband signal (sa) in said time interval based on a Fourier transform of the baseband signal (sa)
in said time interval, and determine a velocity (vestimate) of the target. The computer 220 may bearranged to determine a range (remmfne) to the target based on the determined angular beat
frequency (Ohm) and the determined target velocity (vestimate).
Determining the velocity (vesfimate) of the target comprises:
- forming a first set of time intervals and a second set of time intervals within the selected time interval,
- calculating the complex amplitude of the Fourier transformed baseband signal (sBFT(Q)) at the determined angular beat frequency (Qbeaf) for each time interval of the first and the second set of time intervals, wherein the complex amplitude is calculated based on a complex-valued function of angular frequency, said complex valued function corresponding to an analytical expression for the Fourier transformed baseband signal (sBFT(Q)),
- forming a first quotient between the calculated complex amplitudes for the first set of time intervals and the second set of time intervals,
- forming a second quotient between the analytical expression for the Fourier transformed baseband signal at the angular beat frequency (sBWQbeaJ) corresponding to the first set of time intervals and the second set of time intervals, wherein the second quotient is a function of velocity (v), and
- determining the target velocity (vßfimate) by finding the velocity (v) for which the complex distance
between the first quotient and the second quotient is minimized.
The computer 220 may be arranged to, upon forming a baseband signal (sa), form at least two velocity channels each with a different digital frequency offset of the signal, and wherein the computer 220 is arranged to, for each velocity channel, determine angular beat
frequency, determine target velocity, and determine target range.
The system 200 and frequency-modulated continuous-wave radar 230 may be housed in a radar arrangement 260. ln some examples, the radar arrangement is comprised in a vehicle. ln some examples, the system 200 communicates with a plurality of frequency-modulated continuous-wave
rada rs
Fig. 3 depicts schematically a radar arrangement comprising a system for resolving range and velocity information. The example radar arrangement 300 comprises a frequency-modulated continuous- wave radar 330 arranged to transmit an electromagnetic waveform comprising a linear frequency modulated chirp towards a target 380, measure the reflected electromagnetic waveform and provide a corresponding signal to the signal processing system 310 for resolving range and velocity
information.The signal processing system 310 is arranged to obtain the signal and according to the present
disclosure resolve target range and target velocity. The signal processing system 310 may be the system 200 described in fig
Fig. 4 depicts schematically a data processing unit comprising a computer program product for determining an action for resolving range and velocity information from a chirp. Fig. 4 depicts a data processing unit 410 comprising a computer program product comprising a non-transitory computer- readable storage medium 412. The non-transitory computer-readable storage medium 412 having thereon a computer program comprising program instructions. The computer program is loadable into a data processing unit 410 and is configured to cause a processor 411 to carry out the method
for resolving range and velocity information from a chirp in accordance with the description of fig.
The data processing unit 410 may be comprised in a device 400. ln some examples, the device 400 is
the computation device comprised in the system described in fig. 2. The device 400 may be comprised in a radar arrangement. The device 400 may be comprised in a craft.
The device 400 may be part of a monitoring system in a craft.
Claims (1)
- Claims A chirp Doppler processing method for resolving range and velocity information, the method (100) comprising the steps of transmitting (110) an electromagnetic waveform comprising at least one frequency modulated chirp, obtaining (120) a time domain signal (sk) indicative ofa received electromagnetic waveform reflected off a target (380), and forming (130) a baseband signal (sß) based on the obtained signal (sk), characterized by selecting (150) a time interval of the baseband signal (sß), wherein said time interval corresponds to at least a part of one chirp, determining (160) an angular beat frequency (Qbeaf) of the baseband signal (sß) in said time interval based on a Fourier transform of the baseband signal (sß) in said time interval, determining (170) a velocity (vestimate) of the target (380), wherein said determining (170) comprises: - forming a first set of time intervals and a second set of time intervals within the selected time interval, - calculating the complex amplitude of the Fourier transformed baseband signal (s8FT(Q)) at the determined angular beat frequency (Qbeat) for each time interval of the first and the second set of time intervals, wherein the complex amplitude is calculated based on a complex-valued function of angular frequency, said complex valued function corresponding to an analytical expression for the Fourier transformed baseband signal (sB"(Q)), - forming a first quotient between the calculated complex amplitudes for the first set of time intervals and the second set of time intervals, - forming a second quotient between the analytical expression for the Fourier transformed baseband signal at the angular beat frequency (sBWQbeaJ) corresponding to the first set of time intervals and the second set of time intervals, wherein the second quotient is a function of velocity (v), and- determining the target velocity (vestimate) by finding the velocity (v) for which the complex distance between the first quotient and the second quotient is minimized. The method according to claim 1, further comprising the step of determining (190) a range (restimate) to the target (380) based on the determined angular beat frequency (Qbeat) and the determined target velocity (vestimate). The method according to claim 1 or 2, wherein the step of determining (160) the angular beat frequency (Qbeat) of the baseband signal (sß) further comprises zero-padding the baseband signal (sa) within said the selected time interval, whereupon said zero-padded baseband signal is Fourier transformed. The method according to any previous claim, wherein the step of determining (160) the angular beat frequency (Ohm) of the baseband signal (sß) comprises identifying local modulus maxima by interpolation of the Fourier transform of the baseband signal. The method according to any previous claim, wherein the transmitted electromagnetic waveform comprises at least one linear frequency-modulated chirp, and/or wherein the chirp bandwidth (B) and chirp duration (T) forms a time bandwidth product larger than unity. The method according to any previous claim, wherein the second quotient comprises Fresnel integrals, and said quotient is dependent on velocity (v), whereby the second quotient may be solved for the target velocity (vestimm). The method according to claim 6, wherein the first quotient comprises at least three complex amplitudes corresponding to the first and second set of time intervals, wherein the sum of the complex amplitudes for the first and second set of time intervals, respectively, forms the first quotient. The method according to any previous claim, wherein the complex amplitude is calculated based on a discrete Fourier transform corresponding to the analytical expression for the Fourier transformed baseband signal (sBFT(Q)). A computer program product comprising a non-transitory computer-readable storage medium (412) having thereon a computer program comprising program instructions, the computer program being loadable into a processor (411) and configured to cause the processor (411) to perform the method (100) for resolving range and velocity information according to any one of the preceding claims. A system for resolving range and velocity information, the system (200) comprising control circuitry (210) comprising a computer (220), wherein the control circuitry (210) is arranged to communicate with a frequency-modulated continuous-wave radar (230) providing a signal indicative ofa received electromagnetic waveform comprising at least one chirp, the computer (220) is arranged to obtain a time domain signal (sR) indicative of a received electromagnetic waveform reflected off a target (380), form a baseband signal (sa) based on the obtained signal (sk), select a time interval of the baseband signal (sB), wherein said time interval corresponds to at least a part of one chirp, determine an angular beat frequency (Ohm) of the baseband signal (sa) in said time interval based on a Fourier transform of the baseband signal (sß) in said time interval, and determine a velocity (vemmate) of the target (380), wherein said determining (170) comprises: - forming a first set of time intervals and a second set of time intervals within the selected time interval, - calculating the complex amplitude of the Fourier transformed baseband signal (sBFT(Q)) at the determined angular beat frequency (Qbeat) for each time interval of the first and the second set of time intervals, wherein the complex amplitude is calculated based on a complex-valued function of angular frequency corresponding to an analytical expression for the Fourier transformed baseband signal (sBFT(Q)), - forming a first quotient between the calculated complex amplitudes for the first set of time intervals and the second set of time intervals, - forming a second quotient between the analytical expression for the Fourier transformed baseband signal at the angular beat frequency (sBFWQbeaJ) corresponding to the first set of time intervals and the second set of time intervals, wherein the second quotient is a function of velocity (v), and - determining the target velocity (vesfimate) by finding the velocity (v) for which the complex distance between the first quotient and the second quotient is minimized.The system according to claim 10, wherein the computer (220) is arranged to determine a range (restimate) to the target (380) based on the determined angular beat frequency (Qbeat) and the determined target velocity (vestimate). The system according to claim 10 or 11, wherein the computer (220) is arranged to, upon forming a baseband signal (sa), form at least two velocity channels each with a different digital frequency offset of the signal, and wherein the computer (220) is arranged to, for each velocity channel, determine angular beat frequency (Ohm), determine target velocity (vestimate), and determine target range (restimate). A radar arrangement for resolving range and velocity information, the arrangement (300) comprising a frequency-modulated radar 330 arranged to transmit an electromagnetic waveform, and a system 310 for resolving range and velocity information according to any of claim 10 to 12, wherein the frequency-modulated radar 330 is arranged to provide a signal indicative of a received reflected electromagnetic waveform to the system 310.
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| Application Number | Priority Date | Filing Date | Title |
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| SE2000074A SE545475C2 (en) | 2020-04-07 | 2020-04-07 | A method, computer program product, system and radar arrangement for resolving range and velocity information |
| PCT/SE2021/050305 WO2021206613A1 (en) | 2020-04-07 | 2021-04-06 | A method, computer program product, system and radar arrangement for resolving range and velocity information |
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| SE2000074A SE545475C2 (en) | 2020-04-07 | 2020-04-07 | A method, computer program product, system and radar arrangement for resolving range and velocity information |
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| WO2021206613A1 (en) | 2021-10-14 |
| SE2000074A1 (en) | 2021-10-08 |
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