Process for determining the relative velocity between two moving objects

[0002] 1. Field of the Invention

[0003] The present invention relates to a process for determining the relative velocity in the radial direction between two moving objects, using linear frequency modulation with continuous frequency sweeps, a transmitted signal being multiplied by a received signal for the attainment of a resultant received signal, the phase change of which over a certain time is used to determine the relative velocity.

[0004] 2. Description of Related Art

[0005] A problem in determining the velocity where linear frequency modulation is used is to be able clearly to determine the phase difference. The phase change is normally only known at ±n·2π, where n is a positive integer.

[0006] The object of the present invention is to realize a process in which the phase difference can clearly be determined. The object of the invention is achieved by a process characterized in that the period length for successive frequency sweeps is varied and in that the difference in period length and corresponding phase change is used to determine the velocity. By studying the phase change over a time period which can be made significantly shorter than the period length for a frequency sweep, the phase change can be kept within a clear interval.

[0007] The relative velocity v is advantageously calculated from the relationship:

[0008] v=k·x/ΔT,

[0009] where x is the phase difference during the time ΔT and $k=\frac{c/2\pi }{2\alpha t_c+2f_0},\mathrm{where}$

[0010] c denotes the velocity of the light in air, α denotes the gradient of the frequency sweep, t_cdenotes the clock time and f₀denotes the carrier frequency of the signal.

[0011] The period length from a first to a second frequency sweep is changed by an amount less than or equal to the time difference which is required to be able clearly to determine the phase change on the basis of given limit values for distance apart, velocity and acceleration.

[0012] At least three successive frequency sweeps are expediently assigned a different period length.

[0013] In order to increase the accuracy in the velocity determination, the time interval during which the phase change is studied is progressively increased without any loss of clarity. An advantageous process is characterized in that phase changes, over and above for differences in period lengths, are studied for one or more period lengths and/or one or more added period lengths.

[0014] The invention shall be described in greater detail below with reference to appended drawings, in which:

[0015] FIG. 1 shows examples of an emitted and a received signal in the case of linear frequency modulation.

[0016] FIG. 2 shows examples of frequency sweeps of constant period length.

[0017] FIG. 3 shows examples of frequency sweeps according to the invention of varying period length.

[0018] FIG. 4 shows a diagrammatic example of a FMCW radar device, which can be used in the process according to the invention.

[0019] Firstly, an account is given below of the theory behind linear frequency modulation. The discussion then moves on to linear frequency modulation with continuous frequency sweeps, so-called “linear FMCW”.

[0020] In linear frequency modulation, a signal is ideally transmitted at the frequency f_t(t):

[0021] f_t(t)=f₀+αt, t≧0,

[0022] where α denotes the gradient of the frequency sweep and f₀the carrier frequency of the signal.

[0023] For an emitted frequency sweep, the argument Φ(t) for the transmitted signal can be written:

[0024] Φ(t)=2π₀∫^tf_r(ξ)dξ=Φ(0)+2π[f₀^t+{fraction (1/2 )}αt²]

[0025] In the time domain, the transmitted signal is:

[0026] α(t)=α₀sin[Φ(0)+2π(f₀^t+½αt²)]

[0027] The transmitted signal is reflected and received after the time τ and can be written:

[0028] b(t)=b₀sin[Φ(0)+2π(f₀(t−τ)+½α(t−τ)²)].t≧τ

[0029] The emitted signal has been denoted by 1 and the received by 2 in FIG. 1, which shows the frequency f as a function of the time t. The transit time from the transmitter to the receiver is represented by τ.

[0030] If the transmitted signal and the received signal are multiplied, sorting out the high frequency sub-signal, the resulting signal will, by applying Euler's formula for exponential functions, be:

[0031] c(t)=c₀cos[2π(f₀τ+αtτ−½ατ²)], t>τ

[0032] In the case of linear FMCW modulation, the sweep is allowed to proceed for a certain time, after which the procedure is repeated. FIG. 2 shows examples of linear FMCW modulation with frequency sweeps of constant period length. An emitted sweep is shown by an unbroken line, whilst a return sweep has been shown by a dotted line. The frequency sweeps have been numbered with the index i.

[0033] The instant of each sweep is denoted by t and is regarded as local, with t=0 for the start of each frequency sweep. The actual instant which is global is denoted by T. An object or target in the radial direction at the instant t of the frequency sweep and in respect of frequency sweep i, with the velocity v and the constant acceleration α parallel to the direction of the signal, is parametrized according to:

[0034] r(t)=r_i+vt+½αt²

[0035] r_i=r(0)

[0036] applicable where i is fixed.

[0037] This gives:

[0038] τ_i+2r_i/c+2vt/c+αt²/c,

[0039] where c is the velocity of the light in the medium (air).

[0040] The resultant received signal, substituted by τ_i, can be written: $c_i\left(t\right)=c_0\cos \left[2\pi \left[\frac{2\alpha r_{i}t\left(1-\frac{2v}{c}-\frac{\alpha t}{c}\right)}{c}+\frac{f_{0}t\left(2v+\alpha t\right)}{c}+\frac{2\alpha v{t}^2\left(1-\frac{v}{c}\right)}{c}+\frac{2\alpha \alpha t^3\left(1-\frac{2v}{c}-\frac{\alpha t}{2c}\right)}{c}+\frac{2r_i\left(f_0-\frac{\alpha r_i}{c}\right)}{c}\right]\right],t\ge r$

[0041] The frequency for a received sweep i, f_i, for the resultant received signal, can be written: $f_i\left(t\right)=\frac{d}{dt}\left(\frac{2\alpha r_{i}t\left(1-\frac{2v}{c}-\frac{\alpha t}{c}\right)}{c}+\frac{f_{0}t\left(2v+\alpha t\right)}{c}+\frac{2\alpha v{t}^2\left(1-\frac{v}{c}\right)}{c}+\frac{2\alpha \alpha t^3\left(1-\frac{2v}{c}-\frac{\alpha t}{2c}\right)}{c}\right)=\frac{1}{c}\left[2\alpha r_i\left(1-\frac{2v}{c}\right)+2v{f}_0-\left(\frac{4\alpha r_i\alpha }{c}+2f_0+4\alpha v\left(1-\frac{v}{c}\right)\right)t+6\alpha \alpha \left(1-\frac{2v}{c}\right)t^2-\frac{8\alpha {\alpha }^2}{2c}{t}^3\right]$

[0042] For small values of t, consideration being given to incorporated terms, the expression of the frequency f_ican be simplified without deviating substantially from the actual frequency. The following simplified expression of the frequency can be drawn up:

[0043] f_i(t)=l/c[2αr_i+2vf₀+4αvt].

[0044] We further note that (ar_i/c)/f₀has a small value, thereby legitimately enabling the resultant received signal to be simplified to:

[0045] c_i(t)=c₀cos[2π[2αr_it/c+f₀t2v/c+2αvf−/c+2r₁f₀/c]], t≧τ

[0046] After a certain clock time t_c, see FIG. 1, a first of a plurality of samples is taken of the signal. The argument Θ_ifor the resultant received signal is referred to as the phase and can be written:

[0047] Θ_i=2π[2αr_it_c/c+f₀t_c2v/c+2αvt_c²/c+2r_if₀/c]

[0048] If the phase difference between two sweeps i, j is taken, the following is obtained:

[0049] Θ_j−Θ_i=2π(2αt_c/c+2f₀/c)(r_j−r_i)

[0050] The mean velocity between the instants T_iand T_jcan then be expressed according to the following:

[0051] v=(r_j−r_i)/(T_j−T_i)=(Θ_j−Θ_i)i(T_j−T_i)·(c/2π)/(2αt_c+2f₀)

[0052] A description is provided below of a process according to the invention, using successive frequency sweeps having different period length, reference being made to FIG. 3.

[0053] The aim is to obtain an accurate determination of the velocity v for an instant T. A good approximation of the velocity v is obtained by, according to the invention, instead determining the mean velocity over a period of time during which the velocity can be considered essentially constant on the basis of limited acceleration.

[0054] FIG. 3 illustrates five emitted consecutive FMCW sweeps 1.1-1.5 having different period lengths and the associated return sweeps 2.1-2.5. For a detected object, FFT (Fast Fourier Transform) is taken for five consecutive FMCW sweeps and five adjacent bearings. For these five FFTs, a frequency slot is designated in which the absolute value in the FFT is considered greatest. For this frequency slot, the respective phase value Ψ_iis also taken, which is an approximation to Θ_i.

[0055] From the FFT, five phase values are obtained:

[0056] Ψ₁,Ψ₂, . . . Ψ₅,−π≦Ψ_i≦π,1≦i≦5

[0057] corresponding to the instants

[0058] T_{1, T2, . . . T5}

[0059] The phase difference between two adjacent points then becomes:

[0060] where mod 2π denotes the modulo calculation over the interval [−π. π]₋⁼.

[0061] The time differences ΔTi, 1≦i≦4 correspond to four PRI times (Pulse Repetition Interval). The time for a FMCW sweep can be, for example, 370 μs, the smallest PRI time being able to measure about 500 μs. In order to be able clearly to determine a phase difference under prevailing conditions, a corresponding time difference of no more than about 10 μs is required. This task is managed according to the invention by using a plurality of different PRI times and then taking the difference between these. In the numerical example, the smallest difference in PRI times is 8 μs.

[0062] Any measuring errors on phase values over short time periods will have a high impact. In order to improve the precision in the velocity determination, the phase difference is measured over longer time periods, whilst, at the same time, care is taken to ensure that clarity is not lost. The PRI times are therefore chosen such that clarity is combined with good precision in the velocity determination.

[0063] According to an example, the PRI times can have the following values:

[0064] ΔT₁=512 μs

[0065] ΔT₂=520 μs

[0066] ΔT₃=544 μs

[0067] ΔT₄=640 μs.

[0068] Inter alia, the following differences can herein be created:

[0069] The following prediction ratios can be drawn up:

[0070] Based upon the above data, the velocity is now established by successively calculating the phase difference for the largest difference (the sum) of the PRI times. The requirement is that the first phase difference has been clearly determined. This is the case unless the velocity amount is extremely large. At each stage, firstly the phase change modulo 2π, xt and then the whole phase change x is calculated according to the following:

[0071] x=(ΔΨ₂−ΔΨ₁)_{mod 2π}  1.

[0072] xt=(ΔΨ₃−ΔΨ₁)_{mod 2π}  2.

[0073] x=integer((q₁s−xt+π)/2π)·2π+xt

[0074] xt=(ΔΨ₄−ΔΨ₁)_{mod 2π}  3.

[0075] x=integer((q₂x−xt+π)/2π)·2π+xt

[0076] xt=(ΔΨ₁)  4.

[0077] x=integer((q₃x−xt+π)/2π)·2π+xt

[0078] xt=(ΔΨ₃+ΔΨ₄)_{mod 2π}  5.

[0079] x=integer((q₄x−xt+π)/2π)·2π+xt

[0080] xt=(ΔΨ₁+ΔΨ₂+Ψ₃+Ψ₄)_{mod 2π}  6.

[0081] x=integer((q₅x−xt+π)/2π)·2π+xt

[0082] where integer(.) is the integer component of (.). The velocity v is then obtained by calculating v from the relationship: $v=\left(x/\Delta \Delta T_6\right)·\frac{c/2\pi }{2\alpha t_C+2f_0}$

[0083] The radar device 3 shown in FIG. 4, which can be used for realizing the process according to the invention, comprises a transmitter part 4 and a receiver part 5. An antenna 6 is connected to the transmitter part and the receiver part via a circulator 7. The transmitter part includes an oscillator control device 8 coupled to an oscillator 9 having variable frequency. Frequency sweeps from the oscillator control device 8 control the oscillator 9 such that a signal of periodically varying frequency is generated having varying period lengths for successive frequency sweeps. The generated signal is sent via a direction coupler 10 and the circulator 7 out on the antenna 6. The oscillator can operate within the Gigahertz range, e.g. 77 GHz. A reflected signal received by the antenna 6 is directed via the circulator to a mixer 11, where the reflected signal is mixed with the emitted signal. Following amplification in the amplifier 12 and filtering in the filter 13, the signal is fed to a processor block 14 in which, inter alia, determination of the relative velocity is carried out according to the process described above.

[0084] The invention shall not in any way be seen to be limited to the example above. Within the scope of the invention defined by the patent claims, there is room for a number of alternative embodiments. For example, other combinations of phase changes can be used.