Abstract:
The invention relates to the simultaneous determination of the distance and the speed of a target in a radar system that operates according to the HPRF (High Pulse Repetition Frequency) method. A target spectrum group is determined in the Doppler domain and the distance of the target is then determined from the group delay.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates to a method for the simultaneous determination of the distance and the speed of a target in a radar system. 
     2. Background Information 
     In radar systems operating according to the (High Pulse Repetition Frequency) method, the speed can be determined unequivocally up to a maximum speed of approximately Mach nine. The higher the unambiguity range for the determination of the speed, however, the smaller is the unambiguity range in the distance direction for a determination of the distance of a target. Typically, this unambiguity range is presently limited to a maximum distance of approximately one kilometer. 
     SUMMARY OF THE INVENTION 
     It is the object of the invention to improve a method of this type in that, while maintaining an unambiguous speed range up to a maximum speed of at least Mach nine, it becomes possible to unambiguously determine the distance of a target in a distance range whose maximum distance limit is substantially greater than one kilometer. 
     This is accomplished by determining the group delay of the target spectrum in the Doppler domain and determining the distance of the target from the group delay. 
     One advantage of the invention is that even if a target travels at a maximum speed of Mach nine, its distance can still be unequivocally determined up to a maximum distance of approximately 400 km. 
     The invention is based on the fact that in an HPRF method the transmitted signals put out by the radar antenna and reflected by a moving target are evaluated in the Doppler domain. For this purpose, the group delay of the target spectrum associated with the moving target is initially determined for the received signal, which essentially corresponds to the reflected transmitted signal, and then the desired distance is determined from the group delay. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention will now be described in greater detail with reference to one embodiment thereof in conjunction with the drawings in which: 
     FIG. 1 shows the real component of a transmitted signal versus time; 
     FIG. 2 shows a typical arrangement of an aircraft equipped with a radar system; 
     FIG. 3 shows a processing of radar signals; 
     FIG. 4 shows a phase ranging process; and 
     FIG. 5 shows a non-fluctuating received signal. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     In the example below it is assumed that a pulse modulated Doppler radar system is available in an airborne vehicle, for example an aircraft, and operates at a high pulse repetition rate, called the &#34;HPRF mode&#34; in the English-language literature. Such a radar system suitable for an airborne vehicle is also called &#34;airborne radar&#34;. The HPRF mode is usually employed as a search mode in an airborne radar system. 
     The real component Re{s(t)} (ordinate) of the transmitted signal s(t) of such a search mode is plotted in FIG. 1 over the time t (abscissa). This transmitted signal s(t) is composed of pulses having a time duration τ. The pulses are repeated periodically in time after a pulse repetition time T. The pulses include an alternating voltage signal at a transmitting frequency f O . The points in FIG. 1 indicate that pulses are transmitted successively in time. 
     The transmitted signal s(t) can be described mathematically as follows: ##EQU1## where r r  (t) is the normalized amplitude of the transmitted signal. 
     FIG. 2 shows a typical arrangement of an aircraft F equipped with a radar system operating in the HPRF mode and a target Z which, for the description below, is considered to be dot shaped. 
     From such a dot-shaped target Z, which moves from a distance r at a relative speed v r  toward the antenna, the following reflected received signal s r  (t) is obtained: ##EQU2## 
     In Equation (2) it is not considered that the antenna is directed toward target Z only for a finite time and that the amplitude a of the received signal may fluctuate for real targets. In Equation (2), t r  is the delay of the signal and f D  the Doppler shift. Taking c as the speed of light, the following applies for these two parameters: ##EQU3## 
     The signals are processed in the HPRF search mode as described below. First, the received signal s r  (t) is demodulated with transmitting frequency f O  and then it is sampled exactly once within a pulse repetition period T. Then the DFT (FFT) is formed section by section from the sampled signal y(1) for N points (N=2048) as shown in FIG. 3 according to the following formulas: ##EQU4## 
     The starting point N 1  for the first FFT (&#34;Fast Fourier Transformation&#34;) is arbitrary. The starting points N x  of the subsequent FFTs then depend on the pause times between the FFTs, the length of the preceding FFTs (in this case, this is always constant =N) and the original starting point N 1 . 
     In the so-called &#34;phase ranging&#34; process according to FIG. 4, the transmitted signal is not composed of a pulse train of infinite length but of bursts of a length N B  T. The transmitted signal is further characterized by the burst repetition duration T x . From this it results that the received signal is also divided into bursts. Such a received signal is shown in FIG. 5 for a non-fluctuating target (non-fluctuating received signal). In this case, according to Equation (3a), the delay t r  of the bursts is directly proportional to the distance r of the target. However, if there is a lot of noise interference, the parameter t r  can no longer be determined directly from the time signal. Therefore the delay t r  is estimated with the aid of the phase curve in the FFT. The length N of the FFT must here be selected to be less than the burst repetition duration T x . The following condition results: 
     
         NT+T.sub.P &lt;T.sub.X                                        (5) 
    
     where 
     NT=length of the FFT 
     T P  =pause time 
     T X  =burst repetition duration 
     with T P  being the pause time between the individual FFTs. 
     In such a phase ranging process the transmitted signal can be described by the following formula: ##EQU5## where ##EQU6## with * representing the convolution operator. 
     In contrast to Equation (2), for a non-fluctuating target an associated received signal s r  (t) results according to the following formula: ##EQU7## 
     This received signal is demodulated with the aid of transmitting frequency f O  so that a demodulated signal y(t) results according to the following formula: ##EQU8## 
     If now the Fourier transform is formed for only one burst from this reflected signal which is shifted in time with respect to the transmitted signal, according to the following formulas: ##EQU9## the delay t r  is contained in all phase curves ψ X  (f) proportional to the frequency f, according to the following formulas: 
     
         ψ.sub.X (f)=Im{logY.sub.X (f)} 
    
     
         ψ.sub.x (f)=2πft.sub.r +φ.sub.X                 (11) 
    
     The phase derivation according to the frequency yields the group delay t gx  (f) as follows: ##EQU10## which is then directly proportional to the distance r of the target. 
     For lower signal to noise ratios (S/N&lt;30 dB), t gx  (f) is advantageously estimated at frequency point f=f O . 
     If a radar system operates, for example, in an HPRF mode which employs the following data: 
     pulse repetition duration T (=1 /pulse repetition rate) =5.0 μsec=1/(200 kHz); 
     duty cycle τ/T: 0.1≦τ/T ≦0.4; 
     FFT length N: 2048; 
     burst repetition duration T x  : 11 msec&gt;2048 T+T P  ; 
     such a radar system is able to unequivocally determine the distance of a target, e.g., an aircraft, moving at a high speed up to a maximum distance of approximately 400 km. 
     The invention is not limited to the described embodiment but can be applied in the same sense for others. For example, such a radar system may also be employed in a stationary or mobile surveillance system on the ground.