Contemporary Engineering Sciences, Vol. 10, 017, no. 1, 1-11 HIKARI Lt, www.m-hikari.com https://oi.org/10.1988/ces.017.610164 Statistical Characteristics an Parameters of Spectrum of Doppler Signal Reflecte from Extene Object Vlaimir Mikhaylovich Artyushenko Technological University Gagarin str., 4, Korolev, 141070, Russia Vlaimir Ivanovich Volovach Volga Region State University of Service Gagarin str., 4, Togliatti, 445017, Russia Vyacheslav Grigorievich Kartashevskiy Volga Region State University of Telecommunications an Informatics Leo Tolstoy str., 3, Samara, 443010, Russia Oleg Vlaimirovich Osipov Volga Region State University of Telecommunications an Informatics Leo Tolstoy str., 3, Samara, 443010, Russia Anatoly Ivanovich Tyazhev Volga Region State University of Telecommunications an Informatics Leo Tolstoy str., 3, Samara, 443010, Russia Copyright 016 Vlaimir Mikhaylovich Artyushenko et al. This article is istribute uner the Creative Commons Attribution License, which permits unrestricte use, istribution, an reprouction in any meium, provie the original work is properly cite. Abstract In the article we examine the results of theoretical an experimental stuies of the statistical characteristics an of the parameters of the Doppler signal spectrum for
Vlaimir Mikhaylovich Artyushenko et al. ifferent moels of extene objects transport means. Analysis an generalization of the obtaine results was carrie out base on a big selection of fragments of the Doppler signal spectrum that allows us to consier these results as statistically reliable. It is shown that acceleration motion of the extene object has the greatest influence on the with of the spectrum of the Doppler signal an, consequently, on the accuracy of the measurement of its spee of movement. Keywors: Short Range Raar System, Extene Object, Spectrum of the Doppler Signal, Effective With of Spectrum, Scattering Cross-Section, Spee of Motion, Acceleration of Motion 1. Introuction Short-range raar systems (SRRS) are wiely applie in various systems for measurement of movement parameters, protection systems of various objects, classification ientification systems using the principle of short-range raar-location [1, 8, 1]. Consequently, they shoul also use other characteristics than those applie in the theory of long range raio systems. Doing the theoretical justification an practical implementation of any evices belonging to the class of SRRS, for example, measuring evice of motion parameters of various objects, you shoul consier a number of specific features for short range, such as the extene nature of the etecte object, the comparability of geometric imensions of the object with the istance to it, multipath nature of the reflection of signals from such objects, etc. As a result, it is necessary to analyze the characteristics of reflection of the emitte signal, to efine the with of spectrum of the Doppler signal (SDS), to select the metho of efinition an experimental etermination of the scattering cross-section, an also to create on their basis mathematical moels corresponing the real physical phenomena in SRRS taking into account the extene nature of the etecte objects, constantly changing range, various laws of instantaneous etection probability, a priori uncertainty about the position of the object an its motion parameters [, 11]. A priori knowlege of the statistical characteristics of signals an isturbing influences allows us to formulate more accurate mathematical moels of the reflecte signal as well as interferences influencing this signal an reasonable approach to the evelopment of evices of SRRS. Previously the authors [3] have selecte an justifie moels of isturbing influences on electronic etection evices (EDD) of high frequency type, which is a special case of SRRS taking into account multipath nature of the signals reflecte from extene objects. It was note that the probability ensity of the envelope of such a signal is well approximate by the Nakagami probability ensity istribution (PDD), an the PDD of the instantaneous values at specific values of the istribution parameters is clearly bimoal. To create effective SRRD it is necessary to analyze the characteristics of the reflection of the probing signals from extene objects, to efine the with of the
Statistical characteristics an parameters of spectrum 3 Doppler spectrum of the signal, to choose the efinition metho, to etermine experimentally the effective surface (area) of the scattering, an to etermine the statistical characteristics of signals receive by SRRD. A priori knowlege of the statistical characteristics of signals an isturbing influences allows us to formulate more accurate mathematical moels of the reflecte signal an of the interference influencing this signal, similar to real physical phenomena in SRRD taking into account the extene nature of the etecte objects, constantly changing range, ifferent laws of instantaneous etection probability, a priori uncertainty about the position of the object an its motion parameters [4, 13, 14], an also to get a reasonable approach to the evelopment of SRRD. Characteristics of the receive signal not only influence the range of SRRD, but also largely etermine the number of other important inicators of the quality of their work, for example the probability of correct etection, the probability of skipping, the false alarm probability, the accuracy of measurement of spee an acceleration, the resolution, etc. Note that here by receive SRRD signals we will mean low-frequency (Doppler) signals generate at the output of the high-frequency part of SRRD (microwave sensor) after their conversion. It shoul be note that the analysis an generalization of the results of statistical processing was carrie out by the numerous fragments of the receive signal obtaine uring the etection of the extene object by SRRD (for each experiment transport means of the same moel were use). Thus, the number of consiere fragments from one moel of each type of the extene object was 500...600. In this case the receive signal of SRRD was recore on more than fifty similar sets of raar evices of the microwave type. To obtain the most complete statistical ata the experimental stuies were conucte uner ifferent climatic conitions: clear, sunny weather, usk, rain, fog, frost an snow. One of the objects of etection, changing motion parameters, ensuring traffic safety in the group, etc. SRRS are various transport means of railway transport an roa transport, which by their structure can be attribute to the extene objects of complex shape. Particularly interesting is the stuy of the above mentione transport means in connection with the special character of the reflections of the souning signal coming from them. It is known [5] that a transport means as an object of etection is a complex spatially istribute raar target. Characteristics of the signal reflecte from such a target, not only affect the range of SRRS, but also largely etermine the number of other important inicators for such systems as: the accuracy of measurement of spee, resolution an other. In general case, the signal reflecte from objects of complex shape, contains two components: specular an iffuse. Specular reflection, i.e., the reflection in accorance with the laws of geometrical optics, is characteristic of smooth surfaces. Their characteristic size of roughness h is much less than the wavelength of the fluctuation generate by SRRD (i.e. h ) [6].
4 Vlaimir Mikhaylovich Artyushenko et al.. Spectrum of Doppler signal As it is known [7], when measuring motion parameters of any extene object with raio methos the spee of its movement is etermine by the Doppler frequency shift (DFS) of the signal: Vr Vr f f0 cos cos, с 0 where Vr is the raial velocity of movement of the etecte extene object; λ0 is the wavelength of the probing signal; is the angle between the irection of the axis of the main lobe of raiation pattern (RP) of the antenna an the irection of movement of the extene object. Statistical properties of the receive signal can be escribe [6] by the correlation function B t, t ) Fx( t) x( ), ( 1 t1 efine as the mathematical expectation of the prouct of samples of a ranom process, taken at time points t an t1, or by the spectral ensity S(), efine as the Fourier transformation, of the correlation function, or by the spectral with of the receive signal f 1/, (1) where с is the correlation interval characterizing the rate of change of a ranom process in time [5]. A with of SDS can be estimate by the formula F F cos, where Δα is the angular size of the transport mean (in the horizontal plane). The power of SDS can be etermine from the expression: P P S k H arp rr sin 8, c where Parp is the average raiate power; SΔ is area of the aperture; k = 0,5 0,8 is the utilization factor of the antenna; σrr is the specific effective scattering surface (ESS) of extene object characterizing the reflective properties of the irraiate surface an is a function of the angle to the axis of the trajectory of an extene object ; Н is the istance (perpenicular) from the raar meter to the surface of the irraiate object. The main factors etermining the spectral an correlation characteristics of the receive signals are the ifference in velocities of the elemental reflectors locate on the transport mean boy an of SRRD, an changing the ESS of the elemental reflectors in time. The ifference in velocities is cause by the large angular size of transport mean, exceeing in some cases the with of the raiation pattern (RP) of the SRRD antenna.
Statistical characteristics an parameters of spectrum 5 One of the most important statistical characteristics of the signal reflecte from the extene object, affecting the accuracy of its spee measurement [7], is SDS [11]. The main parameters of the SDS are the average frequency of spectrum f.a, the envelope, the effective with few an the power Р [6]. The envelope an the effective with of the spectrum few are etermine by the resulting RP of the antennas in the plane of the angle. Also the effective with few, as it was note above [1], is affecte by the correlation interval c (1). The effective with of the SDS is equal to its with at the level 0,5 by power an epens on the ranom fluctuations of the initial phase r with the reflection r/t 0 [10], an on the ifferences of Doppler frequencies of the elemental reflectors within the RP of final with. The secon factor is ominant. For the case when the signal phase is change accoring the polynomial law [15] t s t t..., ()! where the first summan Ω characterizes the spee of movement of the object, the secon summan characterizes its acceleration. The energy spectrum of signal () can be escribe by the expression [1]: T Т t S j S texp jt t cos t exp jt t! T Т, (3) where T/ < t < T/. Using [9], we represent the expression (3) in the form X x S j 0,5 exp j exp j x, (4) X 1 Т where X 1 Т, X. In turn, the expression (4) can be represente as: S j 0,5 exp j C X js X C X js X 1 1 x y where CX cos x y y и SX y 0 sin is the Fresnel integrals. 0 It is known that C( X) = C(X) и S( X) = S(X). Previously [6] we obtaine the expressions for the amplitue an phase spectra of the Doppler signal, respectively:,
6 Vlaimir Mikhaylovich Artyushenko et al. 0, 5 S 0,5 С X 1 CX SX 1 SX, (5) F S X1 S X arctg C X C X. (6) 1 The amplitue S(f) an the phase F(f) spectra calculate from the expressions (5) an (6) an built some of the values that characterize the magnitue of the acceleration of the object with the processing interval Т = 0, с; f = ω/, presente in Figure 1. а) b) Figure 1. Amplitue S(f) (а) an phase F(f) (b) spectrum with Т = 0, с
Statistical characteristics an parameters of spectrum 7 It shoul be note that the amplitue spectrum of the signal oscillates aroun some constant value. The number of perios an the amplitue of the oscillations epens on the prouct Т [5]. From the graphs it is seen that the with of the spectrum is influence by two parameters an Т. With a relatively large processing time, the influence of the parameter on the with of the SDS is preominant, which in this case has a trapezoial shape with the oscillating amplitue. With ecreasing T, the expansion of the spectrum, cause by the value, tens to zero, an the amplitue oscillations of the peak of the spectrum ecrease, an its shape assumes a bell-shape appearance. In this case, the ecrease of the value Т leas to expaning the spectrum an reucing its amplitue, an the peak of the curve of the epenency S(f) becomes flat, an the eges assume a slightly sloping look. 3. Results of Doppler signal spectrum stuy Next, let us procee to stuy results of SDS parameters. It shoul be note that the methoology we use now was propose by the authors before [1, 15]. Also earlier on the basis of the propose metho the authors experimentally etermine the average values of scattering cross section (SCS) tm transport means, the with of the SDS is Ftm an root-mean-square eviation of the SCS on the example of ifferent types of transport means. To summarize the obtaine results it was interesting to carry out the research of more extene objects such as transport means of railway transport, as well as the stuy of the influence of acceleration of these objects on the parameters of the SDS. An experimental stuy of the parameters of the SDS reflecte from extene objects (train rolling-stock, single cars, in some cases for a shunting locomotive), was performe using microwave oscillations of serial raar spee gun with wavelength = 8 mm. Analysis an generalization of the stuy results of the parameters of the spectrum prouce from the numerous fragments of the Doppler signal reflecte from the transport mean of the same moel. The number of the consiere fragments from the transport means of each type was 380...400. All of the spectra of the reflecte signals can be ivie into three groups. The first group will inclue the SDS uner irraiation of the transport mean (train rolling-stock) at an angle close to zero when the transport mean is at a relatively large istance of about 50...60 m. For this case is characteristic the spectrum of the reflecte signal, potentially proviing a goo accuracy of measurement of spee an, consequently, acceleration an high resolution. The spectral with at the level of 0,707 is ΔF = 8 10 Hz. The secon group of spectra correspons to positive angles of irraiation of the transport mean α0 17 о. In this case, the with of SDS increases significantly an is ΔF = 0...5 Hz, which correspons to the location the transport mean at relatively small istances of about 10...0 m from the velocity meter. The angular
8 Vlaimir Mikhaylovich Artyushenko et al. imensions of the transport mean often excee the beam with of the antenna. Moving transport mean rapily changes its angle, which is accompanie by rapi fluctuations of reflecting centers, which leas to the expansion of the SDS, the eterioration of the accuracy potential of the velocity meter an frequency resolution. In aition, this case is characterize by a sharp ecrease in the SDS for some types of cars cause by the oblique fall of the ray on a smooth surface of the transport mean (mirror reflection), as well as some ecrease of scatter of the values of SCS for ifferent types of cars, ue to the fact that the narrow beam of antenna irraiates only a part of the surface (projector moe). The thir group of spectra correspons to the eceleration moe of the transport mean from the trigger point to the moment of release the car retarers. In this case the boy of a railroa car as well as the velocity meter is expose to strong vibration. In this case the spectrum of the reflecte signal is expane so that its with reaches ΔF = 30 40 Hz. Uner these conitions the accuracy of the velocity measurement is the worst. A significant expansion of the range is observe in Doppler signals reflecte from shunting locomotives, because their boy continuously vibrates from the running engine. Moreover, SDS oes not only expan, but also has a «parasitic» harmonics, the amplitue of which is comparable with the spectrum of the main signal, which significantly affects the measurement accuracy, an can lea to errors in the velocity measurements. The with of the spectrum of the Doppler signal at the level of 0,707 reflecte from ifferent moels of wagons, are given in table 1, where s F Fs is the relative measurement error of Doppler signal. Table 1 The with of the spectra of the Doppler signals reflecte from various moels of rail cars The with of the SDS signal F, Hz (the level 0,707) The moel The first group The secon group The thir group of car F, Hz s, % F, Hz s, % F, Hz s, % 11-066 8 1,0 5 1,8 38 3,5 1-515 1 1,5 3 1,6 34,8 15-1443 8 1,0 3 1,6 38,8 11-715 1 1,5 6 1,8 36 3,5 13-470 1 1,5 3 1,6 39 3,5 refrigerator 10 1,5 5 1,6 40 3,64 shunting locomotive 1 1,5 6 1,6 4 3,9 Each part of the table reflects the average over many realizations of the spectrum reflecte from an uncoupling of the Doppler signal of moving in the area of the raar meter.
Statistical characteristics an parameters of spectrum 9 The results of processing of the experimental ata show that when rotating wheels of the transport mean or its oscillating parts (for example, the rear an sie oors, hatches, covers an accessories for fastening cargo) are irraiate, in the spectrum of the reflecte signals appear aitional components. Moreover, the frequencies of these components can be both above an below the frequency of the main signal, an their level is 10...40 B below the main signal. It shoul be note that the results obtaine in this part of the stuy are absolutely ientical to the earlier obtaine results of stuy of similar parameters of SDS for roa transport [3]. At low spees of rolling of the transport mean the spectrum of the reflecte signal is expose to stronger «parasitic» effects than the spectrum of the signal reflecte from the transport mean at a higher spee. This is because at low spees of rolling of the transport mean the spectrum of the reflecte signal falls within the frequency omain of aitive noise, whose spectrum an the SDS «overlap». As a result of this not only the expansion of ΔF can occur, but its «splitting» as well, which greatly reuces possibility of accurate measurement of the Doppler frequency signal. As a result of experimental stuies it has been shown that the transport mean movement acceleration has the greatest influence on the with of the SDS an, consequently, on the accuracy of spee measurement of the extene object movement (railway cars, transport means in general). Moreover, the bigger is its absolute value, the wier is the energy spectrum of the reflecte signal, which is fully consistent with the theoretical analysis. 4. Conclusion Consiering a goo compliance between theoretical an experimental results we can raw the following conclusions. The average value of the acceleration of railway cars rolling into brake position is within (+0,45) (+0,55) м/с. At the time of braking, the acceleration is in the range of ( 1,9) (,1) м/с ; respectively, in the output of the moerator it is( 0,05) (+0,05) м/с. It shoul be note that while technically implementing the tracking velocity meter for increasing accuracy of measurement of the average frequency of spectrum of the reflecte signal, the time constant of the measurement must be chosen from the conition of minimum with of the Doppler reflecte signal at the maximum possible acceleration value of the transport mean, taking into account the require processing spee of the meter in receiving an issuing information about velocity of the transport mean movement. As can be seen from the presente results, the time constant of the measurement must be within 80...10 ms. References [1] V. M. Artyushenko, Research an Development of the Motion Parameters Raar Meter for Extene Objects, Finance an Technology Acaemy, Moscow, 013.
10 Vlaimir Mikhaylovich Artyushenko et al. [] V. M. Artyushenko an V. I. Volovach, Measurement Error Estimation of Motion Variables for Extene Objects uner Changing Range Conitions, Raioelectronics an Communications Systems, 58 (015), no. 1, 17-7. https://oi.org/10.3103/s07357715010033 [3] V. M. Artyushenko an V. I. Volovach, Statistical Characteristics of Envelope Outliers Duration of non-gaussian Information Processes, Proceeings of IEEE East-West Design & Test Symposium (EWDTS 013), 137-140. https://oi.org/10.1109/ewts.013.6673139 [4] V. M. Artyushenko an V. I. Volovach, Analysis of influence of uncorrelate aitive non-gaussian noise on accuracy of motion parameters measurement in short-range raio systems, Proceeings of IEEE International Siberian Conference on Control an Communications (SIBCON-015), 714779. https://oi.org/10.1109/sibcon.015.714779 [5] V. M. Artyushenko an V. I. Volovach, Analysis of the spectrum parameters of a signal reflecte from an extene object, News of Higher Eucational Institutions. Instrumentation, 57 (01), no. 9, 6-67. [6] V. M. Artyushenko an V. I. Volovach, The stuy of spectrum of Doppler signal reflecte from moving of extene object, Successes of Moern Raio Electronics, (015), no. 11, 58-66. [7] V. M. Artyushenko an V. I. Volovach, Threshol metho of measurement of extene objects spee of raio engineering evices of short-range etection, Proceeings of IEEE East-West Design & Test Symposium (EWDTS 014), 0-3. https://oi.org/10.1109/ewts.014.707078 [8] G. L. Charvat, Small an Short-Range Raar Systems, CRC Press, 014. [9] Ch. Cook, M. Bernfel, Raar Signals, Sovetskoe raio, Moscow, 1971. [10] A. G. Flerov an V. T. Timofeev, The Doppler Device an Navigation System, Transport, Moscow, 1987. [11] L. Hammarstran, L. Svensson, F. Sanblom an J. Sorstet, Extene object tracking using a raar resolution moe, IEEE Transactions on Aerospace an Electronic Systems, 48 (01), no. 3, 371-386. https://oi.org/10.1109/taes.01.637597 [1] I. V. Komarov, S. M. Smolskiy, Funamentals of Short-Range FM Raar, Artech House, Norwoo, 003.
Statistical characteristics an parameters of spectrum 11 [13] N. Lu an B. Eisenstein, Detection of Weak Signals in non-gaussian Noise, IEEE Transactions on Information Theory, 7 (1981), no. 6, 755-771. https://oi.org/10.1109/tit.1981.1056414 [14] J. J. Sheehy, Optimum Detection of Signals in non-gaussian Noise, The Journal of the Acoustical Society of America, 63 (1978), no. 1, 81-90. https://oi.org/10.111/1.381699 [15] G. I. Tuzov, Allocation an Information Processing in Doppler Systems, Sovetskoe raio, Moscow, 1977. Receive: October 0, 016; Publishe: December 16, 016