Radar technolog Part 8 docx

Multisensor Detection in Randomly Arriving Impulse Interference using the Hough Transform 193 Fig. 14. Аn observation of a target in the range-azimuth plane after N SC radar scans Fig. 15. Аn observation of a target in polar coordinate system after N SC radar scans The polar Hough transform maps points (targets and false alarms) from the observation space (polar data map) into curves in the polar Hough parameter space, termed as the (ρ-θ) space (Fig. 16). The results of transformation are sinusoids with unit magnitudes. Each point in the polar Hough parameter space corresponds to one line in the polar data space with parameters ρ and θ. A single ρ-θ point in the parameter space corresponds to a single straight line in the range-azimuth data space with these ρ and θ values. Each cell from the polar parameter space is intersected by a limited set of sinusoids obtained by the polar Hough transform. The sinusoids obtained by the transform are integrated in the Hough parameter space after each of radar scans (Fig. 17). In each cell of the Hough parameter space is performed binary integration and comparison with the detection threshold. If the number of binary integrations (BI) in the polar Hough parameter space exceeds the detection threshold, target and linear trajectory detection is indicated. Target and linear trajectory detection is carried out cell by cell in the entire polar Hough parameter space. In order to compare the effectiveness of the two detectors, the CFAR BI detector (Fig. 18 and 19) and the Hough detector with a CFAR BI processor (Fig. 20 and 21) their performance is evaluated for the case of RAII using the two methods, analytical and Monte Carlo. Radar Technology 194 Fig. 16. Hough parameter space showing the sinusoids corresponding to the data point from Fig. 14 Fig. 17. Binary integration of data in Hough parameter space for example shows on Fig. 15 -4 -2 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SNR [dB] Probability of detection Pd CFAR BI processor P I =0 P I =0.05, I=5 dB P I =0.1, I=5 dB P I =0.05, I=10 dB P I =0.1, I=10 dB Fig. 18. Probability of detection of CFAR BI processor (analytically calculated) Multisensor Detection in Randomly Arriving Impulse Interference using the Hough Transform 195 -4 -2 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SNR [dB] Probability of detection Pd CFAR BI processor P I =0 P I =0.05, I=5dB P I =0.1, I=5dB P I =0.05, I=10dB P I =0.1, I=10dB Fig. 19. Probability of detection of CFAR BI processor (Monte Carlo simulation) The effectiveness of both detectors is expressed in terms of the detection probability, which is calculated as a function of the signal-to-noise ratio (SNR). The probability of detection is calculated using the same parameters for both detectors. These parameters are: the probability of false alarm - 10 -4 , the decision rule in the polar data space is “10-out-of-16”, the decision rule in the Hough parameter space is “7-out-of 20”, the interference-to-noise ratio is I=5,10dB, and the probability of interference appearance is P I =0; 0.05 and 0.1 (Garvanov, 2003; Doukovska, 2005; Doukovska, 2006; Doukovska, 2007; Garvanov, 2007; Doukovska, 2008). Analysis of the graphical results presented in Fig. 18-21 shows that the calculations of the probability of detection using the two different approaches analytical and Monte Carlo produce the same results. This provides reasons enough to use the simulation method -10 -8 -6 -4 -2 0 2 4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Signal-to-Noise-Ratio [dB] Probability of detection of the Hough detector Hough detector with CFAR BI processor P I =0 P I =0.05, I=5dB P I =0.1, I=5dB P I =0.05, I=10dB P I =0.1, I=10dB Fig. 20. Probability of detection of CFAR BI with Hough (analytically calculated) Radar Technology 196 -10 -8 -6 -4 -2 0 2 4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Signal-to-Noise-Ratio [dB] Probability of detection of the Hough detecto r Hough detector with CFAR BI processor P I =0 P I =0.05, I=5dB P I =0.1, I=5dB P I =0.05, I=10dB P I =0.1, I=10dB Fig. 21. Probability of detection of CFAR BI with Hough (Monte Carlo simulation) described in the previous section for analysis of Hough detectors with the other CFAR processors. It can be also concluded that the combination of the two detectors, CFAR and Hough, improves the joint target and trajectory detectability in conditions of RAII. 5. Multi-sensor (multi-cannel) polar Hough detector with a CFAR processor The target detectability can be additionally improved by applying the concept of multi- sensor detection. The important advantage of this approach is that both the detection probability and the speed of the detection process increase in condition of RAII (Garvanov, 2007; Kabakchiev, 2007; Garvanov, 2008; Kabakchiev, 2008). The speeding of the detection process and the number of channels are directly proportional quantities. The usage of multiple channels, however, complicates the detector structure and requires the data association, the universal timing and the processing in the universal coordinate system. Three radar systems with identical technical parameters are considered in this chapter. Three variants of a multi-sensor Hough nonsynchronous detector in a system with three radars are developed and studied. The first of them is the decentralized (distributed) Hough detector with track association (DTA), whose structure is shown in Fig. 22. Fig. 22. Decentralized (distributed) Hough detector, with track association (DTA) The structure of DTA Hough detector shown in Fig. 22 consists of three single-channel detectors described in Section 4. The final detection of a target trajectory is carried out after association of the output data of channels, where a target trajectory was detected or not Multisensor Detection in Randomly Arriving Impulse Interference using the Hough Transform 197 detected. The signal processing carried out in each channel includes optimum linear filtration, square law detection (SLD), CFAR detection, plot extraction (PE), PHT, inverse PHT, data association in the fusion node and finally, target detection and trajectory estimation. In each channel, the range-azimuth observation space is formed after N SC radar scans. After CFAR detection, using the PHT, all points of the polar data space, where targets are detected, are mapped into curves in the polar Hough parameter space, i.e. the ( ρ - θ ) parameter space. In the Hough parameter space, after binary integration of data, both target and linear trajectory are detected (TD) if the result of binary integration exceeds the detection threshold. The polar coordinates of the detected trajectory are obtained using the inverse PHT of ( ρ - θ ) coordinates. Local decisions are transferred from each channel to the fusion node where they are combined to yield a global decision. In many papers, the conventional algorithms for multi-sensor detection do not solve problems of data association in the fusion node, because it is usually assumed that the data are transmitted without loses. Here, the details related to the data association and the signal losses in the fusion node are reviewed and the problems of the centralized signal processing in a signal processor are considered. Here are provided the size of signal matrixes and their cells; range and azimuth resolution; and data association. Signal detection in radar is done in range- azimuth resolution cells of definite geometry sizes. Detection trajectory is done in the Hough parameter space with cells of specified sizes. The global decision in the fusion node of a radar system is done in result from association of signals or data in a unified coordinate system. The unified coordinate system of the range-azimuth space predicts cell’s size before association of data received from different radars. The radar system is synchronized by determining the scale factor used in a CFAR processor, the size of the Hough parameter space and the binary decision rule of the Hough detector. Unlike the decentralized structure of a multi-sensor Hough detector, in the DPA Hough detector the process of data association is carried out in the global (r-t) space of a Hough detector. The global (r-t) space associates coordinates of the all detected target (plots) in radars, i.e. associates all the data at the plot extractor outputs, as shown in Fig. 23. Fig. 23. Decentralized Hough detector, with plot association (DPA) It can be seen that the decentralized plot association (DPA) Hough detector has a parallel multi-sensor structure. In each channel, the local polar observation space, i.e. (r,a) are the polar coordinates of detected targets, is formed. All coordinate systems associated with radars are North oriented, and the earth curvature is neglected. At the first stage the local polar observation spaces of radars are associated to the Global Coordinate system resulting into the Global polar observation space. At the second stage, the polar Hough transform is applied to the global observation space and then the trajectory detection is performed in each cell of the Hough parameter space. The polar coordinates of the detected trajectory are obtained using the inverse polar Hough transform (IPHT) applied to the Hough parameter space. Radar Technology 198 All factors, such as technical parameters of radar, coordinate measurement errors, rotation rate of antennas and etc. are taken into account when sampling the Hough parameter space. The probability characteristics of such a system are better that those of the decentralized Hough detector. The third structure of a multi- sensor Hough detector called as the centralized Hough detector is the most effective for target trajectory detection (Fig. 24). In this multi-sensor detector data association means association of signals processed in all channels of a system. The effectiveness of a centralized Hough detector is conditioned by the minimal information and energy losses in the multi-sensor signal processing. However, a centralized Hough detector requires the usage of fast synchronous data buses for transferring the large amount of data and the large computational resources. Fig. 24. Centralized Hough detector, with signal association (CSA) In such a multi-sensor Hough detector, the received signals are transferred from all receive/transmit stations (MSRS) to the fusion node. The global polar observation space is formed after N SC radar scans. After CFAR detection, using the polar Hough transform (PHT), all points of the global polar observation space, where targets are detected, are mapped into curves in the polar Hough parameter space, i.e. the ( ρ - θ ) parameter space. The global target and linear trajectory detection is done using the binary decision rule “M-out-of -N SC ”. The polar coordinates of the detected trajectory are obtained using the inverse polar Hough transform (IPHT) applied to the Hough parameter space. 6. Performance analysis of a multi-sensor polar Hough detector with a CFAR processor Тhe first example, given in this section, illustrates the advantages of a three-radar system that operates in the presence of randomly arriving impulse interference. The three radars have the same technical parameters as those in (Carlson et al., 1994; Behar et al. 1997; Behar & Kabakchiev, 1998; Garvanov, 2007; Kabakchiev, 2007; Kabakchiev, 2008; Garvanov, 2008). The radar positions form the equilateral triangle, where the lateral length equals 100km. The performance of a multi-sensor polar Hough detector is evaluated using Monte Carlo simulations. The simulation results are obtained for the following parameters: - Azimuth of the first radar - 45 0 ; - Target trajectory - a straight line toward the first radar; - Target velocity – 1 Mach; - Target radar cross section (RCS) - 1 sq. m; - Target type - Swerling II case; Multisensor Detection in Randomly Arriving Impulse Interference using the Hough Transform 199 - Average SNR is calculated as S=K/R 4 ≅15dB, where K=2.07*10 20 is the generalized power parameter of radar and R is the distance to the target; - Average power of the receiver noise - λ 0 =1; - Average interference-to-noise ratio for random interference noise - I=10dB; - Probability of appearance of impulse noise – P I =0.033; - Size of a CFAR reference window - N=16; - Probability of false alarm in the Hough parameter space - P FA =10 -2 ; - Number of scans - N SC =20; - Size of an observation area – 100 x 30 (the number of range resolution cells is 100, and the number of azimuth resolution cells is 30); - Range resolution - 1 km; - Azimuth resolution -2°; - Size of the Hough parameter space - 91 x 200 ( θ cells -91, and ρ cells – 200); - Sampling in θ - 2°; - Sampling in ρ - 1km; - Binary detection threshold in the Hough parameter space - T M =2÷20. The performance of the three multi-sensor polar Hough detectors, centralized (CSA), decentralized (DTA) and decentralized (DPA), are compared against each other. The detection performance is evaluated in terms of the detection probability calculated for several binary decision rules applied to the Hough parameter space. The simulation results are plotted in Fig. 25. They show that the detection probability of a centralized detector is better than that of a distributed detector. It can be seen that the detection probability of the two types of detectors, centralized and decentralized, decreases with increase of binary decision rules (T M /N SC ). The maximum detection probability is obtained when the binary decision rule is 7/20. 2 4 6 8 10 12 14 16 18 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 T M /N sc Detection probability CSA (r-a) without error DTA (1/3) (r-a) without error DTA (3/3) (r-a) without error DPA (r-a) without error DPA (r-a) with error and bigger cells in HS DPA (r-a) with error Fig. 25. Detection probability of the three multi-sensor Hough detectors - centralized (CSA), decentralized (DTA) and decentralized (DPA) detectors for different binary rules in Hough parameter space Radar Technology 200 These results are in accordance with the results obtained for a single-channel Hough detector (for a single radar) operating in the interference-free environment as in (Finn & Johnson, 1968; Doukovska, 2005). The detection probability is low, because the input average SNR≅15dB and it is commensurate with value of INR=10dB. The results have shown that the detection probability of the TBD Polar Hough Data Association detector is between the curves of detector with binary rules in distributed Hough detector 1/3 - 3/3. It is apparent from Fig. 25 that the potential curve of a decentralized (DPA) Hough detector (Fig. 23) is close to the potential curve of the most effective multi-sensor centralized Hough detector (Fig. 24). It follows that the effective results can be achieved by using the communication structures with low-rate-data channels. The target coordinate measurement errors in the (r-t) space mitigate the operational efficiency of multi- sensor Hough detectors. The needed operational efficiency requires the appropriate sampling of the Hough parameter space. The second example is done in order to compare the effectiveness of the two Hough detectors, single-channel and three-channel decentralized (DPA), operating in conditions of RAII. The effectiveness of each detector is expressed in terms of the probability of detection calculated as a function of the signal-to-noise ratio. The detection probability of these Hough detectors is presented in Fig. 26. The detection probability is plotted for the case when the random pulse appearance probability is in range from 0 to 0.1 (P I ). -15 -10 -5 0 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Signal-to-Noise-Ratio [dB] Probability of detection of the Hough detector Hough detector with CFAR BI processor P I =0 P I =0.1, I=10dB P I =0 P I =0.1, I=10dB Fig. 26. Detection probability of two Hough detectors, single-channel (dash line) and three- channel decentralized with plot association (solid line) with Monte Carlo simulation analysis It is obvious from the results obtained that in conditions of RAII a multi-sensor Hough detector is more effective than a single-channel one. The higher effectiveness is achieved at the cost of complication of a detector structure. Multisensor Detection in Randomly Arriving Impulse Interference using the Hough Transform 201 7. Conclusions In this study, a new and more suitable modification of the Hough transform is presented. The polar Hough transform allows us to employ a conventional Hough detector in such real situations when targets move with variable speed along arbitrary linear trajectories and clutter and randomly arriving impulse interference are present at the detector input. The polar Hough transform is very comfortable for the use in search radar because it can be directly applied to the output search radar data. Therefore, the polar Hough detectors can be attractive in different radar applications. It is shown that the new Hough detectors increase probabilities, detection and coincidence, when the target coordinates are measured with errors. Three different structures of a multi-sensor polar Hough detector, centralized (CSA) and decentralized (DPA), are proposed for target/trajectory detection in the presence of randomly arriving impulse interference. The detection probabilities of the multi-sensor Hough detectors, centralized and decentralized, are evaluated using the Monte Carlo approach. In simulations, the radar parameters are synchronized in order to maintain a constant false alarm rate. The results obtained show that the detection probability of the centralized detector is higher than that of the decentralized detector. The results obtained shows that the required operational efficiency of detection can be achieved by using communication structures with low-rate-data channels. The target coordinate measurement errors in the (r-t) space mitigate the operational efficiency of multi- sensor Hough detectors. The needed operational efficiency requires the appropriate sampling of the Hough parameter space. The proposed multi-sensor Hough detectors are more effective than conventional single- channel ones due to the usage of the Hough transform for data association. This operation increases the effectiveness of trajectory detection in the presence of randomly arriving impulse interference. 8. Acknowledgment This work was partially supported by projects: IIT-010089/2007, DO-02-344/2008, BG051PO001/07/3.3-02/7/17.06.2008, MU-FS-05/2007, MI-1506/2005. 9. References Behar V., Chr. Kabakchiev, Hough detector with adaptive non-coherent integration for target detection in pulse jamming, In: Proc. of IEEE 5-th inter. symp., ISSSTA'98, Sun City, South Africa, vol. 3, 1998, pp. 1003-1007, ISBN:0-7803-4281-X. Behar V., Chr. Kabakchiev, L. Doukovska, Adaptive CFAR PI Processor for Radar Target Detection in Pulse Jamming, Journal of VLSI Signal Processing, vol. 26, 2000, pp. 383 – 396, ISSN:0922-5773. Behar V., L. Doukovska, Chr. Kabakchiev, Target Detection and Estimation using the Hough Transform, Lecture Notes in Computer Science, Springer-Verlag Berlin Heidelberg, LNCS 4310, pp. 525-532, 2007, ISBN:978-3-540-70940-4. Radar Technology 202 Behar V., L. Doukovska, Chr. Kabakchiev, H. Rohling, Comparison of Doppler and Hough Target Velocity Estimation Techniques, Proc. of the International Radar Symposium – 2007, Cologne, Germany, 2007, pp. 157-162. Behar V., B. Vassileva, Chr. Kabakchiev, Adaptive Hough detector with binary integration in pulse jamming, Proc. of Int. Conf. ECCTD'97, Budapest, 1997, pp. 885-889, ISBN:963-420-5232. Carlson B., E. Evans, S. Wilson, Search Radar Detection and Track with the Hough Transform, IEEE Trans., vol. AES - 30.1.1994, Part I, pp. 102-108; Part II, pp. 109-115; Part III, pp. 116-124, ISSN:0018-9251. Doukovska L., Hough Detector with Binary Integration Signal Processor, Comptes rendus de l’Academie bulgare des Sciences, vol. 60, №5, 2007, pp. 525-533, ISSN:0861-1459. Doukovska L., Hough Transform in the CFAR Algorithms in Presence of Randomly Arriving Impulse Interference, PhD Thesis, Institute of Information Technologies, Bulgarian Academy of Sciences, Bulgaria, 2005, Thesis leader: prof. Chr. Kabakchiev, (in Bulgarian). Doukovska L., Chr. Kabakchiev, Performance of Hough Detectors in Presence of Randomly Arriving Impulse Interference, Proc. of the International Radar Symposium – 2006, Krakow, Poland, 2006, pp. 473-476, ISBN: 978-83-7207-621-2. Doukovska L., Chr. Kabakchiev, V. Kyovtorov, I. Garvanov, Hough Detector with an OS CFAR Processor in Presence of Randomly Arriving Impulse Interference, Proc. of the 5-th European Radar Conference - EuRAD, Amsterdam, Holland, 2008, pp. 332- 335., ISBN: 978-2-87487-009-5 Doukovska L., V. Behar, Chr. Kabakchiev, Hough Detector Analysis by means of Monte Carlo Simulation Approach, Proc. of the International Radar Symposium – 2008, Wroclaw, Poland, 2008, pp. 103-106, ISBN: 978-83-7207-757-8 Finn H. M., R. S. Johnson, Adaptive detection mode with threshold control as a function of spatially sampled clutter estimation, RCA Review, 29, 3, 1968, pp. 414-464. Gandhi, P. P., S. A. Kassam, Analysis of CFAR processors in nonhomogeneous background, IEEE Trans., vol. AES-24, No 4, 1988, pp. 443-454. Garvanov I., Methods and algorithms for keeping constant false alarm rate in the presence of pulse jamming, PhD Thesis, Institute of Information Technologies, Bulgarian Academy of Sciences, Bulgaria, 2003, Thesis leader: prof. Chr. Kabakchiev, http://www.iit.bas.bg/staff_en/I_Garvanov/Dissertation_en.pdf. Garvanov I., Chr. Kabakchiev, Radar Detection and Track Determination with a Transform Analogous to the Hough Transform, Proc. of the International Radar Symposium – 2006, Krakow, Poland, 2006, pp. 121-124, ISBN: 978-83-7207-621-2 Garvanov I., Chr. Kabakchiev, Radar Detection and Track in Presence of Impulse Interference by using the Polar Hough Transform, Proc. of the European Microwave Association, Vol. 3, March 2007, pp. 170-175, ISBN 88-8492-324-7 Garvanov I., Chr. Kabakchiev, Sensitivity of API CFAR Detector Towards the Change of Input Parameters of Pulse Jamming, Proc. of the International Radar Symposium 2004, Warsaw, Poland, 2004, pp. 233-238.ISSN: 0885-8985 [...]... vector z1 08 , as well as the last row and the last column in the precision matrix XYZ W1 08 ˆ Now, we can determine Kalman gain K and the state estimate x1 08 , as well as the corresponding covariance matrix P1 08 : −1 −1 −1 K1 08 = P1 08| 100 HT W1 08 ⎡ W1 08 + ⎡ HP1 08| 100 HT ⎤ ⎤ ⎡ HP1 08| 100 HT ⎤ ⎣ ⎦ ⎥ ⎣ ⎦ ⎢ ⎣ ⎦ (103) XYZ ˆ ˆ ˆ x1 08 = x1 08| 100 + K1 08 ( z1 08 − z1 08| 100 ) (103) P1 08 = [1 − K1 08 H ] P1 08| 100 (105)... by the direction finder Accordingly: For the first measurement we have: Δt = 113 .8 − 1 08 = 5 .8 (106) ˆ ˆ x113 .8| 1 08 = F(5 .8) x1 08 (107) The covariance matrix of prediction is: P113 .8| 1 08 = F ( 5 .8 ) P108F ( 5 .8) + Q ( 5 .8) T (1 08) The prediction of the detection at the global coordinate system XYZ ⎡1571.7 ⎤ XYZ z113 .8| 1 08 = ⎢ 56647 ⎥ ⎢ ⎥ ⎢ 2000 ⎥ ⎣ ⎦ (109) We are taking into consideration the direction... (97) we take Z=2000m For the first measurements we have accordingly: Δt = 1 08 − 100 = 8 ˆ ˆ x1 08| 100 = F (8) x100 ⎡ 754 ⎤ ⎢ 127 ⎥ ⎥ ≈⎢ ⎢59161⎥ ⎢ ⎥ ⎣ −114 ⎦ (94) (95) The covariance matrix of the prediction: P1 08| 100 = F ( 8 ) P100F ( 8 ) + Q ( 8 ) T (96) The prediction of the detection at the global coordinate system XYZ: z XYZ 1 08| 100 ⎡ 754 ⎤ = ⎢59161⎥ ⎢ ⎥ ⎢ 2000 ⎥ ⎣ ⎦ (97) In the last formula we use information... Improvement in Radar Detection Through Window Processing in the Hough Space, Proc of the International Radar Symposium – 20 08, Wroclaw, Poland, 20 08, pp 139-144, ISBN: 9 78- 83-7207-757 -8 Garvanov I., V Behar, Chr Kabakchiev, CFAR Processors in Pulse Jamming, Proc of the Int Conf “Numerical Methods and Applications – 02”, Lectures Notes and Computer Science –LNCS 2542, 2003, pp 291-2 98, ISBN:9 78- 3-540-70940-4... follows: For the radar: XYZ Rad W =J −1 T z Rad WRad J −1 z Rad ⎡ 26.9 98 - 18. 659 -5,2424 ⎤ ⎢ ⎥ = ⎢- 18. 659 16.124 -6, 988 1⎥ e − 5 ⎢-5,2424 -6. 988 1 36.713 ⎥ ⎣ ⎦ (67) In case of the GPS device we do not have any change of variables We are only adding the zero values corresponding to additional variable to the precision matrix: XYZ GPS W 0 0⎤ ⎡0.0001 ⎢ 0 0.0001 0 ⎥ =⎢ ⎥ ⎢ 0 0 0⎥ ⎣ ⎦ ( 68) For the direction... the radar R1 The prediction of the detection at the radar local coordinate system: ⎡59200 ⎤ Rad z1 08| 100 = ⎢ 0.013 ⎥ ⎢ ⎥ ⎢ 0.034 ⎥ ⎣ ⎦ ( 98) The radar measures all coordinates It is not necessary to increase measuring vector and to use the prediction ⎡59025⎤ Rad z1 08 = ⎢ 0.117 ⎥ ⎢ ⎥ ⎢ 0.212 ⎥ ⎣ ⎦ (99) The dispersion of the radar measurements is described by the precision matrix of the form: Rad 1 08 W... following form: ⎡552 ⎢ C R1 = ⎢ 0 ⎢ 0 ⎣ 0 0. 082 0 0 ⎤ ⎥ 0 ⎥ 0.152 ⎥ ⎦ ( 78) The next position measurements of the tracking target took place at the time: T 2 = 113 .8 (79) We obtain the bearing of tracked target The direction finder was located at the point: ⎡10000 ⎤ N2 = ⎢ 40000 ⎥ ⎢ ⎥ ⎢ 100 ⎥ ⎣ ⎦ (80 ) z N 2 = [ −0. 385 3] (81 ) C N 2 = ⎡0.052 ⎤ ⎣ ⎦ (82 ) T 3 = 114 (83 ) The bearings value is: The covariance... International Radar Symposium – 2007, Cologne, Germany, 2007, pp 80 9 -81 3 Kabakchiev Chr., I Garvanov, L Doukovska, V Kyovtorov, H Rohling, Data Association Algorithm in Multiradar System, Proc of the 20 08 IEEE Radar Conference, Rome, Italy, 20 08, pp 1771-1774 ISSN: 1097-5659, ISBN: 1-4244-1593Kabakchiev Chr., I Garvanov, L Doukovska, V Kyovtorov, H Rohling, Data Association Algorithm in TBD Multiradar System,... Arriving Impulse Interference, Proc of the IET International Conference on Radar Systems, RADAR 2007, UK, 2007, CD ROM 7a.1, pp.5, ISSN: 0537-9 989 , ISBN: 9 78- 086 341 -84 9-5 Kabakchiev Chr., I Garvanov, L Doukovska, Excision CFAR BI detector with Hough transform in Randomly Arriving Impulse Interference, Proc of the International Radar Symposium-2005, Berlin, Germany, 2005, pp 259 – 264 Kabakchiev Chr.,... ⎤ ⎢ ⎥ =⎢ 0 1 / 0 .82 0 ⎥ ⎢ 0 0 1 / 0.152 ⎥ ⎣ ⎦ After transformation to the global coordinate system XYZ we obtain: (100) 222 Radar Technology ⎡6732.7 ⎤ XYZ z1 08 = ⎢ 57306 ⎥ ⎢ ⎥ ⎢ 2000 ⎥ ⎣ ⎦ (101) The precision matrix is transformed according to formula: XYZ Rad W1 08 = J −1T W1 08 J −1 ˆ ˆ z z (102) ˆ Rad where J zˆ is Jacobian matrix of transformation (66) calculated at the point z1 08 Because we are . 1997, pp. 88 5 -88 9, ISBN:963-420-5232. Carlson B., E. Evans, S. Wilson, Search Radar Detection and Track with the Hough Transform, IEEE Trans., vol. AES - 30.1.1994, Part I, pp. 102-1 08; Part II,. Carlo Simulation Approach, Proc. of the International Radar Symposium – 20 08, Wroclaw, Poland, 20 08, pp. 103-106, ISBN: 9 78- 83-7207-757 -8 Finn H. M., R. S. Johnson, Adaptive detection mode. Input Parameters of Pulse Jamming, Proc. of the International Radar Symposium 2004, Warsaw, Poland, 2004, pp. 233-2 38. ISSN: 088 5 -89 85 Multisensor Detection in Randomly Arriving Impulse Interference