Adaptive real‐time recursive radial distance‐time plane Hough transform track‐before‐detect algorithm for hypersonic target

IET Radar, Sonar & NavigationVolume 14, Issue 1 p. 138-146 Research ArticleFree Access Adaptive real-time recursive radial distance-time plane Hough transform track-before-detect algorithm for hypersonic target Lin Li, Corresponding Author Lin Li fengzhite@126.com Institute of Information Fusion, Naval Aviation University, 264001 Yantai, People's Republic of ChinaSearch for more papers by this authorGuohong Wang, Guohong Wang Institute of Information Fusion, Naval Aviation University, 264001 Yantai, People's Republic of ChinaSearch for more papers by this authorXiangyu Zhang, Xiangyu Zhang Institute of Information Fusion, Naval Aviation University, 264001 Yantai, People's Republic of ChinaSearch for more papers by this authorHongbo Yu, Hongbo Yu Institute of Information Fusion, Naval Aviation University, 264001 Yantai, People's Republic of ChinaSearch for more papers by this author Lin Li, Corresponding Author Lin Li fengzhite@126.com Institute of Information Fusion, Naval Aviation University, 264001 Yantai, People's Republic of ChinaSearch for more papers by this authorGuohong Wang, Guohong Wang Institute of Information Fusion, Naval Aviation University, 264001 Yantai, People's Republic of ChinaSearch for more papers by this authorXiangyu Zhang, Xiangyu Zhang Institute of Information Fusion, Naval Aviation University, 264001 Yantai, People's Republic of ChinaSearch for more papers by this authorHongbo Yu, Hongbo Yu Institute of Information Fusion, Naval Aviation University, 264001 Yantai, People's Republic of ChinaSearch for more papers by this author First published: 01 January 2020 https://doi.org/10.1049/iet-rsn.2019.0198Citations: 2AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Under the condition of low signal-to-noise ratio (SNR), the track-before-detect algorithm based on Hough transform (HT-TBD) is an effective means to detect and track hypersonic targets. In view of the problem that the existing HT-TBD algorithms cannot detect hypersonic multi-target in real time and some targets may be missed, an adaptive real-time recursive radial distance-time plane HT-TBD (RTHT-TBD) algorithm for a hypersonic target is proposed in this study. Firstly, RTHT-TBD technology is used to perform the non-coherent integration detection of the first n frames measurement data, and the initial accumulation matrix and storage array are obtained. Then the data of 2∼n + 1, 3∼n + 2,… frames are processed recursively in turn. In order to solve the problem that the parameter space accumulation matrix cannot accumulate normally when the parameter space accumulation matrix changes in the recursive process, the adaptive technology is used to adjust the parameter space to realise the recursive detection at all times. The simulation results show that the proposed algorithm can realise real-time detection and tracking of hypersonic multi-target under low SNR, and effectively reduce the computational complexity. 1 Introduction In recent years, with the continuous development of hypersonic vehicle technology, the detection and tracking of the hypersonic target have attracted widespread attention. Especially under the condition of low signal-to-noise ratio (SNR), the real-time detection and tracking problem of hypersonic multi-target has always been the focus and difficulty of the research [1-3]. The traditional detection and tracking method is to detect before tracking, i.e. to suppress the noise and clutter of single-frame radar echo signal, complete the constant false alarm rate (CFAR) detection through threshold processing, and extract the processing result to perform target tracking [4, 5]. However, with the improvement of target stealth performance and the influence of the clutter environment, the SNR of echo signal received by radar is low. In addition, the CFAR processing in the conventional detection process also has a loss of SNR, which further reduces the detectability of the target under low SNR conditions. Therefore, when the SNR of echo signal is low, it is difficult to extract the target trace from using single-frame data in traditional algorithms. If the threshold is lowered to solve this problem, it will lead to more false tracks in the follow-up, which cannot achieve effective detection and tracking of the target [6]. Track-before-detect (TBD), as an inter-frame integration technology, uses the continuity of target motion in space and the correlation of radar echoes in time series to realise the detection of weak targets by non-coherent integration of multi-frame radar echo data [7-9]. Yan et al. [10] present a dynamic programming TBD technology based on video data processing, which effectively solves the detection problem of extended multi-target in the sea clutter background. In [11, 12], a dynamic programming TBD algorithm based on the generalised likelihood ratio is proposed for multi-target detection under a specific detection background. Luis et al. [13] propose a new multi-target tracking particle filter target measurement model for dimensional problems in particle filter-based TBD algorithm, achieving good tracking performances. In [14], the characteristics of targets in strong clutter are analysed, and a multi-dimensional TBD algorithm based on the Hough transform is proposed, which can better detect multi-targets in linear motion. In view of the multi-frame TBD processing, an efficient recursive multi-frame TBD (R-MF-TBD) algorithm is proposed in [15] to realise a complexity reduction of the detection. The TBD algorithm based on the Hough transform is a typical batch processing TBD algorithm. Its basic principle is to transform the problem of track detection in data space into the problem of peak detection in parameter space. The weak target is detected by non-coherent integration of multi-frame measurement data, and the target track is obtained by track backtracking [16]. In 1994, Carlson et al. applied Hough transform to search radar for the first time, and established the theory of low observable target detection based on Hough transform [17-19]. Since then, many scholars have made a series of developments and improvements on the HT-TBD algorithm under different backgrounds and conditions [20-23]. Among them, aiming at the problems of MIMO radar's range walk and UWB multistate radar's high false alarm probability, the authors of [20, 22] improve the original algorithm by using Hough transform and effectively improving the system performance. Bi et al. [21] improve the HT-TBD algorithm by increasing the dimension of feature parameters and multistage filtering, and achieves better performance to multi-target detection and tracking. In [23], a new random HT-TBD algorithm is proposed to solve the range ambiguity problem of high pulse repetition frequency radar, which can detect and track weak targets effectively. As for hypersonic targets, in view of their different motion characteristics from conventional targets, a radial distance-time plane HT-TBD algorithm is proposed by the project team to achieve effective detection and tracking of hypersonic targets [24]. The current HT-TBD algorithms are all processed for single batch measurement data with fewer frames. However, with the increase of target detection time and much more processing frames, the existing algorithms mainly have the following three shortcomings: (i) there is a detection delay problem in target detection. For example, for HT-TBD detection with a length of seven frames, if the target appears in the fifth frame measurement and is detected by radar, when 4/7 criterion is used to discriminate, the target cannot be detected because there are at most three frames measurements of the target. Only in the next batch processing period (i.e. 8–14 frames measurement), the target can be detected, resulting in the delay of target detection. (ii) The existing HT-TBD algorithms also have the problem of target missing detection. For example, when measuring from frames 5 to 10, the target moves in a straight line, while in a curve manoeuvring from frame 11. Because the HT-TBD algorithm integrates the track of the straight line, only three frames of measurement can be effectively integrated into batch processing sections of frames 1–7 and frames 8–14, which cannot realise the target detection, leading to the target missing detection. In addition, for the current TBD algorithms, when continuous long-time processing is performed, the existing algorithm performs multiple single-batches processing only by simple sliding window processing, which undoubtedly causes a large number of repeated calculations and reduces the real-time performance of the algorithm. Aiming at the problem that the existing HT-TBD algorithms cannot realise real-time detection of hypersonic multi-target and some targets may be missed, an adaptive real-time recursive RTHT-TBD (A-RTHT-TBD) algorithm for the hypersonic target is proposed in this paper. First, according to the characteristics of hypersonic target, the non-coherent integration detection of the first n frames measurement data is carried out by the RTHT-TBD algorithm, and the initial accumulation matrix and storage array are obtained. Then the data of frames is processed recursively in turn. In order to solve the problem that the parameter space accumulation matrix cannot accumulate normally when the parameter space accumulation matrix changes in the recursive process, the adaptive technology is used to adjust the parameter space to realise the recursive detection at all times. When the sliding window processing is performed, the last frames data of the previous processing result is used, and only one frame of new measurement data is introduced for recursion, which greatly reduces the amount of calculation, avoids repeated calculation and improves the real-time performance of the algorithm. Finally, the real-time detection and track backtracking of hypersonic multi-target are realised by merging the tracks of each detection result. The remaining part of the paper is arranged as follows. Section 2 introduces the target model used in this paper, Section 3 describes the principle of the algorithm, Section 4 describes the specific implementation steps of the algorithm, Section 5 analyses the performance of the algorithm based on the simulation results, and finally, Section 6 draws the conclusion of this paper. 2 Target model 2.1 Target state model Considering the point target motion scene, set the target state vector at the time k to (1) where denote the location information of the target at the time k, denote the target velocity information at time k, and denote the acceleration information of the target at a time k. , K denotes the total frames of measurement data. Then the target motion equation can be expressed as (2) where denotes the state transition matrix and is the zero-mean, white Gaussian process noise sequence (3) where T denotes the radar measurement period, denotes the unit matrix of , denotes the Kronecker product. According to the target motion equation, when , the target moves in a uniform, straight line. When and the initial velocity direction of the target is the same as the acceleration direction, the target moves in a uniformly accelerated straight line. And when and the initial velocity direction of the target is not the same as the acceleration direction, the target moves in a uniformly accelerated curve. 2.2 Target measurement model For the target state vector at a time k, the radial distance of the target measured by radar is as follows: (4) where , , and denotes the radar range measurement error. The azimuth angle is (5) where , , and denotes the radar angle measurement error. If represents the echo energy information of point i at the time k, then is defined as (6) where denotes the white Gaussian noise, and the measurement points are independent of each other, satisfying . denotes the strength contribution of a target at the time k to this measurement point. For the K frames of measured data received by the radar, the set of radar measurement data for each frame can be expressed as (7) where denotes the measurement information of the ith measurement point in the kth frame measurement data. , , and , respectively, represent the radial distance information, azimuth angle information and echo energy information of the measurement point. denotes the total number of measurement points included in the kth frame measurement. 3 RTHT-TBD algorithm based on adaptive real-time recursion The proposed algorithm in this paper can be divided into three parts. Firstly, RTHT-TBD is used to process the first batch of initial measurement data to obtain the initial accumulation matrix and initial storage array. Then, adaptive real-time recursive processing of subsequent data is carried out. Finally, the track of the target is obtained by merging the detection results of each batch to realise the detection and tracking of the target. The overall flowchart of the algorithm is shown in Fig. 1. Fig. 1Open in figure viewerPowerPoint Overall flowchart of the algorithm 3.1 RTHT-TBD processing of initial time First, in order to get the initial point accumulation matrix, initial energy accumulation matrix and the corresponding storage array, RTHT-TBD algorithm based on m/n criterion is used to detect the non-coherent integration detection of the first n frames measurement data, so as to prepare the data for the subsequent recursive processing. For conventional targets, TBD algorithm based on Hough transform in [20-23] usually uses position measurement data to transform, and its transformation equation is as follows: (8) where denotes the location information of measurement data, and denote the eigenvalues of target tracking in parameter space. The basic principle of Hough transform is: in data and parameter space, the measurement points in data space are transformed into a curve in parameter space by using Hough transform equation, and the parameter space is discretised into resolution units. Each resolution unit corresponds to a point accumulation unit , an energy accumulation unit and a storage unit , respectively. For the parameter space curve corresponding to the measurement point , all the resolution units which the curve passes correspond to , , . When the parameter space curves corresponding to all measurement points are accumulated, point accumulation matrix , energy accumulation matrix and storage array can be obtained, where , . And the accumulation matrix and storage array corresponding to the first n frames measurement data are the initial accumulation matrix and the initial storage array. For hypersonic targets, in order to achieve early warning and ensure sufficient warning time, when radar detects targets, the distance between targets and radar is usually very far. When the azimuth measurement accuracy of radar is low, the measurement data of the target position has a large error, destroying the original motion characteristics of target track and making it difficult to achieve effective detection and tracking of the target. According to Section 2.2, assuming that the azimuth measurement error of radar is and the radial distance between radar and target is r, then the target lateral deviation caused by the azimuth measurement error of radar is as follows: (9) It can be seen from (9) that the lateral deviation of the target caused by the radar angle measurement error has a great influence on the target position measurement data. However, through analysis, it can be found that the radial distance measurement data of the target is only affected by the radar ranging error, while the accuracy of it is high. In addition, the time data of the measurement points directly represent the time sequence information of the target motion, and a large number of false trajectories that do not conform to the law of motion can be eliminated by using the time information. Therefore, the use of radial distance-time plane measurement data can effectively avoid the influence of angle measurement error and eliminate false tracks. Therefore, the radial distance-time plane measurement data is used for Hough transform in this paper, and the motion trajectory of the target in the radial distance-time plane can be expressed as (10) Although the target can be detected after RTHT processing, the possible tracks obtained by Hough transform may still contain false tracks and clutter points due to the influence of clutter. In order to further eliminate the false tracks and clutter points in the obtained tracks, it is necessary to further screen the candidate tracks by using information such as angle and velocity, and merge tracks belong to the same target to realise the output of the target track, and obtain the final confirmed track. 3.2 Subsequent adaptive recursive processing After RTHT-TBD processing of the first n frames measurement data in Section 2.1, the initial point accumulation matrix , the initial energy accumulation matrix and the corresponding storage matrix can be obtained. The real-time adaptive recursive algorithm in this paper is used to process the subsequent batches of data, such as . The analysis shows that for the two adjacent recursive processing, there are frames data duplicated between the measurement data. At this time, if n frames data after translation are all re-transformed, it will cause a large number of duplicate calculations and reduce the efficiency of the algorithm. Therefore, this paper does not re-transform the translated n frames data, but by eliminating the first frame data in the previous batch of data, retaining the intermediate frames data, only accumulating and storing the new frame data in the next batch of data, to update the accumulative matrices , and storage array , and realise the sequential recursive detection at all times, effectively reducing the amount of calculation and improving the computational efficiency of the algorithm. The recursive process is shown in Fig. 2. Fig. 2Open in figure viewerPowerPoint Diagram of recursive processing According to the principle of Hough transform, after mapping the measurement data from data space to parameter space by (10), it is necessary to discretise the parameter space for accumulation. Assuming that the parameter space is discretised into resolution units, the parameter space discretisation method is (11) (12) where and , respectively, denote the widths of the parametric spatial resolution unit in the axis and axis directions. , denotes the maximum value of t in the current batch measurement data, i.e. the maximum measurement time. And denotes the maximum radial distance of measurement data [24]. Through the analysis of the equation , we can see that, while increases with the increase of recurrence time, is bounded and , where L denotes the radar range. Therefore, for different recursive frames, the change of leads to the change of , which makes in the two Hough transforms before and after. At this time, due to the change of the accumulation matrix before and after, the same measurement of frames between two adjacent batches of data cannot be used directly by the latter recursive processing for effective detection. To solve the above problems, in order to keep the accumulation matrix and storage array corresponding to the same measurement data of frames unchanged during the two recursive processing, and apply them directly in the recursive processing, an adaptive method is used to adjust the parameter space in real time. Based on the analysis of (12), since changes with the change of recursive time, it is necessary to adjust the value of in real time in order to keep unchanged during the two recursive processes (i.e. the accumulation matrix and storage array corresponding to the same frames measurement data do not change). Through calculation, the axis direction resolution unit does not change while the axis direction resolution unit extends to both ends with the increase of the recurrence time. Therefore, according to the latest measurement frame data, the parameter space accumulation matrix and storage array can be adjusted by the method of left translation and the right extension to achieve recursive detection at all times. The principle of the method is shown in Fig. 3. Fig. 3Open in figure viewerPowerPoint Principle of adaptive processing Where denotes the number of axis resolution units in the ith recursive processing parameter space, denotes the number of units that need to be extended this time, denotes the total number of resolution units translations in the previous i recursive processing, denotes the number of units that need to be translated this time, C denotes the set of curves corresponding to the measurement points that transformed into parameter space at this recursive time, CC denotes the accumulation matrix and storage array of this recursive processing, and denote the maximum and minimum values of the axis resolution units in the parameter space before this recursive time's measurement data are translated and extended. 3.3 Track merging After processing in Sections 3.1 and 3.2, the detection results of the initial first batch measurement data and the recursive batches measurement data can be obtained. Next, the obtained detection results of each batch need to be processed to merge the tracks belonging to the same target, and then the detection result of the final K frames measurement data can be obtained to achieve the track output. According to the principle of recursive processing in Section 3.2, there are frames same measurements in two adjacent batches of measurement data. Therefore, for the same target, there should be frames track overlap includes in the two adjacent batches detection results under ideal condition. Although the two adjacent batches detection results of the same target should ideally have frames track overlap, considering that there may be missed detection of a target at some frames and the existing of clutter points in the track in the single batch detection process, the algorithm sets the track merging threshold . By comparing the output tracks of two adjacent batches of measurement data, when the number of identical points in two tracks exceeds the threshold , it is considered that the two tracks correspond to the same target, and track merging is necessary. For different measurement points at the same time, when track merging is carried out, the point with larger echo energy is selected as the target measurement point at that time. For each batch of n frames measurement data, define the threshold as (13) where denotes the integer operation. Track merging for the detection results of each batch not only integrates the track of each segment, but also realises the following two functions: First, the overlapping parts of two tracks can be complemented by track merging, which avoids the possible missing detection of some frames in a single track. Second, for the same target, there is only one measurement point in a single measurement. When the same time corresponds to different measurement points, there must be clutter points. Through track merging, the clutter points in the track can be eliminated effectively. 4 Algorithm implementation The algorithm proposed in this paper mainly includes the following steps: Step 1: RTHT-TBD is used to process the first n frames radar measurement data, and the initial accumulation matrix, initial storage array and the initial detection result are obtained. The specific process is as follows: (i) The radial distance-time data in the first n frames measurements is normalised to prevent the loss of time dimension information due to the disparity of magnitude. According to the normalisation coefficient , the processed radial distance-time data is obtained (14) where denote the maximum radial distance and time in the previous n frames measurement data, respectively, and denotes the smallest integer greater than . (ii) Select the measurement data of the first n frames in turn, and carry out the transformation accumulation and peak detection. Hough inverse mapping is applied to the point sets beyond the threshold to obtain possible tracks. (iii) Velocity constraints are applied to the possible tracks output from Hough inverse mapping. The target position , at two different moments in the possible track, the maximum velocity and the minimum velocity of the target are used to establish the annular gate for velocity constraints. The constraints are (15) where , , similarly available and , and . (iv) Heading constraints are applied to the output track after velocity constraints, and then the detection results of the first n frames can be obtained. Assuming that the target position at k frame is , then the target positions at and frames are , . Definition the vectors , , then the target heading angle is defined as (16) If the maximum manoeuvring angle of the target is defined as , the heading constraint condition is as follows: (17) Step 2: From the frame measurement data, the following measurement is processed by adaptive recursion. The specific process is as follows: (i) Hough transform is performed on the latest frame measurement data after normalisation, and obtaining the parameter space transformation curves set C corresponding to each measurement point. (ii) Extract the maximum and minimum of in parameter space from C, then translate and extend the accumulation matrix and storage array according to and . (iii) Remove the accumulated value and the stored value corresponding to the first frame measurement data in the previous batch from the accumulation matrix and the storage array. (iv) According to the result of the transformation, the latest frame measurement data is accumulated in points, energy and data storage. (v) Peak detection and track constraints are performed by using the updated accumulation matrix and storage array to obtain the detection results of this recursive processing. Step 3: Repeat step 2 until all K frames measurement data are processed. Step 4: Process the detection results of each batch, merge the tracks belonging to the same target, obtain the final detection results, and output the tracks. 5 Simulation analysis 5.1 Setting of simulation parameters In order to verify the effectiveness of the proposed algorithm and to analyse its performance, it is necessary to simulate and analyse the proposed algorithm. Suppose that there are two near-space hypersonic targets moving in the range of radar detection. Target 1 moves in a uniformly accelerated curve from the first frame of radar measurement data. The initial state of target 1 is . Target 2 moves in a uniform, straight line from the fifth frame radar measurement data. The initial state of target 2 is . Setting radar at coordinate origin, the scanning period is , radar range measurement error is , and angle measurement error is . The total detection frame number frames, the single integrated measurement frames, the clutter number of each frame data obeys Poisson distribution, the clutter density is , and the generated clutter distributes randomly in the radar horizon according to the uniform distribution. Normalisation coefficient . When the parameter space is discretised, the parameter space is discretised into resolution units. Velocity constraints , , heading angle constraints , and track merging threshold . And the definition of SNR is as follows: (18) For the selection problem of the measurement data frames number n in the single integration process, the non-coherent integration detection principle shows that as the number of integrated frames increases, the SNR improves and the target detection probability increases. In order to determine the number of single integrated frames required for the simulation of the algorithm, both targets are moved from the first frame, and the first n frames of measurement data are selected for single integration detection. By selecting different integrated frame numbers, 400 Monte Carlo simulations are carried out under the condition of clutter density and SNR . The change of the target single batch detection probability with the number of integrated frames is shown in Table 1. Table 1. Change of the target single-batch detection performance with the number of integrated frames Integration frames 3 4 5 6 7 8 0.39 0.62 0.76 0.83 0.86 0.87 time 4.41 6.43 8.64 11.21 14.19 17.57 Define single batch target detection probability : (19) where Q denotes the number of Monte Carlo simulations, m denotes the target number, and denotes whether the output track contains the track of target k in the qth simulation (20) It can be seen from the analysis of Table 1 that the probability of single batch detection increases with the increase of integrated frames, but with the increase of integrated frames, the calculation amount of single batch detection also increases. Therefore, com