CN106019229B - Airdrome scene target acoustical localization method, sound sensing device and system - Google Patents
Airdrome scene target acoustical localization method, sound sensing device and system Download PDFInfo
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Abstract
本发明提供一种机场场面目标声学定位方法、声传感装置及系统,该机场场面目标声学定位方法通过在机场场面的不同区域,采用不同方式布设声传感器节点阵元阵,拾取声传感器节点阵元阵布设区域的目标声波,基于该声波信息,对场面目标进行定位。该声传感器节点阵元阵能够形成具有空间选择性的固定空间波束,能够获得具有理想信干噪比的声波信息。本发明提供的机场场面目标声学定位方法、声传感装置及系统,能够最大限度地拾取声波信息,对噪声有效抑制,合理利用声传感器。
The present invention provides an airport scene target acoustic positioning method, an acoustic sensing device and a system. The airport scene target acoustic positioning method adopts different ways to lay out acoustic sensor node array element arrays in different areas of the airport scene, and picks up the acoustic sensor node array. Target sound waves in the area where the element array is deployed, and based on the sound wave information, the target on the scene is located. The acoustic sensor node array element array can form a fixed spatial beam with spatial selectivity, and can obtain acoustic wave information with an ideal signal-to-interference-to-noise ratio. The airport scene target acoustic positioning method, acoustic sensing device and system provided by the present invention can pick up acoustic wave information to the greatest extent, effectively suppress noise, and rationally utilize acoustic sensors.
Description
技术领域technical field
本发明涉及声学定位技术领域,尤其是涉及一种机场场面目标声学定位方法、声传感装置及系统。The invention relates to the technical field of acoustic positioning, in particular to an acoustic positioning method for an airport scene target, an acoustic sensing device and a system.
背景技术Background technique
目前,机场场面的电磁波环境复杂,以电磁波为媒介的定位监视技术容易受到干扰,导致定位性能降低,甚至失效,并且,通常电磁能量辐射和检测的技术复杂,成本较高。声学定位技术应用于机场场面目标定位,具有一些独特的优点,例如:定位信号容易获取,不会向周围环境辐射能量;不受机场电磁环境影响;设备体积小、成本低、远程部署方便。声学定位备受研究者重视。At present, the electromagnetic wave environment of the airport scene is complex, and the positioning monitoring technology using electromagnetic waves as the medium is susceptible to interference, resulting in reduced positioning performance or even failure. In addition, the technology of electromagnetic energy radiation and detection is usually complicated and the cost is high. Acoustic positioning technology is applied to target positioning on the airport scene, and has some unique advantages, such as: positioning signals are easy to obtain, and will not radiate energy to the surrounding environment; it is not affected by the electromagnetic environment of the airport; the equipment is small in size, low in cost, and convenient for remote deployment. Acoustic positioning has attracted much attention from researchers.
但是,机场场面的声场具有复杂性和多变性,会存在多种声音信号,例如:不同声源的不相干信号,地面、建筑物等各种障碍物对声波的反射,低空飞行器噪声,远场声源目标干扰等。在大量噪声和干扰的机场复杂环境下,难以获取理想的信干噪比,不易实现国际民航组织规定的目标高精度定位。国际民航组织规定7.5m以下的机场场面目标定位精度要求。为实现声源目标的有效定位,需声源接收装置(例如,麦克风)提供充足的声音信息。若声源接收装置的布设个数较多,一定程度上能够提供足够的声音信息,但后续阵列信号处理的复杂度上升,目标定位准确度下降,并且,多数声源接收装置不能为后续声源目标定位提供信息支持,或声源接收装置不能够得到更充分的应用,设备利用率低。若声源接收装置的个数减少,且布设结构不合理,或声源接收装置接收的信号中,噪声或干扰较多,有效信号较少,则该声源接收装置不能为后续声源目标定位提供信息支持,同样,也会降低目标定位准确度,影响飞行器的定位。However, the sound field of an airport scene is complex and variable, and there will be a variety of sound signals, such as: irrelevant signals from different sound sources, reflections of sound waves by various obstacles such as the ground and buildings, low-altitude aircraft noise, far-field Sound source target interference, etc. In the complex environment of the airport with a lot of noise and interference, it is difficult to obtain an ideal signal-to-interference-noise ratio, and it is difficult to achieve the goal of high-precision positioning stipulated by the International Civil Aviation Organization. The International Civil Aviation Organization stipulates the accuracy requirements for the positioning accuracy of the airport surface target below 7.5m. In order to effectively locate the sound source target, it is necessary for the sound source receiving device (for example, a microphone) to provide sufficient sound information. If the number of sound source receiving devices is large, it can provide sufficient sound information to a certain extent, but the complexity of subsequent array signal processing increases, and the accuracy of target positioning decreases, and most sound source receiving devices cannot provide sound information for subsequent sound sources. Target positioning provides information support, or the sound source receiving device cannot be fully applied, and the utilization rate of the equipment is low. If the number of sound source receiving devices is reduced, and the layout structure is unreasonable, or the signal received by the sound source receiving device has more noise or interference and less effective signals, then the sound source receiving device cannot locate the subsequent sound source target Providing information support will also reduce the accuracy of target positioning and affect the positioning of aircraft.
为了最大限度的拾取声波信息,对噪声进行有效抑制,如何合理利用声源接收装置,是本领域技术人员亟需解决的问题。In order to pick up the sound wave information to the maximum and effectively suppress the noise, how to rationally utilize the sound source receiving device is an urgent problem to be solved by those skilled in the art.
发明内容Contents of the invention
本发明旨在提供一种机场场面目标声学定位方法、声传感装置及系统,能够最大限度地拾取声波信息,对噪声有效抑制,合理利用声传感器。The present invention aims to provide an acoustic positioning method, acoustic sensing device and system for an airport scene target, which can pick up acoustic wave information to the greatest extent, effectively suppress noise, and rationally utilize acoustic sensors.
第一方面,本发明提供一种机场场面目标声学定位方法,其具体说明如下:In a first aspect, the present invention provides a method for acoustic positioning of an airport scene target, which is specifically described as follows:
本发明提供一种机场场面目标声学定位方法,具体步骤如下:The present invention provides a method for acoustic positioning of an airport scene target, the specific steps are as follows:
步骤S1,根据机场场面的不同区域,布设声传感器节点阵元阵,拾取声传感器节点阵元阵布设区域的目标声波;Step S1, according to different areas of the airport scene, lay out the array of acoustic sensor nodes, and pick up the target sound waves in the area where the array of acoustic sensor nodes is arranged;
步骤S2,基于声传感器节点阵元阵获取的声波信息,对场面目标进行定位。Step S2, based on the acoustic wave information acquired by the acoustic sensor node array, locate the target on the scene.
进一步地,在步骤S1中,直线机场跑道的声传感器节点阵元阵通过如下方式布设:声传感器节点阵元阵对称均匀布设于直线机场跑道两侧,构成直线式声传感器节点阵元阵列,声传感器节点阵元阵形成第一固定空间波束,第一固定空间波束具有第一俯视扇面角和第一俯仰角,以使第一固定空间波束拾取直线机场跑道的目标声波。Further, in step S1, the acoustic sensor node array of the straight-line airport runway is laid out in the following way: the acoustic sensor node array is symmetrically and evenly arranged on both sides of the straight-line airport runway to form a linear acoustic sensor node array, and the acoustic sensor node array is The sensor node array forms a first fixed space beam, and the first fixed space beam has a first overlooking sector angle and a first elevation angle, so that the first fixed space beam picks up target sound waves on a straight-line airport runway.
进一步地,在步骤S1中,机场联络弯道的声传感器节点阵元阵通过如下方式布设:声传感器节点阵元阵布设于机场联络弯道两侧,且联络弯道的圆心所在侧布设个数少于对侧的布设个数,构成弯曲式声传感器节点阵元阵列,声传感器节点阵元阵形成第二固定空间波束,第二固定空间波束具有第二俯视扇面角和第二俯仰角,以使第二固定空间波束拾取联络弯道的目标声波。Further, in step S1, the acoustic sensor node element array of the airport connecting curve is arranged in the following way: the acoustic sensor node array is arranged on both sides of the airport connecting curve, and the number of arrays arranged on the side where the center of the connecting curve is located The number of layouts is less than that on the opposite side to form a curved acoustic sensor node array, the acoustic sensor node array forms a second fixed space beam, and the second fixed space beam has a second overlooking sector angle and a second pitch angle, so that Make the second fixed space beam pick up the target sound wave connecting the curve.
进一步地,第二固定空间波束包括第二内固定空间波束和第二外固定空间波束,第二外固定空间波束的第二外俯视扇面角度小于第二内固定空间波束的第二内俯视扇面角度,第二内固定空间波束由位于联络弯道圆心所在侧的声传感器阵元阵形成,第二外固定空间波束由位于联络弯道圆心相对侧的声传感器阵元阵形成。Further, the second fixed spatial beam includes a second inner fixed spatial beam and a second outer fixed spatial beam, and the second outer overlooking sector angle of the second outer fixed spatial beam is smaller than the second inner overlooking sector angle of the second inner fixed spatial beam , the second inner fixed spatial beam is formed by the acoustic sensor element array located on the side where the center of the connecting curve is located, and the second outer fixed spatial beam is formed by the acoustic sensor array located on the opposite side of the connecting curve center.
进一步地,在步骤S1中,机场直角转弯道的声传感器节点阵元阵通过如下方式布设:声传感器节点阵元阵布设于机场直角转弯道两侧,且直角转弯道的圆心所在侧布设个数少于对侧的布设个数,构成直角式声传感器节点阵元阵列,声传感器节点阵元阵形成第三固定空间波束,第三固定空间波束具有第三俯视扇面角和第三俯仰角,以使第三固定空间波束拾取直角转弯道的目标声波。Further, in step S1, the acoustic sensor node array of the airport right-angle turn is arranged in the following way: the acoustic sensor node array is arranged on both sides of the airport right-angle turn, and the number of arrays on the side where the center of the circle of the right-angle turn is located The number of layouts is less than that on the opposite side to form a right-angle acoustic sensor node array, the acoustic sensor node array forms a third fixed space beam, and the third fixed space beam has a third overlooking sector angle and a third elevation angle, so that Make the third fixed spatial beam pick up the target sound wave of the right-angled curve.
进一步地,第三外固定空间波束的第三外俯视扇面角度小于第三内固定空间波束的第三内俯视扇面角度,第三固定空间波束包括第三内固定空间波束和第三外固定空间波束,第三内固定空间波束由位于直角转弯道圆心所在侧的声传感器阵元阵形成,第三外固定空间波束由位于直角转弯道圆心相对侧的声传感器阵元阵形成。Further, the third outer overlooking sector angle of the third outer fixed space beam is smaller than the third inner overlooking sector angle of the third inner fixed space beam, and the third fixed space beam includes the third inner fixed space beam and the third outer fixed space beam , the third inner fixed spatial beam is formed by the acoustic sensor array on the side where the center of the right-angle turn is located, and the third outer fixed spatial beam is formed by the acoustic sensor array on the opposite side to the center of the right-angle turn.
基于上述任意机场场面目标声学定位方法实施例,进一步地,第一俯视扇面角小于第二俯视扇面角,第二俯视扇面角小于第三俯视扇面角。Based on the embodiment of the acoustic positioning method for any airport scene target above, further, the first top view fan angle is smaller than the second top view fan angle, and the second top view fan angle is smaller than the third top view fan angle.
本发明提供的机场场面目标声学定位方法,该方法通过在机场场面的不同区域,采用不同方式布设声传感器节点阵元阵,该声传感器节点阵元阵形成具有空间选择性的固定空间波束,能够最大限度地拾取所布设区域的目标声波,尽可能抑制地面声杂波、远场杂波及噪声,降低干扰声源数目,有利于获得理想的信干噪比,再根据获取的声波信息,对场面目标进行定位。该机场场面目标声学定位方法能够最大限度地拾取声波信息,对噪声有效抑制,合理利用声传感器,以快速有效对场面目标进行定位。The present invention provides an airport scene target acoustic positioning method. The method adopts different ways to lay out acoustic sensor node arrays in different areas of the airport scene. The acoustic sensor node arrays form fixed spatial beams with spatial selectivity, which can Pick up the target sound waves in the deployed area to the greatest extent, suppress the ground acoustic clutter, far-field clutter and noise as much as possible, reduce the number of interfering sound sources, and help to obtain an ideal signal-to-interference-noise ratio. target positioning. The airport surface target acoustic positioning method can pick up the acoustic wave information to the greatest extent, effectively suppress the noise, and reasonably use the acoustic sensor to quickly and effectively locate the surface target.
第二方面,本发明提供一种机场场面目标声传感装置,其具体说明如下:In a second aspect, the present invention provides an airport scene target acoustic sensing device, which is specifically described as follows:
本发明提供一种机场场面目标声传感装置,该装置包括直线式声传感器节点阵元阵列、弯曲式声传感器节点阵元阵列和直角式声传感器节点阵元阵列。直线式声传感器节点阵元阵列包括对称均匀布设于直线机场跑道两侧的声传感器节点阵元阵,声传感器节点阵元阵形成具有第一俯视扇面角和第一俯仰角的第一固定空间波束,以使第一固定空间波束拾取直线机场跑道的目标声波。弯曲式声传感器节点阵元阵列包括布设于机场联络弯道两侧的声传感器节点阵元阵,联络弯道的圆心所在侧布设个数少于对侧的布设个数,声传感器节点阵元阵形成具有第二俯视扇面角和第二俯仰角的第二固定空间波束,以使第二固定空间波束拾取联络弯道的目标声波。直角式声传感器节点阵元阵列包括布设于机场直角转弯道两侧的声传感器节点阵元阵,直角转弯道的圆心所在侧布设个数少于对侧的布设个数,声传感器节点阵元阵形成具有第三俯视扇面角和第三俯仰角的第三固定空间波束,以使第三固定空间波束拾取直角转弯道的目标声波。The invention provides an airport scene target acoustic sensing device, which comprises a linear acoustic sensor node array, a curved acoustic sensor node array and a right-angle acoustic sensor node array. The linear acoustic sensor node array includes acoustic sensor node arrays symmetrically and uniformly arranged on both sides of the straight-line airport runway, and the acoustic sensor node array forms a first fixed spatial beam with a first overlooking sector angle and a first pitch angle , so that the first fixed space beam picks up the target sound wave of the straight airport runway. The curved acoustic sensor node array includes acoustic sensor node arrays arranged on both sides of the connecting curve of the airport. A second fixed spatial beam with a second overlooking fan angle and a second elevation angle is formed, so that the second fixed spatial beam picks up the target sound wave connecting the curve. The right-angle acoustic sensor node array includes acoustic sensor node arrays arranged on both sides of the airport right-angle turn. A third fixed spatial beam with a third top-view fan angle and a third elevation angle is formed, so that the third fixed spatial beam picks up target sound waves on the right-angled curve.
本发明提供的机场场面目标声传感装置,该声传感装置包括直线式声传感器节点阵元阵列、弯曲式声传感器节点阵元阵列和直角式声传感器节点阵元阵列。根据机场场面的不同区域,布设声传感器节点阵元阵。直线式声传感器节点阵元阵列位于直线机场跑道两侧,弯曲式声传感器节点阵元阵列位于机场联络弯道两侧,直角式声传感器节点阵元阵列位于机场直角转弯道两侧。不同区域布设的声传感装置能够形成具有不同俯视扇面角的固定空间波束,覆盖直线机场跑道、机场联络弯道和机场直角转弯道,以拾取三种机场区域的目标声波。同时,该固定空间波束具有俯仰角,使固定空间波束的交叉区域尽可能落在目标声波的集中区域,以形成具有空间选择性的固定空间波束,能够最大限度地拾取目标声波,抑制地面声杂波、远场杂波及噪声,获得理想的信干噪比,合理利用声传感器。The present invention provides an acoustic sensing device for an airport scene target. The acoustic sensing device includes a linear acoustic sensor node array, a curved acoustic sensor node array and a right-angle acoustic sensor node array. According to the different areas of the airport scene, the acoustic sensor node array is arranged. The linear acoustic sensor node array is located on both sides of the straight airport runway, the curved acoustic sensor node array is located on both sides of the airport contact curve, and the right-angle acoustic sensor node array is located on both sides of the airport right-angle turn. Acoustic sensing devices deployed in different areas can form fixed spatial beams with different overlooking fan angles, covering straight airport runways, airport contact curves and airport right-angle turns, so as to pick up target sound waves in three airport areas. At the same time, the fixed space beam has a pitch angle, so that the intersection area of the fixed space beam falls as much as possible in the concentrated area of the target sound wave, so as to form a fixed space beam with spatial selectivity, which can pick up the target sound wave to the maximum extent and suppress ground noise Waves, far-field clutter and noise, to obtain an ideal signal-to-interference-noise ratio, and rationally use acoustic sensors.
第三方面,本发明提供一种机场场面的目标声学定位系统,其具体说明如下:In a third aspect, the present invention provides a target acoustic positioning system for an airport scene, which is specifically described as follows:
本发明提供一种机场场面的目标声学定位系统,该定位系统包括机场场面目标声传感装置,以及处理器,处理器用于接收机场场面目标声传感装置接收的声波信息,并根据声波信息,对场面目标进行定位。The present invention provides a kind of target acoustic positioning system of airport scene, and this positioning system comprises airport scene target acoustic sensor device, and processor, and processor is used for receiving the sound wave information that airport scene target acoustic sensor device receives, and according to the sound wave information, Position the target on the scene.
本发明提供的机场场面的目标声学定位系统,该定位系统通过机场场面目标声传感装置形成具有空间选择性的固定空间波束,以采集机场场面不同区域的目标声波,并且能够抑制干扰和噪声,再通过处理器对声波信息进行处理,由于获得的声波信息具有理想的信干噪比,有利于对场面目标进行定位。The target acoustic positioning system of the airport scene provided by the present invention, the positioning system forms a fixed space beam with spatial selectivity through the target acoustic sensing device of the airport scene to collect target sound waves in different areas of the airport scene, and can suppress interference and noise, Then the sound wave information is processed by the processor, because the obtained sound wave information has an ideal signal-to-interference-noise ratio, which is beneficial to the positioning of the scene target.
因此,本发明提供的机场场面目标声学定位方法、声传感装置及系统,能够最大限度地拾取声源目标信号,对噪声有效抑制,合理利用声传感器。Therefore, the airport scene target acoustic positioning method, acoustic sensing device and system provided by the present invention can pick up sound source target signals to the greatest extent, effectively suppress noise, and rationally utilize acoustic sensors.
附图说明Description of drawings
图1是本发明机场场面目标声学定位方法提供的一个方法流程图;Fig. 1 is a flow chart of a method provided by the airport scene target acoustic positioning method of the present invention;
图2是本发明机场场面目标声学定位方法提供的一个基于直线机场跑道目标声学定位方法流程图;Fig. 2 is a method flow chart based on the acoustic positioning method of the straight-line airport runway target provided by the acoustic positioning method of the airport scene target of the present invention;
图3是本发明机场场面目标声学定位方法提供的一个基于联络弯道目标声学定位方法流程图;Fig. 3 is a flow chart of an acoustic positioning method based on a connecting curve target provided by the airport scene target acoustic positioning method of the present invention;
图4是本发明机场场面目标声学定位方法提供的一个基于机场直角转弯道目标声学定位方法流程图;Fig. 4 is a flow chart of a method for acoustic location based on an airport right-angle turn target provided by the method for acoustic location of an airport scene target in the present invention;
图5是本发明机场场面目标声传感装置提供的一个俯视图;Fig. 5 is a top view provided by the airport scene target acoustic sensing device of the present invention;
图6是本发明机场场面目标声传感装置提供直线式声传感器节点阵元阵列示意图;Fig. 6 is a schematic diagram of a linear acoustic sensor node array element array provided by the airport scene target acoustic sensing device of the present invention;
图7是本发明机场场面目标声传感装置提供弯曲式声传感器节点阵元阵列示意图;Fig. 7 is a schematic diagram of a curved acoustic sensor node array element array provided by the airport scene target acoustic sensing device of the present invention;
图8是本发明机场场面目标声传感装置提供直角式声传感器节点阵元阵列示意图;Fig. 8 is a schematic diagram of a right-angle acoustic sensor node array element array provided by the airport scene target acoustic sensing device of the present invention;
图9是本发明机场场面目标声传感装置提供的一个截面图。Fig. 9 is a cross-sectional view provided by the airport scene target acoustic sensing device of the present invention.
具体实施方式Detailed ways
下面通过具体的实施例进一步说明本发明,但是,应当理解为,这些实施例仅仅是用于更详细具体地说明之用,而不应理解为用于以任何形式限制本发明。The present invention will be further illustrated by specific examples below, but it should be understood that these examples are only used for more detailed description, and should not be construed as limiting the present invention in any form.
第一方面,本实施例提供一种机场场面目标声学定位方法,其具体说明如下:In the first aspect, the present embodiment provides a method for acoustic positioning of an airport scene target, which is specifically described as follows:
本实施例提供一种机场场面目标声学定位方法,结合图1,具体步骤如下:This embodiment provides an airport scene target acoustic positioning method, in conjunction with Figure 1, the specific steps are as follows:
步骤S1,根据机场场面的不同区域,布设声传感器节点阵元阵,拾取声传感器节点阵元阵布设区域的目标声波;Step S1, according to different areas of the airport scene, lay out the array of acoustic sensor nodes, and pick up the target sound waves in the area where the array of acoustic sensor nodes is arranged;
步骤S2,基于声传感器节点阵元阵获取的声波信息,对场面目标进行定位。Step S2, based on the acoustic wave information acquired by the acoustic sensor node array, locate the target on the scene.
本实施例提供的机场场面目标声学定位方法,该方法通过在机场场面的不同区域,布设不同的声传感器节点阵元阵,该声传感器节点阵元阵形成具有空间选择性的固定空间波束,能够最大限度地拾取所布设区域的目标声波,尽可能抑制地面声杂波、远场杂波及噪声,降低干扰声源数目,有利于获得理想的信干噪比,再根据获取的声波信息,对场面目标进行定位。该机场场面目标声学定位方法能够最大限度地拾取声波信息,对噪声有效抑制,合理利用声传感器,以快速有效对场面目标进行定位。The airport scene target acoustic positioning method provided by this embodiment, the method is by laying out different acoustic sensor node arrays in different areas of the airport scene, and the acoustic sensor node arrays form fixed spatial beams with spatial selectivity, which can Pick up the target sound waves in the deployed area to the greatest extent, suppress the ground acoustic clutter, far-field clutter and noise as much as possible, reduce the number of interfering sound sources, and help to obtain an ideal signal-to-interference-noise ratio. target positioning. The airport surface target acoustic positioning method can pick up the acoustic wave information to the greatest extent, effectively suppress the noise, and reasonably use the acoustic sensor to quickly and effectively locate the surface target.
优选地,基于机场场面的直线机场跑道,本实施例机场场面目标声学定位方法,结合图2,具体步骤如下:Preferably, based on the straight-line airport runway of the airport scene, the acoustic positioning method of the airport scene target in this embodiment, in conjunction with Figure 2, the specific steps are as follows:
步骤S21,直线机场跑道的声传感器节点阵元阵通过如下方式布设:声传感器节点阵元阵布设于直线机场跑道两侧,构成直线式声传感器节点阵元阵列,声传感器节点阵元阵形成第一固定空间波束,第一固定空间波束具有第一俯视扇面角和第一俯仰角,以使第一固定空间波束拾取直线机场跑道的目标声波;其中,为了对直线机场跑道的目标声波进行有效提取,且抑制其它方向的噪声或干扰,第一俯视扇面角不超过180度,且多个第一固定空间波束能够覆盖直线机场跑道的道面。同时,由于飞机的发动机距离地面有一定的高度,为抑制地面反射的和高空的噪声或干扰,第一俯仰角与地面的夹角范围约为5°~20°。Step S21, the acoustic sensor node array of the straight-line airport runway is laid out in the following way: the acoustic sensor node array is arranged on both sides of the straight-line airport runway to form a linear acoustic sensor node array, and the acoustic sensor node array forms the second A fixed space beam, the first fixed space beam has a first overlooking sector angle and a first pitch angle, so that the first fixed space beam picks up the target sound wave of the straight-line airport runway; wherein, in order to effectively extract the target sound wave of the straight-line airport runway , and suppress noise or interference from other directions, the first viewing angle of the sector does not exceed 180 degrees, and the multiple first fixed space beams can cover the runway surface of the straight-line airport runway. At the same time, since the engine of the aircraft is at a certain height from the ground, in order to suppress ground reflection and high-altitude noise or interference, the included angle range between the first pitch angle and the ground is about 5°-20°.
步骤S22,基于直线式声传感器节点阵元阵列获取的声波信息,对场面目标进行定位。Step S22, based on the acoustic wave information acquired by the linear acoustic sensor node array, locate the target on the scene.
基于机场场面的直线机场跑道特点,声传感器节点阵元阵对称分布在直线机场跑道两侧,形成具有第一俯视扇面角和第一俯仰角的第一固定空间波形。第一固定空间波束具有第一俯视扇面角,能够适应直线机场跑道的直线特性,且覆盖直线机场跑道。第一固定空间波束还具有俯仰角,以尽可能拾取直线机场跑道上方一定高度的目标声波,抑制低仰角的地面声杂波、远端来波及低空飞行器的噪声等。从空域滤波的角度,第一固定空间波束能够最大限度拾取目标声波信息,抑制噪声或/和干扰,获得理想的信干噪比。Based on the characteristics of the straight-line airport runway in the airport scene, the acoustic sensor node arrays are symmetrically distributed on both sides of the straight-line airport runway, forming a first fixed spatial waveform with a first overlooking sector angle and a first pitch angle. The first fixed spatial beam has a first overlooking sector angle, can adapt to the straight line characteristic of the straight airport runway, and covers the straight airport runway. The first fixed space beam also has an elevation angle, so as to pick up target sound waves at a certain height above the straight airport runway as much as possible, and suppress ground acoustic clutter at low elevation angles, noise from far-end waves, and low-altitude aircraft. From the perspective of spatial filtering, the first fixed spatial beam can maximize the pickup of target acoustic wave information, suppress noise or/and interference, and obtain an ideal signal-to-interference-noise ratio.
优选地,基于机场场面的机场联络弯道,本实施例机场场面目标声学定位方法,结合图3,具体步骤如下:Preferably, based on the airport contact curve of the airport scene, the acoustic positioning method of the airport scene target in this embodiment, in combination with Figure 3, the specific steps are as follows:
步骤S31,机场联络弯道的声传感器节点阵元阵通过如下方式布设:声传感器节点阵元阵布设于机场联络弯道两侧,且联络弯道的圆心所在侧布设个数少于对侧的布设个数,构成弯曲式声传感器节点阵元阵列,声传感器节点阵元阵形成具有第二俯视扇面角和第二俯仰角的第二固定空间波束,以使第二固定空间波束拾取联络弯道的目标声波;由于飞机的发动机距离地面有一定的高度,为抑制地面反射的和高空的噪声或干扰,第二俯仰角与地面的夹角范围约为5°~20°。Step S31, the acoustic sensor node array of the airport connecting curve is laid out in the following way: the acoustic sensor node array is arranged on both sides of the airport connecting curve, and the number of arrays on the side where the center of the connecting curve is located is less than that on the opposite side The number of layouts constitutes a curved acoustic sensor node array, and the acoustic sensor node array forms a second fixed spatial beam with a second top view fan angle and a second elevation angle, so that the second fixed spatial beam picks up the connecting curve The target sound wave; since the engine of the aircraft is at a certain height from the ground, in order to suppress ground reflection and high-altitude noise or interference, the angle range between the second pitch angle and the ground is about 5° to 20°.
步骤S32,基于弯曲式声传感器节点阵元阵列获取的声波信息,对场面目标进行定位。Step S32, based on the acoustic wave information acquired by the curved acoustic sensor node array, locate the target on the scene.
基于机场场面的机场联络弯道的弯曲特点,声传感器节点阵元阵布设在机场联络弯道两侧,且两侧的布设个数不同,兼顾连接处多条通道,以形成具有第二俯视扇面角和第二俯仰角的第二固定空间波束。第二固定空间波束具有空间选择性,能够尽可能拾取联络弯道上方的目标声波,抑制低仰角的地面声杂波及低空飞行器的噪声等。Based on the bending characteristics of the airport connecting curve in the airport scene, the acoustic sensor node arrays are arranged on both sides of the airport connecting curve, and the number of layouts on both sides is different, taking into account the multiple channels at the connection to form a second overlooking fan angle and a second fixed spatial beam at a second elevation angle. The second fixed space beam has space selectivity, which can pick up the sound waves of the target above the contact curve as much as possible, and suppress the ground sound clutter at low elevation angles and the noise of low-altitude aircraft.
优选地,第二固定空间波束包括第二内固定空间波束和第二外固定空间波束,第二外固定空间波束的第二外俯视扇面角度小于第二内固定空间波束的第二内俯视扇面角度,第二内固定空间波束由位于联络弯道圆心所在侧的声传感器阵元阵形成,第二外固定空间波束由位于联络弯道圆心相对侧的声传感器阵元阵形成。其中,为了对机场联络弯道的目标声波进行有效提取,且抑制其它方向的噪声或干扰,第二外俯视扇面角小于180度,第二内俯视扇面角大于180度,且多个第二固定空间波束能够覆盖机场联络弯道的道面,或与联络弯道相连接的跑道、滑行道等,有利于更全面地拾取目标声波,抑制噪声或/和干扰。Preferably, the second fixed spatial beam includes a second inner fixed spatial beam and a second outer fixed spatial beam, and the second outer bird's eye view sector angle of the second outer fixed space beam is smaller than the second inner bird's eye fan angle of the second inner fixed space beam , the second inner fixed spatial beam is formed by the acoustic sensor element array located on the side where the center of the connecting curve is located, and the second outer fixed spatial beam is formed by the acoustic sensor array located on the opposite side of the connecting curve center. Among them, in order to effectively extract the target sound waves of the airport contact curve and suppress noise or interference from other directions, the second outer looking fan angle is less than 180 degrees, the second inner looking fan angle is greater than 180 degrees, and multiple second fixed The space beam can cover the road surface of the airport contact curve, or the runway, taxiway, etc. connected with the contact curve, which is beneficial to more comprehensively picking up the target sound wave and suppressing noise or/and interference.
优选地,基于机场场面的机场直角转弯道,本实施例机场场面目标声学定位方法,结合图4,具体步骤如下:Preferably, based on the airport right-angle turn road of the airport scene, the acoustic positioning method of the airport scene target in this embodiment, in conjunction with Figure 4, the specific steps are as follows:
步骤S41,机场直角转弯道的声传感器节点阵元阵通过如下方式布设:声传感器节点阵元阵布设于机场直角转弯道两侧,且直角转弯道的圆心所在侧布设个数少于对侧的布设个数,构成直角式声传感器节点阵元阵列,声传感器节点阵元阵形成第三固定空间波束,第三固定空间波束具有第三俯视扇面角和第三俯仰角,第三固定空间波束用于拾取直角转弯道的目标声波;由于飞机的发动机距离地面有一定的高度,为抑制地面反射的和高空的噪声或干扰,第三俯仰角与地面的夹角范围约为5°~20°。Step S41, the acoustic sensor node array of the airport right-angle turn is laid out in the following way: the acoustic sensor node array is arranged on both sides of the airport right-angle turn, and the number of arrays on the side where the center of the right-angle turn is located is less than that on the opposite side The number of layouts constitutes a right-angle acoustic sensor node array. The acoustic sensor node array forms a third fixed space beam. The third fixed space beam has a third overlooking sector angle and a third elevation angle. The third fixed space beam is used for It is used to pick up the target sound wave on the right-angle turn road; since the engine of the aircraft is at a certain height from the ground, in order to suppress ground reflection and high-altitude noise or interference, the angle range between the third pitch angle and the ground is about 5°-20°.
步骤S42,基于直角式声传感器节点阵元阵列获取的声波信息,对场面目标进行定位。Step S42, based on the sound wave information acquired by the rectangular acoustic sensor node array element array, the scene target is located.
基于机场场面的机场直角转弯道的直角特点,如直角型、丁字型的转弯处,声传感器节点阵元阵布设在机场直角转弯道两侧,且两侧的布设个数不同,以形成具有第三俯视扇面角和第三俯仰角的第三固定空间波束,确保第三固定空间波束能够覆盖机场直角转弯道,且第三固定空间波束的交叉区域尽可能与目标声波的集中区域相一致,使第三固定空间波束具有空间选择性,尽可能拾取目标声波,抑制噪声或/和干扰。Based on the right-angle characteristics of airport right-angle turns based on the airport scene, such as right-angle and T-shaped turns, the acoustic sensor node arrays are arranged on both sides of the airport right-angle turn, and the number of deployments on both sides is different. The third fixed space beam with three overlooking sector angles and the third elevation angle ensures that the third fixed space beam can cover the right-angled turn of the airport, and the intersection area of the third fixed space beam is as consistent as possible with the concentration area of the target sound wave, so that The third fixed space beam has space selectivity, and picks up the target sound wave as much as possible to suppress noise or/and interference.
优选地,第三外固定空间波束的第三外俯视扇面角度小于第三内固定空间波束的第三内俯视扇面角度,第三固定空间波束包括第三内固定空间波束和第三外固定空间波束,第三内固定空间波束由位于直角转弯道圆心所在侧的声传感器阵元阵形成,第三外固定空间波束由位于直角转弯道圆心相对侧的声传感器阵元阵形成。其中,为了对机场直角转弯道的目标信息进行有效提取,且抑制其它方向的噪声或干扰,第三外俯视扇面角小于180度,第三内俯视扇面角大于180度,且多个第三固定空间波束能够覆盖机场直角转弯道的道面,以兼顾连接处的多条通道,或与机场直角转弯道相连接的跑道、滑行道等,有利于更全面地拾取目标声波。Preferably, the third outer overlooking sector angle of the third outer fixed space beam is smaller than the third inner overlooking sector angle of the third inner fixed space beam, and the third fixed space beam includes the third inner fixed space beam and the third outer fixed space beam , the third inner fixed spatial beam is formed by the acoustic sensor array on the side where the center of the right-angle turn is located, and the third outer fixed spatial beam is formed by the acoustic sensor array on the opposite side to the center of the right-angle turn. Among them, in order to effectively extract the target information of the right-angle turn at the airport and suppress noise or interference from other directions, the third outer looking fan angle is less than 180 degrees, the third inner looking fan angle is greater than 180 degrees, and multiple third fixed The space beam can cover the road surface of the right-angle turn of the airport to take into account the multiple channels at the connection, or the runway, taxiway, etc. connected to the airport right-angle turn, which is conducive to more comprehensive pickup of target sound waves.
基于上述任意机场场面目标声学定位方法实施例,优选地,第一俯视扇面角小于第二俯视扇面角,第二俯视扇面角小于第三俯视扇面角。基于机场场面的直线机场跑道、联络弯道和机场直角转弯道,其分别具有直角特性、弯曲特性和直角特性,为适应其特性,且保证能够全面有效拾取机场场面不同区域上方的目标声波,其俯视扇面角度依次增大的固定空间波束,能够最大限度拾取有效目标声波。Based on any embodiment of the above-mentioned acoustic positioning method for an airport scene target, preferably, the first bird's-eye view fan angle is smaller than the second bird's-eye view fan angle, and the second bird's-eye view fan angle is smaller than the third bird's-eye view fan angle. Straight-line airport runways, connecting curves and airport right-angle turns based on the airport scene have right-angle characteristics, bending characteristics and right-angle characteristics respectively. The fixed space beam with increasing angle of looking down on the sector can pick up effective target sound waves to the maximum extent.
第二方面,本实施例还提供一种机场场面目标声传感装置,具体说明如下:In the second aspect, this embodiment also provides an airport scene target acoustic sensing device, which is specifically described as follows:
本实施例提供一种机场场面目标声传感装置,结合图5,该定位装置包括直线式声传感器节点阵元阵列、弯曲式声传感器节点阵元阵列和直角式声传感器节点阵元阵列。This embodiment provides an acoustic sensor device for an airport scene target. Referring to FIG. 5 , the positioning device includes a linear acoustic sensor node array, a curved acoustic sensor node array, and a right-angle acoustic sensor node array.
直线式声传感器节点阵元阵列包括对称均匀布设于直线机场跑道两侧的声传感器节点阵元阵,声传感器节点阵元阵形成具有第一俯视扇面角和第一俯仰角的第一固定空间波束,第一固定空间波束用于拾取直线机场跑道的目标声波。结合图6,在直线机场跑道的两侧,对称分布直线式声传感器节点阵元阵列,如第一NEA声传感器阵元阵61、第二NEA声传感器阵元阵62、第三NEA声传感器阵元阵63和第四NEA声传感器阵元阵64的分布特征,其分别形成第一节点固定空间波束611、第二节点固定空间波束621、第三节点固定空间波束631和第四节点固定空间波束641,从俯视角度,每个固定空间波束具有相同的第一俯视扇面角,其角度不超过180°,且能够覆盖直线机场跑道,以最大限度拾取直线跑道上方目标飞行器60的声波信号。同时每个固定空间波束具有相同的第一俯仰角,其角度范围为5°~20°。The linear acoustic sensor node array includes acoustic sensor node arrays symmetrically and uniformly arranged on both sides of the straight-line airport runway, and the acoustic sensor node array forms a first fixed spatial beam with a first overlooking sector angle and a first pitch angle , the first fixed spatial beam is used to pick up target sound waves on straight airport runways. Combined with Figure 6, on both sides of the straight-line airport runway, there are symmetrically distributed linear acoustic sensor node arrays, such as the first NEA acoustic sensor array 61, the second NEA acoustic sensor array 62, and the third NEA acoustic sensor array The distribution characteristics of the element array 63 and the fourth NEA acoustic sensor array element array 64, which respectively form the first node fixed space beam 611, the second node fixed space beam 621, the third node fixed space beam 631 and the fourth node fixed space beam 641. From a bird's eye view angle, each fixed space beam has the same first bird's-eye view sector angle, the angle of which does not exceed 180°, and can cover the straight airport runway, so as to pick up the sound wave signal of the target aircraft 60 above the straight runway to the maximum. At the same time, each fixed space beam has the same first elevation angle, and the angle range is 5°-20°.
弯曲式声传感器节点阵元阵列包括布设于机场联络弯道两侧的声传感器节点阵元阵,联络弯道的圆心所在侧布设个数少于对侧的布设个数,声传感器节点阵元阵形成具有第二俯视扇面角和第二俯仰角的第二固定空间波束,第二固定空间波束用于拾取联络弯道的目标声波。结合图7,在联络弯道的两侧,布设声传感器节点阵元阵,如第一NEA声传感器阵元阵71、第二NEA声传感器阵元阵72、第三NEA声传感器阵元阵73、第四NEA声传感器阵元阵74和第五NEA声传感器阵元阵75,分别形成第一节点固定空间波束711、第二节点固定空间波束721、第三节点固定空间波束731、第四节点固定空间波束741和第五节点固定空间波束751。如第一NEA声传感器阵元阵71和第四NEA声传感器阵元阵74分别位于联络弯道的圆心所在侧,如第二NEA声传感器阵元阵72、第三NEA声传感器阵元阵77和第五NEA声传感器阵元阵75位于联络弯道的圆心所在侧的对侧,其固定空间波束的第二俯视扇面角大于直线机场跑道的固定空间波形的第一俯视扇面角,且第二外俯视扇面角小于180度,第二内俯视扇面角大于180度,多个固定空间波束能够覆盖机场联络弯道的道面。同时每个固定空间波束具有相同的第二俯仰角,其角度范围为5°~20°。The curved acoustic sensor node array includes acoustic sensor node arrays arranged on both sides of the connecting curve of the airport. A second fixed spatial beam is formed with a second overlooking fan angle and a second elevation angle, and the second fixed spatial beam is used to pick up the target sound wave connecting the curve. In combination with Fig. 7, on both sides of the connecting curve, the acoustic sensor node arrays are arranged, such as the first NEA acoustic sensor array 71, the second NEA acoustic sensor array 72, and the third NEA acoustic sensor array 73 , the fourth NEA acoustic sensor array 74 and the fifth NEA acoustic sensor array 75 respectively form the first node fixed space beam 711, the second node fixed space beam 721, the third node fixed space beam 731, the fourth node The fixed spatial beam 741 and the fifth node fixed spatial beam 751 . For example, the first NEA acoustic sensor array 71 and the fourth NEA acoustic sensor array 74 are respectively located at the side of the center of the connecting curve, such as the second NEA acoustic sensor array 72, the third NEA acoustic sensor array 77 And the fifth NEA acoustic sensor element array 75 is located on the opposite side of the side where the center of circle of the contact curve is located, and the second overlooking sector angle of its fixed spatial beam is greater than the first overlooking sector angle of the fixed spatial waveform of the straight airport runway, and the second The outer overlooking sector angle is less than 180 degrees, the second inner overlooking sector angle is greater than 180 degrees, and multiple fixed space beams can cover the road surface of the airport contact curve. At the same time, each fixed space beam has the same second elevation angle, and the angle range is 5°-20°.
直角式声传感器节点阵元阵列包括布设于机场直角转弯道两侧的声传感器节点阵元阵,直角转弯道的圆心所在侧布设个数少于对侧的布设个数,声传感器节点阵元阵形成具有第三俯视扇面角和第三俯仰角的第三固定空间波束,第三固定空间波束用于拾取直角转弯道的目标声波。结合图8,在机场直角转弯道的两侧,布设声传感器节点阵元阵,如第一NEA声传感器阵元阵81、第二NEA声传感器阵元阵82、第三NEA声传感器阵元阵83、第四NEA声传感器阵元阵84、第五NEA声传感器阵元阵85和第六NEA声传感器阵元阵86,其形成第一节点固定空间波束811、第二节点固定空间波束821、第三节点固定空间波束831、第四节点固定空间波束841、第五节点固定空间波束851和第六节点固定空间波束861,其俯视扇面角度均大于联络弯道的第二固定空间波束的俯视扇面角,且第三外俯视扇面角小于180度,第三内俯视扇面角大于180度,能够拾取机场直角转弯道上方的声波信号,抑制干扰和噪声。同时每个固定空间波束具有相同的第二俯仰角,其角度范围为5°~20°。结合图9,该机场场面目标声传感装置形成的固定空间波束具有俯仰角,如在直线机场跑道、联络弯道或机场直角转弯道的两侧,设有第一声传感器阵元阵91和第二声传感器阵元阵92,其分别形成具有俯仰角的第一节点固定空间波束911和第二节点固定空间波束922,两波束的交叉区域尽可能落在目标声波的集中区域,能够最大限度拾取目标声波,抑制地面杂波、远端或低空噪声。The right-angle acoustic sensor node array includes acoustic sensor node arrays arranged on both sides of the airport right-angle turn. A third fixed spatial beam with a third top view fan angle and a third pitch angle is formed, and the third fixed spatial beam is used to pick up target sound waves on right-angled curves. Combined with Figure 8, on both sides of the right-angle turn road at the airport, the acoustic sensor node arrays are arranged, such as the first NEA acoustic sensor array 81, the second NEA acoustic sensor array 82, and the third NEA acoustic sensor array 83. The fourth NEA acoustic sensor array 84, the fifth NEA acoustic sensor array 85, and the sixth NEA acoustic sensor array 86, which form the first node fixed spatial beam 811, the second node fixed spatial beam 821, The fixed space beam 831 of the third node, the fixed space beam 841 of the fourth node, the fixed space beam 851 of the fifth node and the fixed space beam 861 of the sixth node, the top view sector angles of which are larger than the top view sector of the second fixed space beam connecting the curve angle, and the third outer overlooking sector angle is less than 180 degrees, and the third inner overlooking sector angle is greater than 180 degrees, which can pick up the sound wave signal above the right-angle turn road at the airport and suppress interference and noise. At the same time, each fixed space beam has the same second elevation angle, and the angle range is 5°-20°. In conjunction with Fig. 9, the fixed spatial beam formed by the airport surface target acoustic sensing device has a pitch angle, such as on both sides of a straight airport runway, a connecting curve or an airport right-angle turn, a first acoustic sensor element array 91 and The second acoustic sensor element array 92, which respectively forms a first node fixed space beam 911 and a second node fixed space beam 922 with an elevation angle, the intersection area of the two beams falls on the concentrated area of the target sound wave as much as possible, and can maximize Pick up target sound waves, suppress ground clutter, far-end or low-altitude noise.
本实施例机场场面目标声传感装置,该声传感装置包括直线式声传感器节点阵元阵列、弯曲式声传感器节点阵元阵列和直角式声传感器节点阵元阵列。根据机场场面的不同区域,布设不同的声传感装置。直线式声传感器节点阵元阵列位于直线机场跑道两侧,以适应直线机场跑道的直线特性。弯曲式声传感器节点阵元阵位于机场联络弯道两侧,以适应机场联络弯道的弯曲特性。直角式声传感器节点阵元阵位于机场直角转弯道两侧,以适应机场直角转弯道的直角特性。不同区域布设的声传感装置,能够形成具有俯视扇面角依次增大的固定空间波束,覆盖直线机场跑道、机场联络弯道和机场直角转弯道,以拾取三种机场区域上方的目标声波。同时,机场场面上方由下到上依次存在地杂波区、声信号区和低空噪声区,例如低空飞行器噪声。该固定空间波束具有俯仰角,以使其具有空间选择性,即固定空间波束的交叉区域尽可能落在目标声波的集中区域,如此的固定空间波束能够将空间分成多个不同的区域,如地杂波抑制区、声信号集中区和低空噪声抑制区,该机场场面目标声传感装置能够最大限度地拾取声信号增强区的目标声波,抑制地面声杂波、远端地面噪声及低空噪声,获得理想的信干噪比,合理利用声传感器。The acoustic sensor device for an airport scene target in this embodiment includes a linear acoustic sensor node array, a curved acoustic sensor node array, and a right-angle acoustic sensor node array. According to different areas of the airport scene, different acoustic sensing devices are deployed. The linear acoustic sensor node arrays are located on both sides of the straight airport runway to adapt to the straight line characteristics of the straight airport runway. The node array of the curved acoustic sensor is located on both sides of the airport contact curve to adapt to the bending characteristics of the airport contact curve. The right-angle acoustic sensor node array is located on both sides of the airport right-angle turn to adapt to the right-angle characteristics of the airport right-angle turn. Acoustic sensing devices deployed in different areas can form fixed spatial beams with sequentially increasing fan angles, covering straight airport runways, airport contact curves, and airport right-angle turns, so as to pick up target sound waves above the three airport areas. At the same time, there are ground clutter areas, acoustic signal areas, and low-altitude noise areas from bottom to top above the airport scene, such as low-altitude aircraft noise. The fixed space beam has an elevation angle to make it spatially selective, that is, the intersection area of the fixed space beam falls on the concentration area of the target sound wave as much as possible, such a fixed space beam can divide the space into multiple different areas, such as the ground Clutter suppression area, acoustic signal concentration area and low-altitude noise suppression area, the airport surface target acoustic sensing device can pick up target sound waves in the acoustic signal enhancement area to the maximum, suppress ground acoustic clutter, far-end ground noise and low-altitude noise, To obtain the ideal signal to interference and noise ratio, make reasonable use of the acoustic sensor.
第三方面,本实施例还提供一种机场场面的目标声学定位系统,具体说明如下:In the third aspect, this embodiment also provides an acoustic target positioning system for an airport scene, which is specifically described as follows:
本实施例提供一种机场场面的目标声学定位系统,该定位系统包括机场场面目标声传感装置,以及处理器,处理器用于接收机场场面目标声传感装置接收的声波信息,并根据声波信息,对场面目标进行定位。This embodiment provides a target acoustic positioning system for an airport scene. The positioning system includes an airport target acoustic sensing device, and a processor. The processor is used to receive the acoustic wave information received by the airport target acoustic sensing device, and , to locate the scene target.
本实施例提供的机场场面的目标声学定位系统,该定位系统通过机场场面目标声传感装置形成具有空间选择性的固定空间波束,固定空间波束具有一定的俯视扇面角和俯仰角,使该机场场面目标声传感装置能够最大限度获取目标声波信息,抑制地面杂波、远端噪声及低空噪声,获得理想的信干噪比。处理器根据机场场面目标声传感装置接收的声波信息,对场面目标进行定位,由于机场场面目标声传感装置能够获得理想信干噪比的声波信息,能够减少定位计算复杂度,有利于对场面目标进行定位。The target acoustic positioning system of the airport scene provided by this embodiment, the positioning system forms a fixed space beam with spatial selectivity through the target acoustic sensing device of the airport scene, and the fixed space beam has a certain overlooking sector angle and pitch angle, so that the airport The surface target acoustic sensing device can maximize the acquisition of target acoustic wave information, suppress ground clutter, far-end noise and low-altitude noise, and obtain an ideal signal-to-interference-noise ratio. The processor locates the surface target according to the acoustic wave information received by the airport surface target acoustic sensing device. Since the airport surface target acoustic sensing device can obtain the sound wave information with an ideal signal-to-interference-noise ratio, it can reduce the complexity of positioning calculations and is beneficial to The scene target is positioned.
尽管本发明已进行了一定程度的描述,明显地,在不脱离本发明的精神和范围的条件下,可进行各个条件的适当变化。可以理解,本发明不限于实施方案,而归于权利要求的范围,其包括每个因素的等同替换。While the invention has been described to a certain extent, it will be obvious that various changes may be made in various conditions without departing from the spirit and scope of the invention. It is to be understood that the invention is not limited to the embodiments, but belongs to the scope of the claims, which include equivalents of each element.
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