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四象限方位解算的算法誤差分析及補償

熱度0票  瀏覽62次 時間:2018年7月17日 14:57
  摘要:通過對四象限方位探測原理和解算方法的分析,得到了在歸一化光敏面半徑的情況下,不同光斑半徑對應的解算誤差曲線。根據仿真結果,提出了分段擬合的方法,通過修正系數對算法進行補償。經仿真驗證,分段補償的實現方法簡單,對四象限算法線性度的補償效果明顯。
  關鍵詞:四象限;方位解算;誤差分析;補償
  中圖分類號:V249.1 文獻標識碼:A 文章編號:1673-1131(2015)10-0034-02.
  0 引言
  四象限光電探測器用于方位探測時,若接收系統的光軸對準目標,則目標光斑位于探測器中心,光斑在四個象限中的面積相等,因此各路輸出相等;當目標偏離光軸時,光斑在四個象限上的分布面積不相等,因此各路輸出信號不相等[1]。通過解算四象限輸出之間的關系,即可判別目標偏離接收系統光軸的情況,從而實現對目標的方位探測。
  本文從四象限方位解算的基本方法入手,分析不同光斑半徑的四象限方位探測算法誤差,并提出了一種有效解算區內的算法補償方法,對算法的誤差進行補償,以提高系統的解算精度。
  1 四象限方位解算法
  四象限的目標成像光斑示意圖如圖 1 所示。為了表述方便,建立以四象限探測器分割線為基準的坐標系,將探測器的 其中一條分割線水平放置,設為系統的X軸,另一條垂直方向的分割線設為 Y 軸,探測器的中心設為原點 O。光斑中心 O’
  在探測器坐標系的位置標為(dx,dy)。
  圖 1 四象限成像光斑示意圖
  假設照射到探測器光敏面上的光斑為均勻的彌散斑,光斑在四個象限上的面積分別為 S1、S2、S3 和 S4,光斑中心 O’的 坐標值的計算式為[2]:
  式中:k 為和光斑半徑 r 相關的系數,理想情況下 k=r。
  根據求得的和 dx、dy,再由三角關系便可以得到目標與光軸的夾角 在 X 軸和 Y 軸上的分量 x=arctan (dx/f),y=arctan(dx/f),其中 f 為探測器光敏面至光學系統的距離。對于確定的系統,f 為確定的值,因此系統的方位解算可以等效為光斑中心在光敏面上的位置的解算。
  2 算法的誤差分析
  設光敏面的半徑為 R,當光斑半徑為 r1<R/2 或 r2=R/2 時,在(-r1,r1)或(-r2,r2)的范圍內,光斑不會超出探測器光敏面,如圖2(a)所示。當光斑半徑為 r3>R/2 時,在 x∈(R-r3,r3)的范圍內,部分光斑會超出探測器光敏面[3,4],如圖 2(b)所示。
  (a) (b)
  圖 2 光斑示意圖
  當光斑半徑為 r1 或 r2 時,根據式(1)通過光斑的幾何關系可以得到 dx 為:
  式中:t = x/r。
  圖 2(b)中的陰影部分面積 S’為:
  式中:x’為光斑和光敏面兩個圓的交點在X軸上的坐標。
  因此,當光斑半徑為 r3 時,可得
  將dx與實際偏移量x相減即可得到四象限的解算誤差為:
  令 k=r,將光敏面半徑 R 歸一化后進行仿真可以得到三種情況下四象限位置解算的算法誤差曲線如圖 3 所示。
  圖 3 不同光斑半徑下的算法誤差曲線
  從圖中可以看出,對于三種不同半徑的光斑,當光斑中心 位于探測器中心位置及偏移量達到±ri(i=1,2,3)時,解算誤差為零。當光斑中心偏移量在(-ri,0)及 (0,ri)的范圍內時,誤差較小;大于該范圍以后誤差直線增加,這是由于當光斑中心超出±ri 的范圍后,光斑只能落到光敏面的左側或右側區域,導致四象限系統無法判別光斑中心的確切坐標位置。
  3 誤差補償
  通過上節的分析可知,當 x/r 的比值一定時,通過和差法解算得到的光斑中心位置僅與 k 有關。由于 dx 與 x/r 之間是非線性的[5],要獲取精確的函數關系式并不容易,而且太多未知量的迭代會增加系統計算的復雜度,影響系統的實時性。因此,采用分段擬合的方式,對不同的解算區間用預定的系數進行校正。這樣即可減小系統計算的復雜度,也能大幅降低系統的解算誤差。
  對于確定的光斑半徑 r,比例系數 b=dx/x 的值在 1.27 ~ 1之間的范圍內。以將 x 分為(0 ~ 0.6r)、[0.6r,0.8r)、[0.8r,0.9r)、[0.9r,r)和 r 等 5 個區間為例,從 b 曲線上分別取值 1.27、1.19、1.12、1.07 和 1,使各段區間上的求解值 dx’=dx/b。補償前后的解算值及誤差如圖 4 所示。從圖中可以明顯看到,經過校正以后,和差法的解算值已經非常接近理論值,誤差由未校正前的最大 11.57%降到了最大 1.17%,效果十分明顯。
  圖 4 補償前后的解算曲線和誤差曲線
  分段區間的數量及系數 b 的取值可以根據實際應用進行靈活調整,以實現系統解算的最佳效率和精度。
  4 結語
  本文對四象限和差法方位解算的原理和算法進行了詳細的分析,通過仿真獲得了歸一化光敏面半徑 R 的情況下,光斑半徑r1<R/2、r2=R/2以及r3>R/2 時的方位解算的算法誤差曲線。
  并根據仿真結果,提出采用分段擬合的方法,通過修正系數對算法誤差進行補償。經仿真驗證,分段補償的實現方法簡單,并且對誤差補償的效果十分明顯,具有較強的實際應用意義。
  參考文獻:
  [1] 雷玉唐.光電檢測技術(第 2 版) [M].北京:中國計量出版社,2009:103-106.
  [2] 劉華柏.激光半主動制導半實物仿真系統中目標方位探測電路的研究[D].長沙:國防科學技術大學,2008.
  [3] 張雷,張國玉,劉云清.影響四象限探測器探測精度的因素[J].中國激光,2012,39(6): 0605007-1-0605007-5.
  [4] 余峰,何燁,李松,張繼濤.四象限光電檢測系統的定位算法研究及改進[J].應用光學,2008,29(4):493-497.
  [5] 呂生強. 四象限探測器的激光探測與定位研究[D].南京:南京理工大學,2008



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