بهبود اجرای فیلتر چگالی فرض احتمال کاردینالی توسط فیلتر ذرهای با متغیر کمکی

نویسنده

استادیار، دانشگاه جامع امام حسین (ع)، تهران، ایران

چکیده

معادلات چگالی فرض احتمال (PHD) برای قابل پیاده‌سازی‌نمودن محاسبات سنگین و غیرقابل اجرای فیلترینگ چندهدفه بیزین طراحی شده‌اند. هدف این معادلات به‌روزرسانی و انتشار تابع شدت پسین از مجموعه محدود تصادفی (RFS) اهداف در طول زمان می-باشد. در همین راستا، فیلتر PHD کاردینالی (CPHD) به‌عنوان توسعه‌ای بر روابط فیلتر PHD ارائه گردیده است تا ضعف عدم دقت کافی در تخمین تعداد اهداف را برطرف نماید. در فیلتر CPHD تابع شدت پسین و توزیع کاردینالی پسین مشترکاً بروز می‌گردند. در این مقاله با استفاده از فیلتر ذره‌ای با متغیر کمکی، به پیاده‌سازی فیلتر CPHD خواهیم پرداخت. حسن پیاده‌سازی مطرح‌شده آن است که، در فضایی با ابعاد بالاتر از ابعاد فضای‌‌‌‌ اهداف تحت بررسی کار خواهد شد تا نمونه‌های تقریب‌زننده فیلتر CPHD تولید شوند، که این امر به بهبود دقت تخمین فیلتر خواهد انجامید. به این منظور، در ابتدا معادلات بازگشتی فیلتر CPHD را به‌نحوی دوباره‌نویسی می‌کنیم که مناسب کار با فیلتر ذره‌ای‌‌‌ با متغیر کمکی باشد. سپس، برای نمونه‌برداری در فضای با ابعاد بالاتر، ابتدا از متغیر کمکی برابر نمایه نمونه‌های از قبل تولیدشده و سپس از متغیر کمکی نمایه مشاهدات جاری استفاده می‌کنیم تا بر دقت تخمین تعداد اهداف و تخمین موقعیت اهداف افزوده گردد. مقایسه شبیه‌سازی‌های عددی برمبنای واریانس و میانگین تخمین کاردینالی و خطای تخمین موقعیت اهداف بیانگر بهبود عملکرد الگوریتم پیشنهادی ما نسبت به شیوه رایج پیاده‌سازی از الگوریتم CPHD توسط فیلتر ذره‌ای SIR می‌باشند.

کلیدواژه‌ها


عنوان مقاله [English]

On Improvement of Cardinalized Probability Hypothesis Density Filter Implementation by using Auxiliary Particle Filter

نویسنده [English]

  • Meysam Raeis Danaei
Assistant Professor, Imam Hossein University (AS), Tehran, Iran
چکیده [English]

The PHD filter recursion is introduced to enable the implementation of expensive computational        algorithms of multitarget Bayesian filtering. The goal of this recursion is to update and propagate the    posterior intensity of a Random Finite Set during time steps. To that end, Cardinalized PHD is introduced as an extension of PHD filter to overcome the PHD’s weakness in estimating the number of targets. In the CPHD filter, the posterior intensity function and the cardinality distribution are updating at the same time. In this paper, we use auxiliary particle filter to implement the CPHD filter. The benefit of the proposed   algorithm is to sample at the higher dimensional space compared to the dimensional of the target space in order to generate approximating samples of the CPHD filter and this will improve the estimation accuracy. To that end, we first reformulize the CPHD recursion in a way which is suitable for auxiliary particle filter. Then, to sample in a  higher dimensional space, we first use an auxiliary variable which is the index of   previously generated samples and then we apply another auxiliary variable which is the index of current measurements to improve the estimation of the number and position of multiple targets. Comparison between mean and variance of estimated cardinality and error of multitarget position estimation obtained from simulation results indicate the superiority of our proposed algorithm compared to the current implementation method of the CPHD filter by using SIR particle filter.

کلیدواژه‌ها [English]

  • Multitarget tracking
  • Random Finite Set
  • Probability hypothesis density filter
  • Cardinalized PHD
  • Auxiliary particle filter
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