تخمین حالت سیستم‌های غیر خطی با استفاده از فیلتر کالمن مکعبی جمع گوسی بر اساس قانون شعاعی- کروی سیمپلکس
محورهای موضوعی : مهندسی برق و کامپیوترمحمدامین احمدپور کاخک 1 , بهروز صفری نژادیان 2 *
1 - دانشگاه صنعتی شیراز
2 - دانشگاه صنعتی شیراز
کلید واژه: سیستم‌های غیر خطی, تخمین حالت, قانون مکعبی سیمپلکس, فیلتر جمع گوسی,
چکیده مقاله :
در این مقاله الگوریتم جدیدی از فیلترهای جمع گوسی برای تخمین حالت سیستم‌های غیر خطی ارائه شده است. روش پیشنهادی شامل اجرای چند فیلتر کالمن مکعبی به شکل موازی است به صورتی که هر کدام از این فیلترها بر اساس قوانین شعاعی- کروی سیمپلکس پیاده‌سازی می‌شوند. در این روش تابع چگالی احتمال حالت به صورت مجموع وزنی از چند تابع گوسی است که مقادیر میانگین، کواریانس و همچنین ضرایب وزنی این توابع گوسی به صورت بازگشتی و در طول زمان محاسبه می‌شوند و هر کدام از فیلترهای کالمن مکعبی نیز مسئول به روز رسانی یکی از این توابع هستند. در نهایت عملکرد فیلتر پیشنهادی با استفاده از دو مسأله تخمین حالت غیر خطی مورد بررسی قرار گرفته و نتایج آن با فیلترهای غیر خطی مرسوم مقایسه می‌شود. شبیه‌سازی‌های صورت‌گرفته نشان از دقت مناسب الگوریتم پیشنهادی در تخمین حالت سیستم‌های غیر خطی دارد.
In this paper, a new algorithm of Gaussian sum filters for state estimation of nonlinear systems is presented. The proposed method consists of several parallel Cubature Kalman filters each of which is implemented according to the simplex spherical-radial rule. In this method, the probability density function is the sum of the weights of several Gaussian functions. The mean value, covariance, and weight coefficients of these Gaussian functions are calculated recursively over time, and each of the Cubature Kalman filters are responsible for updating one of these functions. Finally, the performance of the proposed filter is investigated using two nonlinear state estimation problems and the results are compared with conventional nonlinear filters. The simulation results show the appropriate accuracy of the proposed algorithm in state estimation of nonlinear systems.
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