Unscented and square‐root unscented Kalman filters for quaternionic systems

Menegaz Henrique M.T.; Ishihara Jo?o Y.

摘要

Summary >Proper construction of an unscented Kalman filter (UKF) for unit quaternionic systems is not straightforward due to the incompatibility between the algebraic properties of the unit quaternions and the common real vector space operations (additions and scalar multiplications) needed in the steps of a filter algorithm. This work studies, in detail, all UKFs and square‐root UKFs for quaternionic systems proposed in the literature. First, we classify the algorithms according to the preservation of the unity norm of the quaternion variables. Second, we propose two new algorithms: the quaternionic additive unscented Kalman filter (QuAdUKF) and a square‐root variant of it. The QuAdUKF encompasses all known UKFs for quaternionic systems of the literature preserving, in all steps, the norm of the unit quaternion variables. Besides, it can also yield new UKFs with this norm preservation property. The QuAdUKF's square‐root variant has better properties in comparison with all the square‐root UKFs for quaternionic systems of the literature. Numerical experiments for a spacecraft attitude estimation problem illustrate the theoretical results. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract XMLNS =“http://www.wiley.com/namespaces/wiley”type =“main”xml：lang =“en”xml：id =“rnc4249-abb-abs-abs-0001”> <标题类型=“main” >摘要</标题> >由于单位四元数的代数特性和常见的真实矢量空间操作之间的不相容性，单位四元系统的正确构造是单位四元系统的不相容性并不简单（添加和标量乘法）在过滤器算法的步骤中需要。详细的这项工作研究，所有UKFS和Square-Root UKF用于文献中的四元系统。首先，我们根据季鎓变量的统一标准的保存来分类算法。其次，我们提出了两个新的算法：四元增添了无味的卡尔曼滤光片（Quadukf）和它的平方根变体。 Quadukf在所有步骤中包含所有已知的ukfs，用于各个步骤，单位四元数变量的标准。此外，它还可以使用此常规保存属性产生新的UKFS。与文献的四元系统的所有平方根UKF相比，Quadukf的平方根变体具有更好的性质。航天器姿态估计问题的数值实验说明了理论结果。</ p> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-21736/'>《International Journal of Robust and Nonlinear Control》</a> <b style="margin: 0 2px;">|</b><span>2018年第15期</span><b style="margin: 0 2px;">|</b><span>共28页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Menegaz Henrique M.T.&option=202" target="_blank" rel="nofollow">Menegaz Henrique M.T.;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Ishihara Jo?o Y.&option=202" target="_blank" rel="nofollow">Ishihara Jo?o Y.;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Faculdade GamaUniversidade de BrasíliaBrasília DF Brazil;</p> <p>Laboratório de Robótica e Automa??oUniversidade de BrasíliaBrasília DF Brazil;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/7742.html" title="自动化系统">自动化系统;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=attitude estimation&option=203" rel="nofollow">attitude estimation;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=square‐root unscented Kalman filter (SRUKF)&option=203" rel="nofollow">square‐root unscented Kalman filter (SRUKF);</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=unit quaternion&option=203" rel="nofollow">unit quaternion;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=unscented Kalman filter (UKF)&option=203" rel="nofollow">unscented Kalman filter (UKF);</a> </p> <div class="translation"> 机译：态度估计;方形无需卡尔曼滤波器（SRUKF）;单位四元管;无名的卡尔曼滤波器（UKF）; 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href="/conference-cn-59395/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 2007'信息与通信工程、电子科学与技术、计算机科学与技术、机械工程全国博士生学术论坛 </a> <span> <span> . 2007</span> </span> </div> </li> <li> <div> <b>7. </b><a class="enjiyixqcontent" href="/academic-degree-domestic_mphd_thesis/020312166158.html">无人直升机导航系统改进型Unscented卡尔曼滤波</a> <b>[A] </b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=曾文武&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 曾文武</a> <span> . 2009</span> </span> </div> </li> </ul> <ul style="display: none;"> <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/patent-detail/06120103907051.html">基于Kalman滤波器的航天器姿控系统故障诊断方法</a> <b>[P]</b> . <span> 中国专利： CN111240297A </span> <span> . 2020-06-05</span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/patent-detail/06120100874369.html">一种混合不确定系统保性能鲁棒Kalman滤波器设计方法</a> <b>[P]</b> . <span> 中国专利： CN109787584A </span> <span> . 2019-05-21</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130403166892.html">System and Method for Adaptive Unscented Kalman Filter Using Selective Scaling</a> <b>[P]</b> . <span> 外国专利：  KR101979085B1 </span> <span> . 2019-08-28</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：使用选择性缩放的自适应无味卡尔曼滤波器的系统和方法 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130403365265.html">System and Method for Adaptive Unscented Kalman Filter Using Selective Scaling</a> <b>[P]</b> . <span> 外国专利：  KR20180129407A </span> <span> . 2018-12-05</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：使用选择性缩放的自适应无味卡尔曼滤波器的系统和方法 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130422452361.html">METHOD FOR ESTIMATING A HUMAN POSE USING AN UNSCENTED KALMAN FILTER BASED ON NUMERICAL INVERSE KINEMATICS, COMPUTER-READABLE MEDIUM, AND SERVER SYSTEM THEREFOR</a> <b>[P]</b> . <span> 外国专利：  WO2012046913A1 </span> <span> . 2012-04-12</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：基于数值逆运动学，计算机可读介质和服务器系统的基于无味卡尔曼滤波器的人体姿态估计方法 </span> </p> </li> </ul> </div> </div> </div> <div class="theme cardcommon" style="overflow: auto;display:none"> <h3 class="all_title" id="enpatent55">相关主题</h3> <ul id="subject"> </ul> </div> </div> </div> </div> <div class="right rightcon"> <div class="details_img cardcommon clearfix" style="margin-bottom: 10px;display:none;" > </div> </div> </div> <div id="thesis_get_original1" class="downloadBth" style="bottom: 19px;z-index: 999;" onclick="ywcd('0704023066982','4',7,2,1,'',this,24)" 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