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資源簡介

收到一些國內外朋友的來信，咨詢關于容積卡爾曼濾波的問題(CKF)，大家比較疑惑的應該就是generator或G-orbit的概念。考慮到工作以后，重心必然轉移，不可能再像現在這樣詳細的回答所有人的問題，更不可能再幫大家改論文、寫(或改)代碼了，請各位諒解！在此，上傳一個CKF和五階CKF用于目標跟蹤的示例代碼，代碼中包含詳細的注釋，希望對大家以后的學習和研究有所幫助！ 此代碼利用C++對五階CKF的第二G-軌跡進行了封裝(Perms.exe)，能理解最好，如果無法理解，也無須深究其具體構造方法！可執行文件底層是用字符串+遞歸算法實現的，理論上可以應用于任意維模型。但考慮到遞歸算法可能存在的棧溢出，重復壓棧出棧帶來的時間消耗等問題，我們利用矩陣的稀疏性和群的完全對稱性，并通過分次調用，來盡可能減少棧的深度，提高計算速度。 容積點一次生成后，可以一直使用，通過對50維G-軌跡的生成速度(Core T6600@2.2GHz)進行測試，包含數據讀寫在內的速度約為1.5秒，速度尚可。而目前為止，本人尚未遇到達到甚至超過50維的系統，因此，暫時不作算法層面的優化。 注意：Perms.exe可以用于任意維模型，將可執行文件復制至工作目錄下，調用時選擇N/n，并輸入你的模型維數，即可生成所需的第二G-軌跡。如果無法理解相關的概念，請參考示例代碼，并記住如何使用即可~~~ 相關理論基礎及所用模型，請參考以下文獻： References (you may cite one of the articles in your paper): [1] X. C. Zhang, C. J. Guo, "Cubature Kalman filters: Derivation and extension," Chinses Physics B, vol.22, no.12, 128401, DOI: 10.1088/1674-1056/22/12/128401 [2] X. C. Zhang, Y. L. Teng, "A new derivation of the cubature Kalman filters," Asian Journal of Control, DOI: 10.1002/asjc.926 [3] X. C. Zhang, "Cubature information filters using high-degree and embedded cubature rules," Circuits, Systems, and Signal Processing,vol.33, no.6,pp.1799-1818,DOI: 10.1007/s00034-013-9730-0

資源截圖

代碼片段和文件信息 

function?[x?P]?=?Fifth_degree_CKF（xhat?Pplus?z）
global?Q?R?T?m?kesi_5?b_5?w2_5?w_5?w4_5;
%%?--------------------------5th-degree?CKF-----------------------

%%?---------------------------Time?Update-------------------------
%?Evaluate?the?Cholesky?factor
Shat?=?chol（Pplus?‘lower‘）;
for?cpoint?=?1?:?b_5
????%?Evaluate?thecubature?points
????rjpoint_5（:?cpoint）?=?Shat?*?kesi_5（:?cpoint）?+?xhat;
????%?Evaluate?the?propagated?cubature?points
????fai3?=?[1?sin（rjpoint_5（5?cpoint）?*?T）?/?rjpoint_5（5?cpoint）?0?-（1?-?...
????????cos（rjpoint_5（5?cpoint）?*?T））?/?rjpoint_5（5?cpoint）?0;
????????0?cos（rjpoint_5（5?cpoint）?*?T）?0?-sin（rjpoint_5（5?cpoint）?*?T）?0;
????????0?（1?-?cos（rjpoint_5（5?cpoint）?*?T））?/?rjpoint_5（5?cpoint）?1?...
????????sin（rjpoint_5（5?cpoint）?*?T）?/?rjpoint_5（5?cpoint）?0;
????????0?sin（rjpoint_5（5?cpoint）?*?T）?0?cos（rjpoint_5（5?cpoint）?*?T）?0;
????????0?0?0?0?1];
????Xminus_5（:?cpoint）?=?fai3?*?rjpoint_5（:?cpoint）;
end

%?Estimate?the?predicted?state
xminus_5?=?w2_5?*?Xminus_5（:?1）?+?w_5?*?sum（Xminus_5（:?2?:?m?+?1）?2）?+?...
????w4_5?*?sum（Xminus_5（:?m?+?2?:?b_5）?2）;

%?Estimate?the?predicted?error?covariance
Pminus_5?=?Q?+?w2_5?*?（Xminus_5（:?1）?-?xminus_5）?*?（Xminus_5（:?1）?-?xminus_5）‘...
????+?w_5?*?（Xminus_5（:?2?:?m?+?1）?-?repmat（xminus_5?1?m））?*?...
????（Xminus_5（:?2?:?m?+?1）?-?repmat（xminus_5?1?m））‘?+?...
????w4_5?*?（Xminus_5（:?m?+?2?:?b_5）?-?repmat（xminus_5?1?b_5?-?m?-?1））?...
????*?（Xminus_5（:?m?+?2?:?b_5）?-?repmat（xminus_5?1?b_5?-?m?-?1））‘;
%%?---------------------------------------------------------------

%%?-------------------------Measurement?Update--------------------
%?Evaluate?the?Cholesky?factor
Sminus_5?=?chol（Pminus_5?‘lower‘）;
for?cpoint?=?1?:?b_5
????%?Evaluate?the?cubature?points
????rjpoint1_5（:?cpoint）?=?Sminus_5?*?kesi_5（:?cpoint）?+?xminus_5;
????%Evaluate?the?propagated?cubature?points
????Z_5（:?cpoint）?=?[sqrt（rjpoint1_5（1?cpoint）?^?2?+?rjpoint1_5（3?cpoint）?^?2）?...
????????atan（rjpoint1_5（3?cpoint）?/?rjpoint1_5（1?cpoint））]‘;
end
%?Estimate?the?predicted?measurement
zhat_5?=?w2_5?*?Z_5（:?1）?+?w_5?*?sum（Z_5（:?2?:?m?+?1）?2）?+?w4_5?*?...
????sum（Z_5（:?m?+?2?:?b_5）?2）;

%?Estimate?the?innovation?covariance?matrix
Pzminus_5?=?R?+?w2_5?*?（Z_5（:?1）?-?zhat_5）?*?（Z_5（:?1）?-?zhat_5）‘?+?...
????w_5?*?（Z_5（:?2?:?m?+?1）?-?repmat（zhat_5?1?m））?*?（Z_5（:?2?:?m?+?1）?...
????-?repmat（zhat_5?1?m））‘+?w4_5?*?（Z_5（:?m?+?2?:?b_5）?-?...
????repmat（zhat_5?1?b_5?-?m?-?1））?*?（Z_5（:?m?+?2?:?b_5）?-?repmat（zhat_5?1?b_5?-?m?-?1））‘;

%?Estimate?the?cross-covariance?matrix
Pxzminus_5?=?w2_5?*?（rjpoint1_5（:?1）?-?xminus_5）?*?（Z_5（:?1）?-?zhat_5）‘?+?...
????w_5?*?（rjpoint1_5（:?2?:?m?+?1）?-?repmat（xminus_5?1?m））?*?...
????（Z_5（:?2?:?m?+?1）?-?repmat（zhat_5?1?m））‘...
????+?w4_5?*?（rjpoint1_5（:?m?+?2?:?b_5）?-?repmat（xminus_5?1?b_5?-?m?-?1））?...
????*?（Z_5（:?m?+?2?:?b_5）?-?repmat（zhat_5?1?b_5?-?m?-?1））‘;

%?Estimate?th

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????3274??2014-06-21?14:47??Target?tracking\Fifth_degree_CKF.m

?????文件????1092608??2014-06-21?15:08??Target?tracking\Perms.exe

?????文件????????925??2013-01-23?11:16??Target?tracking\rms.m

?????文件???????2188??2014-06-21?14:46??Target?tracking\Three_degree_CKF.m

?????文件???????7034??2014-06-21?15:00??Target?tracking\TR_Main.m

?????目錄??????????0??2014-06-21?15:09??Target?tracking

-----------?---------??----------?-----??----

??????????????1106029????????????????????6


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