diff --git a/blitherboom-blog/.valaxy/components.d.ts b/blitherboom-blog/.valaxy/components.d.ts deleted file mode 100644 index 1dfb124a..00000000 --- a/blitherboom-blog/.valaxy/components.d.ts +++ /dev/null @@ -1,79 +0,0 @@ -/* eslint-disable */ -/* prettier-ignore */ -// @ts-nocheck -// Generated by unplugin-vue-components -// Read more: https://github.com/vuejs/core/pull/3399 -export {} - -declare module 'vue' { - export interface GlobalComponents { - AppLink: typeof import('./../node_modules/.pnpm/valaxy@0.18.5_@types+markdown-it@14.0.0_@unhead+shared@1.9.4_postcss@8.4.38_typescript@5.4.4_unhead@1.9.4/node_modules/valaxy/client/components/AppLink.vue')['default'] - README: typeof import('./../components/README.md')['default'] - RouterLink: typeof import('vue-router')['RouterLink'] - RouterView: typeof import('vue-router')['RouterView'] - ShadowRoot: typeof import('./../node_modules/.pnpm/valaxy@0.18.5_@types+markdown-it@14.0.0_@unhead+shared@1.9.4_postcss@8.4.38_typescript@5.4.4_unhead@1.9.4/node_modules/valaxy/client/components/internals/ShadowRoot.vue')['default'] - ValaxyAddons: typeof import('./../node_modules/.pnpm/valaxy@0.18.5_@types+markdown-it@14.0.0_@unhead+shared@1.9.4_postcss@8.4.38_typescript@5.4.4_unhead@1.9.4/node_modules/valaxy/client/components/ValaxyAddons.vue')['default'] - ValaxyCopyright: typeof import('./../node_modules/.pnpm/valaxy@0.18.5_@types+markdown-it@14.0.0_@unhead+shared@1.9.4_postcss@8.4.38_typescript@5.4.4_unhead@1.9.4/node_modules/valaxy/client/components/ValaxyCopyright.vue')['default'] - ValaxyDecrypt: typeof import('./../node_modules/.pnpm/valaxy@0.18.5_@types+markdown-it@14.0.0_@unhead+shared@1.9.4_postcss@8.4.38_typescript@5.4.4_unhead@1.9.4/node_modules/valaxy/client/components/ValaxyDecrypt.vue')['default'] - ValaxyDevtools: typeof import('./../node_modules/.pnpm/valaxy@0.18.5_@types+markdown-it@14.0.0_@unhead+shared@1.9.4_postcss@8.4.38_typescript@5.4.4_unhead@1.9.4/node_modules/valaxy/client/components/debug/ValaxyDevtools.vue')['default'] - ValaxyGalleryDecrypt: typeof import('./../node_modules/.pnpm/valaxy@0.18.5_@types+markdown-it@14.0.0_@unhead+shared@1.9.4_postcss@8.4.38_typescript@5.4.4_unhead@1.9.4/node_modules/valaxy/client/components/ValaxyGalleryDecrypt.vue')['default'] - ValaxyHamburger: typeof import('./../node_modules/.pnpm/valaxy@0.18.5_@types+markdown-it@14.0.0_@unhead+shared@1.9.4_postcss@8.4.38_typescript@5.4.4_unhead@1.9.4/node_modules/valaxy/client/components/ValaxyHamburger.vue')['default'] - ValaxyLogo: typeof import('./../node_modules/.pnpm/valaxy@0.18.5_@types+markdown-it@14.0.0_@unhead+shared@1.9.4_postcss@8.4.38_typescript@5.4.4_unhead@1.9.4/node_modules/valaxy/client/components/ValaxyLogo.vue')['default'] - ValaxyMain: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/ValaxyMain.vue')['default'] - ValaxyMd: typeof import('./../node_modules/.pnpm/valaxy@0.18.5_@types+markdown-it@14.0.0_@unhead+shared@1.9.4_postcss@8.4.38_typescript@5.4.4_unhead@1.9.4/node_modules/valaxy/client/components/ValaxyMd.vue')['default'] - ValaxyMermaid: typeof import('./../node_modules/.pnpm/valaxy@0.18.5_@types+markdown-it@14.0.0_@unhead+shared@1.9.4_postcss@8.4.38_typescript@5.4.4_unhead@1.9.4/node_modules/valaxy/client/components/builtin/ValaxyMermaid.vue')['default'] - ValaxyOverlay: typeof import('./../node_modules/.pnpm/valaxy@0.18.5_@types+markdown-it@14.0.0_@unhead+shared@1.9.4_postcss@8.4.38_typescript@5.4.4_unhead@1.9.4/node_modules/valaxy/client/components/ValaxyOverlay.vue')['default'] - ValaxyPagination: typeof import('./../node_modules/.pnpm/valaxy@0.18.5_@types+markdown-it@14.0.0_@unhead+shared@1.9.4_postcss@8.4.38_typescript@5.4.4_unhead@1.9.4/node_modules/valaxy/client/components/ValaxyPagination.vue')['default'] - ValaxySvgLogo: typeof import('./../node_modules/.pnpm/valaxy@0.18.5_@types+markdown-it@14.0.0_@unhead+shared@1.9.4_postcss@8.4.38_typescript@5.4.4_unhead@1.9.4/node_modules/valaxy/client/components/ValaxySvgLogo.vue')['default'] - YunAiExcerpt: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunAiExcerpt.vue')['default'] - YunAlbum: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunAlbum.vue')['default'] - YunAlbumList: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunAlbumList.vue')['default'] - YunAlgoliaSearch: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/third/YunAlgoliaSearch.vue')['default'] - YunAside: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunAside.vue')['default'] - YunBackToTop: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunBackToTop.vue')['default'] - YunBanner: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunBanner.vue')['default'] - YunBg: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunBg.vue')['default'] - YunCard: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunCard.vue')['default'] - YunCategories: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunCategories.vue')['default'] - YunCategory: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunCategory.vue')['default'] - YunCloud: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunCloud.vue')['default'] - YunComment: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunComment.vue')['default'] - YunConfig: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunConfig.vue')['default'] - YunFireworks: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunFireworks.vue')['default'] - YunFooter: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunFooter.vue')['default'] - YunFuseSearch: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunFuseSearch.vue')['default'] - YunGallery: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunGallery.vue')['default'] - YunGirls: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunGirls.vue')['default'] - YunGoDown: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunGoDown.vue')['default'] - YunLayoutPostTag: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunLayoutPostTag.vue')['default'] - YunLinks: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunLinks.vue')['default'] - YunLoading: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunLoading.vue')['default'] - YunMdTimeWarning: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunMdTimeWarning.vue')['default'] - YunNotice: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunNotice.vue')['default'] - YunOutline: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunOutline.vue')['default'] - YunOutlineItem: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunOutlineItem.vue')['default'] - YunOverview: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunOverview.vue')['default'] - YunPageHeader: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunPageHeader.vue')['default'] - YunPostCard: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunPostCard.vue')['default'] - YunPostCategories: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunPostCategories.vue')['default'] - YunPostCategoriesAndTags: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunPostCategoriesAndTags.vue')['default'] - YunPostCollapse: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunPostCollapse.vue')['default'] - YunPostList: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunPostList.vue')['default'] - YunPostMeta: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunPostMeta.vue')['default'] - YunPostNav: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunPostNav.vue')['default'] - YunPostTags: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunPostTags.vue')['default'] - YunSay: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunSay.vue')['default'] - YunSearchBtn: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunSearchBtn.vue')['default'] - YunSearchTrigger: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunSearchTrigger.vue')['default'] - YunSelect: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunSelect.vue')['default'] - YunSidebar: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunSidebar.vue')['default'] - YunSidebarLinks: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunSidebarLinks.vue')['default'] - YunSidebarNav: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunSidebarNav.vue')['default'] - YunSocialLinks: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunSocialLinks.vue')['default'] - YunSponsor: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunSponsor.vue')['default'] - YunToggleLocale: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/YunToggleLocale.vue')['default'] - YunTwikoo: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/third/YunTwikoo.vue')['default'] - YunWaline: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/third/YunWaline.vue')['default'] - YunWalineMeta: typeof import('./../node_modules/.pnpm/valaxy-theme-yun@0.18.5/node_modules/valaxy-theme-yun/components/third/YunWalineMeta.vue')['default'] - } -} diff --git a/source/_posts/StaSP.md b/source/_posts/StaSP.md index 7a8ac83b..ae4853a1 100644 --- a/source/_posts/StaSP.md +++ b/source/_posts/StaSP.md @@ -1064,3 +1064,48 @@ $$ \hat{s}\left[n\mid n\right]=\underbrace{\hat{s}\left[n\mid n-1\right]}_{预测}+\underbrace{K\left[n\right]\left(x\left[n\right]-\hat{s}\left[n\mid n-1\right]\right)}_{新息修正} $$ +#### 最小 MSE + +MSE 修正： + +$$ +M[n|n] = (1 - K[n])M[n|n - 1] +$$ + +### 非零均值信号模型 + +![1714360809348](../images/StaSP/1714360809348.png) + +初始化：$\hat{s} [ - 1|- 1] = E\begin{pmatrix} s[ - 1] \end{pmatrix} = \mu _s$ $M[ - 1|- 1] = E\left ( \begin{pmatrix} s[ - 1] - \hat{s} [ - 1|- 1] \end{pmatrix} ^2\right ) = \sigma _s^2$ + +估计量预测：$\hat{s}[n|n-1]=a\hat{s}[n-1|n-1]$ + +MSE预测：$M\left[n\mid n-1\right]=a^2M\left[n-1\mid n-1\right]+\sigma_u^2$ + +卡尔曼增益：$K[n]=\frac{M\left[n|n-1\right]}{M\left[n|n-1\right]+\sigma_n^2}$ + +估计量修正：$\hat{s}[n|n]=\hat{s}[n|n-1]+K[n]\left(x[n]-\hat{s}[n|n-1]\right)$ + +MSE修正: $M\left [ n\mid n\right ] = \left ( 1- K\left [ n\right ] \right ) M\left [ n\mid n- 1\right ]$ + +### 矢量状态-标量观测信号模型 + +![1714360717248](../images/StaSP/1714360717248.png) + +### 矢量状态-矢量观测信号模型 + +![1714360742651](../images/StaSP/1714360742651.png) + +### 非线性信号模型 + +![1714360782259](../images/StaSP/1714360782259.png) + +![1714361011137](../images/StaSP/1714361011137.png) + +![1714361027958](../images/StaSP/1714361027958.png) + +### 总结 + +* 不同时刻的待估计参数并不完全一样，但是存在某些内在联系 +* 卡尔曼滤波利用这种联系进行 LMMSE 估计，并减少了运算量 +* 如果信号与噪声是高斯的，则卡尔曼滤波在 MMSE 准则下最佳，否则，在 LMMSE 准则下是最佳的。 diff --git a/source/images/StaSP/1714360717248.png b/source/images/StaSP/1714360717248.png new file mode 100644 index 00000000..ec34b5fe Binary files /dev/null and b/source/images/StaSP/1714360717248.png differ diff --git a/source/images/StaSP/1714360742651.png b/source/images/StaSP/1714360742651.png new file mode 100644 index 00000000..67ad6ec8 Binary files /dev/null and b/source/images/StaSP/1714360742651.png differ diff --git a/source/images/StaSP/1714360782259.png b/source/images/StaSP/1714360782259.png new file mode 100644 index 00000000..0447c528 Binary files /dev/null and b/source/images/StaSP/1714360782259.png differ diff --git a/source/images/StaSP/1714360809348.png b/source/images/StaSP/1714360809348.png new file mode 100644 index 00000000..02929a22 Binary files /dev/null and b/source/images/StaSP/1714360809348.png differ diff --git a/source/images/StaSP/1714361011137.png b/source/images/StaSP/1714361011137.png new file mode 100644 index 00000000..21a548fc Binary files /dev/null and b/source/images/StaSP/1714361011137.png differ diff --git a/source/images/StaSP/1714361027958.png b/source/images/StaSP/1714361027958.png new file mode 100644 index 00000000..248d702a Binary files /dev/null and b/source/images/StaSP/1714361027958.png differ