转载自:http://www.cnblogs.com/rubbninja/p/4512765.html 各种研究领域(包括无线定位方向)都会碰到参数估计的问题,这时常常会看到克拉美罗界 (Cramér–Rao bound) 这个东西.很多随机信号的书都会介绍什么是克拉美罗界,但初学者学起来往往很吃力,本文从直观上简单讨论一下克拉美罗界的各个方面. 什么是参数估计问题 假设一种最简单的情况: 一个物理量为,我们使用某种方式去观测它,观测值为,由于存在噪声,此时,为高斯噪声,. 这种情况下,我们自然

克拉美-罗界.又称Cramer-Rao lower bounds(CRLB),克拉美-罗下界. 克拉美罗界是对于参数估计问题提出的,为任何无偏估计量的方差确定了一个下限.无偏估计量的方差只能无限制的逼近CRB,而不会低于CRB,因此这个界也可以称为CRLB,意为克拉美罗下界. CRLB可以用于计算无偏估计中能够获得的最佳估计精度,因此经常用于计算理论能达到的最佳估计精度,和评估参数估计方法的性能(是否接近CRLB下界). 克拉美罗界本身不关心具体的估计方式,只是去反映:利用已有信息所能估计参数的

题目链接 http://acm.split.hdu.edu.cn/showproblem.php?pid=5410 Problem Description Today is CRB's birthday. His mom decided to buy many presents for her lovely son.She went to the nearest shop with M Won(currency unit).At the shop, there are N kinds of pr

CRB and Tree Time Limit: 8000/4000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others) Total Submission(s): 2112    Accepted Submission(s): 635 Problem Description CRB has a tree, whose vertices are labeled by 1, 2, …, N. They are connected

CRB and His Birthday Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 430    Accepted Submission(s): 237 Problem Description Today is CRB's birthday. His mom decided to buy many presents for her

CRB and String Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others) Total Submission(s): 543 Accepted Submission(s): 208 Problem Description CRB has two strings s and t. In each step, CRB can select arbitrary character c o

CRB and His Birthday Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others) Total Submission(s): 357 Accepted Submission(s): 191 Problem Description Today is CRB's birthday. His mom decided to buy many presents for her lovel

题目连接 http://acm.hdu.edu.cn/showproblem.php?pid=5412 CRB and Queries Description There are $N$ boys in CodeLand. Boy i has his coding skill $A_{i}$. CRB wants to know who has the suitable coding skill. So you should treat the following two types of qu

http://acm.hdu.edu.cn/showproblem.php?pid=5414 题意:给定字符串s和t,可以在s里面选一个字符c,然后任选一个字符d(d!=c)将d插入到c的后面,问能不能将s变为t. 分析:只要前面t串连续的字符==s字符串,而且保证s是t的子串.本来想不通s:aabaa,t:aabaaaa,后面四个a怎么插,后来才想明白,后面的a都可以插在b后面,就可以了. CRB and String Time Limit: 2000/1000 MS (Java/Others

Problem Description Today is CRB's birthday. His mom decided to buy many presents for her lovely son. She went to the nearest shop with M Won(currency unit). At the shop, there are N kinds of presents. It costs Wi Won to buy one present of i-th kind.

Problem Description There are N boys in CodeLand.Boy i has his coding skill Ai.CRB wants to know who has the suitable coding skill.So you should treat the following two types of queries.Query 1: 1 l vThe coding skill of Boy l has changed to v.Query 2

CRB and Roads Time Limit: 12000/6000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)Total Submission(s): 495    Accepted Submission(s): 225 Problem Description There are N cities in Codeland.The President of Codeland has a plan to con

判断一个估计量“好坏”,至少可以从以下三个方面来考虑: 无偏估计 有效性 一致性 参考内容: 如何理解无偏估计量?https://www.matongxue.com/madocs/808.html 衡量点估计量好坏的标准:https://wenku.baidu.com/view/e98b2f77f90f76c661371ae7.html

CRB and Puzzle Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 1177    Accepted Submission(s): 468 Problem Description CRB is now playing Jigsaw Puzzle.There are N kinds of pieces with infinite

无偏估计是参数的样本估计量的期望值等于参数的真实值. 一个简单的例子(https://www.zhihu.com/question/22983179/answer/23470969): 比如我要对某个学校一个年级的上千个学生估计他们的平均水平(真实值,上帝才知道的数字),那么我决定抽样来计算. 我抽出一个10个人的样本,可以计算出一个均值.那么如果我下次重新抽样,抽到的10个人可能就不一样了,那么这个从样本里面计算出来的均值可能就变了,对不对? 因为这个均值是随着我抽样变化的,而我抽出哪10个人

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=5407 题目: Problem Description CRB has N different candies. He is going to eat K candies.He wonders how many combinations he can select.Can you answer his question for all K(0 ≤ K ≤ N)?CRB is too hungry to

题目地址:pid=5407">HDU 5407 题意:CRB有n颗不同的糖果,如今他要吃掉k颗(0<=k<=n),问k取0~n的方案数的最小公倍数是多少. 思路:首先做这道题我们须要必备的几个技能点. 1. LCM(C(n,0), C(n,1),-, C(n,n))=LCM(1,2,3,-n+1)/(n+1).额,这个有一篇证明Kummer定理 2.(1) 乘法逆元定义: 满足a*k≡1 (mod p)的k值就是a关于p的乘法逆元(a,p互质). (2)为什么要用乘法逆元: 当

CRB and Candies Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 722    Accepted Submission(s): 361 Problem Description CRB has N different candies. He is going to eat K candies.He wonders how ma

CRB and Queries Time Limit: 12000/6000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)Total Submission(s): 1602    Accepted Submission(s): 409 Problem Description There are N boys in CodeLand.Boy i has his coding skill Ai.CRB wants to

CRB and Puzzle Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 558    Accepted Submission(s): 227 Problem Description CRB is now playing Jigsaw Puzzle.There are N kinds of pieces with infinite s