{"title":"The use of the method of maximum likelihood in estimating continuous-modulated intelligence which has been corrupted by noise","authors":"D. Youla","doi":"10.1109/IREPGIT.1954.6373402","DOIUrl":null,"url":null,"abstract":"A signal is received in the time interval (t ? T ? ? ? t). It is known that this signal is composed of noise plus intelligence a(t) which is statistical in nature and which has been modulated in some known way. Assuming that both intelligence and noise are Gaussian (although not necessarily stationary) time series, the analog of the classical maximum-likelihood estimate for ?(t) is derived. The advantage of this approach is that it can handle arbitrary types of modulation. For unmodulated stationary intelligence and stationary noise, the solution reduces to that of Zadeh and Ragazzini. In the general case, the optimum estimate is given as the solution of a pair of integral equations. The amplitude-modulated case is treated in some detail. The application of the maximum-likelihood technique to problems involving arbitrary modulation was first suggested, as far as the author is aware, by F. W. Lehan and R. J. Parks of the Jet Propulsion Laboratory.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"95 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1954-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"54","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Trans. IRE Prof. Group Inf. Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IREPGIT.1954.6373402","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 54
Abstract
A signal is received in the time interval (t ? T ? ? ? t). It is known that this signal is composed of noise plus intelligence a(t) which is statistical in nature and which has been modulated in some known way. Assuming that both intelligence and noise are Gaussian (although not necessarily stationary) time series, the analog of the classical maximum-likelihood estimate for ?(t) is derived. The advantage of this approach is that it can handle arbitrary types of modulation. For unmodulated stationary intelligence and stationary noise, the solution reduces to that of Zadeh and Ragazzini. In the general case, the optimum estimate is given as the solution of a pair of integral equations. The amplitude-modulated case is treated in some detail. The application of the maximum-likelihood technique to problems involving arbitrary modulation was first suggested, as far as the author is aware, by F. W. Lehan and R. J. Parks of the Jet Propulsion Laboratory.
在时间间隔(t ?T ?? ? 众所周知,这个信号是由噪声加智能a(t)组成的,本质上是统计的,并以某种已知的方式进行了调制。假设智能和噪声都是高斯时间序列(尽管不一定是平稳的),我们推导出了经典的最大似然估计。这种方法的优点是它可以处理任意类型的调制。对于无调制的平稳智能和平稳噪声,该解决方案简化为Zadeh和Ragazzini的解决方案。在一般情况下,最优估计是作为一对积分方程的解给出的。对调幅情况作了详细的讨论。据作者所知,喷气推进实验室的F. W. Lehan和R. J. Parks首先提出了将最大似然技术应用于涉及任意调制的问题。