Maximum Likelihood Estimates of Linear Dynamic Systems. Rauch, H E, Tung, F, & Striebel, C T 3(8):1445–1450.
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This paper considers the problem of estimating the states of linear dynamic systems in the presence of additive Gaussian noise. Difference equations relating the estimates for the prob- lems of filtering and smoothing are derived as well as a similar set of equations relating the covariance of the errors. The derivation is based on the method of maximum likelihood and depends primarily on the simple manipulation of the probability density functions. The solutions are in a form easily mechanized on a digital computer. A numerical example is in- cluded to show the advantage of smoothing in reducing the errors in estimation. In the Appendix the results for discrete systems are formally extended to continuous systems.
@article{rauchMaximumLikelihoodEstimates1965,
  title = {Maximum Likelihood Estimates of Linear Dynamic Systems},
  volume = {3},
  issn = {0001-1452},
  doi = {10.2514/3.3166},
  abstract = {This paper considers the problem of estimating the states of linear dynamic systems in the presence of additive Gaussian noise. Difference equations relating the estimates for the prob- lems of filtering and smoothing are derived as well as a similar set of equations relating the covariance of the errors. The derivation is based on the method of maximum likelihood and depends primarily on the simple manipulation of the probability density functions. The solutions are in a form easily mechanized on a digital computer. A numerical example is in- cluded to show the advantage of smoothing in reducing the errors in estimation. In the Appendix the results for discrete systems are formally extended to continuous systems.},
  number = {8},
  journaltitle = {AIAA Journal},
  date = {1965},
  pages = {1445--1450},
  author = {Rauch, H E and Tung, F and Striebel, C T},
  file = {/home/dimitri/Nextcloud/Zotero/storage/PSFG5VU2/Rauch, Tung, Striebel - 1965 - Maximum Likelihood Estimates of Linear Dynamic Systems.pdf}
}
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