Table Of Contents
  • Kalman gain derivation
  • Sensitivity analysis
  • Kalman-Bucy filter
  • Bayesian estimation
  • Rauch-Tung-Striebel

Kalman gain derivation

Kalman gain derivation can be described as a minimum mean-square error estimator. The Kalman gain derivation formula is relatively cheaper, which is why it is used in practice. However, if you use a non-optimal Kalman gain, you cannot apply the Kalman gain derivation. The optimal Kalman gain, when used, yields the MMSE estimates.

Sensitivity analysis

The sensitivity analysis helps one anticipate a decision's outcome through a specific range of variables. It shows that independent variables impact dependent variables, with several factors, held constant. The sensitivity analysis usage depends on input variables within known boundaries—one good thing about sensitivity analysis is used in any system or activity.

Kalman-Bucy filter

The Kalman-Bucy Filter is a continued time counterpart to the time Kalman Filter. It is designed to enable the estimation of unmeasured states of different processes to control the processes. You can also use it to estimate unmeasured states and the actual process outputs. It does not use the predictor-corrector algorithm to update the state estimates since it uses the differential Riccati equation to be put together through time.

Bayesian estimation

Bayesian estimation is used in the formulation of statistical inference problems. It works by combining evidence in the signal with previous knowledge of the probability distribution of the said process. The Bayesian estimation has estimators like maximum mean square error (MMSE), maximum-likelihood (ML), and the maximum a posteriori (MAP). In Bayesian, the study is always on using a previous model on variance and mean of the estimate.


The Rauch-Tung-Striebel is an offline state estimator that uses the Kalman filter as its building block. RTS is known to have a better estimation accuracy than the Kalman filter. Its accuracy is used in large apps such as navigation, signal processing, and positioning. Accuracy estimation of RTS degrades dramatically with non-Gaussian noises for a state-space model.