Baidu Encyclopedia version
The estimation theory is a theory of estimating the parameters or states of a signal by statistically measuring the mixed noise signal received at the receiving end. Estimation is divided into two categories: parameter estimation and state estimation. The difference between a parameter and a state is that the former remains constant or only changes slowly over time; the latter continuously changes over time.
For example, three spatial position vectors and three velocity vectors for a continuously changing satellite at each moment are estimated from radar echoes, which is a state estimate. Estimates of satellite mass and inertia are part of the parameter estimates. The estimated parameters can be divided into two types: random variables and non-random variables. The state to be estimated has the difference between discrete time and continuous time.
Estimation theory is a branch of statistics that processes estimated parameter values based on measured empirical data with random components. The parameters describe the underlying physical settings in such a way that their values affect the distribution of the measured data. An unknown parameter that attempts to use an approximate measurement. When data consists of multiple variables and one estimates the relationship between them, the estimate is called regression analysis.
In the estimation theory, two methods are usually considered.
- The probabilistic approach (described herein) assumes that the measurement data is random and the probability distribution depends on the parameters of interest.
- The set membership method assumes that the measurement data vector belongs to a group that depends on the parameter vector.