Concepts in Kalman Filter

What is a Kalman filter?

The Kalman filter is an optimized recursive processing algorithm (optimal recursive Data Processing Algorithm ).

(1) The optimal (optimal) depends on the performance evaluation criterion. The kalman filter makes full use of the following information to estimate the current value of the variable of Interest:. dynamic Characteristics of systems and measuring devices; B. statistical description of system noise, measurement errors, and uncertainty of dynamic models; C. information about the initial conditions of variables of interest.

(2) recursion means that Kalman does not need to store the previous data and does not need to process the original data when performing a new measurement.

(3) filter (DPA) is actually a data processing algorithm, but a program processed in computing. Therefore, it can process Discrete Time Measurement samples instead of continuous time input.

• Basic Assumptions

It is reasonable to use a linear model. This is a typical engineering model that is linear at some major points or tracks. linear models are simpler than non-linear models. Therefore, linear models are used for approximation.

White Noise means that the noise value is irrelevant to the time. White Noise refers to the noise with the same frequency characteristics throughout the frequency. In practical applications, the frequency is set to a constant value. The noise with a bandwidth that greatly exceeds the system bandwidth is called white noise. It can be simulated with Gaussian white noise to greatly simplify the model.

It is feasible to use Gaussian density functions in practice. It is easy to use Gaussian Functions in mathematics. In the absence of Higher-Order Statistics, except for the Gaussian density, there is no better function form that can be expressed. Gaussian white noise can be fully described using first-order and second-order statistics.