当前位置：网站首页>[station B up dr_can learning notes] Kalman filter 1

[station B up dr_can learning notes] Kalman filter 1

2022-06-27 04:23:00 【Tomorrow at hiahiahia】

Optimized recursive digital processing algorithm

When we describe a system , Uncertainty is mainly reflected in three aspects ：

（1） There is no perfect mathematical model

（2） The disturbance of the system is uncontrollable , It's also difficult to model

（3） There is an error in the measuring sensor

Estimate true results , The most natural method is to take an average of several measurements .

$\hat{x}_k= \frac{1}{k}(z_1+z_2+...+z_k))$

$\hat{x}_k= \frac{1}{k} (z_1+z_2+...+z_{k-1})+\frac{1}{k}z_k$

$\hat{x}_k= \frac{k-1}{k} {\color{Red} \frac{1}{k-1} (z_1+z_2+...+z_{k-1})}+\frac{1}{k}z_k$

$\hat{x}_k = \frac{k-1}{k} \hat{x}_{k-1} +\frac{1}{k}z_k$

$\hat{x}_k = \hat{x}_{k-1} + {\color{Red} \frac{1}{k}}(z_k-\hat{x}_{k-1})$

review , When $k\rightarrow \infty$ when , $\frac{1}{k}\rightarrow 0$ , $\hat{x}_k \rightarrow \hat{x}_{k-1}$ , More measurements are no longer important .

another $K_k=\frac{1}{k}$ , be

$\hat{x}_k = \hat{x}_{k-1} + {\color{Red} K_k}(z_k-\hat{x}_{k-1})$

The current estimate = Last estimate + coefficient ×（ Current measured value - Last estimate ）

${\color{Red} K_k}$ This is the Kalman gain .

Summary ： Only the current measured value and the last estimated value are required , No earlier data is required .

If the estimation error is assumed to be $e_{EST}$ , The measurement error is $e_{MEA}$ , be

$K_k=\frac{{e_{EST}}_{k-1}}{{e_{EST}}_{k-1}+{e_{MEA}}_k}$

When the estimation error is much larger than the measurement error , The Kalman gain is 1, The estimated value is the measured value ;

When the measurement error is much larger than the estimation process , The Kalman gain is 0, The estimated value is the estimated value .

The method is divided into three steps ：

step （1） Calculate Kalman gain

${\color{Red} K_k}=\frac{{e_{EST}}_{k-1}}{{e_{EST}}_{k-1}+{e_{MEA}}_k}$

step （2） Update estimates

$\hat{x}_k = \hat{x}_{k-1} + {\color{Red} K_k}(z_k-\hat{x}_{k-1})$

step （3） Update estimation error

${e_{EST}}_k={\color{Red} (1-K_k)}{e_{EST}}_{k-1}$

Summary ： The error of the measured value is fixed , The error of the estimated value is updated step by step according to the measurement error .

原网站

版权声明
本文为[Tomorrow at hiahiahia]所创，转载请带上原文链接，感谢
https://yzsam.com/2022/178/202206270408501004.html

当前位置：网站首页>[station B up dr_can learning notes] Kalman filter 1

[station B up dr_can learning notes] Kalman filter 1

边栏推荐

猜你喜欢

随机推荐