当前位置：网站首页>[station B up dr_can learning notes] Kalman filter 2

[station B up dr_can learning notes] Kalman filter 2

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

When $z_1=30g,\sigma_1=2g;z_2=32g,\sigma_2=4g$ , How to make the real value Minimum estimated variance of ？

According to the formula of Kalman gain $z=z_1+{\color{Red} K}(z_1-z_2)$ , How to get bring $\sigma{z}$ Minimum ？

$(\sigma{z})^2\\=var(z_1+K(z_2-z_1))\\=var((1-K)z_1+Kz_2)$

Due to measurement results z_1 and z_2 Are independent of each other , Then the above formula

$(\sigma{z})^2\\=var(z_1+K(z_2-z_1))\\=var((1-K)z_1+Kz_2)\\=var((1-K)z_1)+var(Kz_2)\\=(1-K)^2(\sigma1)^2+K^2(\sigma2)^2$ ,

namely

$(\sigma{z})^2=(1-K)^2(\sigma1)^2+K^2(\sigma2)^2$

In order to make $(\sigma{z})^2$ Minimum , be $\frac{d(\sigma{z})^2}{dK}=0$ ,

namely

$-2(1-K)(\sigma1)^2+2K(\sigma2)^2=0$ ,

Solution ：

${\color{Red} K=\frac{\sigma_{1}^{2}}{\sigma_{1}^{2}+\sigma_{2}^{2}}}$

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/2022/178/202206270408500663.html

边栏推荐

猜你喜欢

随机推荐