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从零开始的 IMU 状态模型推导的疑问 #4

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gaochq opened this issue May 19, 2017 · 3 comments

gaochq commented May 19, 2017

你好，看了关于你的从零开始的 IMU 状态模型推导收获很多，但是在高斯白噪声和随机游走部分的离散化的证明中，我的推导和你的推导不太一致。
我的推导如下，
$E(n_{d}[k]^{2})=E(\frac{1}{\Delta t^{2}}\int_{t_{0}}^{t_{0}+\Delta t}\int_{t_{0}}^{t_{0}+\Delta t}n(\tau )n(t)d\tau dt)$
$=\frac{1}{\Delta t^{2}}\int_{t_{0}}^{t_{0}+\Delta t}\int_{t_{0}}^{t_{0}+\Delta t}\delta (\tau -t)d\tau dt$
$=\frac{\sigma _{g}^{2}}{\Delta t}$
$E(n_{d}[k]^{2})=E(\sigma _{gd}^{2}\omega [k]^{2})=\frac{\sigma _{g}^{2}}{\Delta t}$
$\sigma _{gd}^{2}=\frac{\sigma _{g}^{2}}{\Delta t}$
随机游走的推导类似。

Owner

izhengfan commented May 19, 2017

hi，是不是你对公式里的狄利克雷函数的理解和我不一样？

Author

gaochq commented May 19, 2017

我和你的这部分推导是一致的。我和你不一样的地方在：我的期望符号在我上面式子中的第二步就去了，

Owner

izhengfan commented May 19, 2017

原来这样，算到第二步括号里已经是常数，有没有期望符号都无所谓了。

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