```python
%pylab inline
import sympy
sympy.init_printing()
```

    Populating the interactive namespace from numpy and matplotlib



```python
t0, t1, tau, Q, P, dt, T = sympy.symbols(
    't0, t1, tau, Q, P, \Delta_t, T',
    real=True, positive=True)
```


```python
def Phi(t, tau):
    return sympy.exp(-(t - tau)/T)
```


```python
Q_d = sympy.integrate(Phi(t1, tau)*Q*Phi(t1, tau),
                    (tau, t0, t1)).simplify()
simp_subs = {
    2*(t1 - t0): 2*dt,
    (2*t0 - 2*t1)/T: -2*dt/T
}
Q_d = Q_d.simplify().subs(simp_subs)
Q_d
```


```python
dt = 1.0/250
T = 1000
gyro_sigma_rrw = 1e-5
gyro_sigma_rrw*gyro_sigma_rrw*T/2*(1 - exp(-2*dt/1000))
```

97c933919cbea181d4ff21b06f68eb7318d10e4d
ipynb
Jupyter Notebook
Sensor Noise Derivation.ipynb
jgoppert/iekf_analysis
d41ad34b37ef2636e20680accf399ea4a9332811
BSD-3-Clause
2018-01-16T06:46:38.000Z
2019-06-19T10:17:12.000Z
Sensor Noise Derivation.ipynb
jgoppert/iekf_analysis
d41ad34b37ef2636e20680accf399ea4a9332811
BSD-3-Clause
Sensor Noise Derivation.ipynb
jgoppert/iekf_analysis
d41ad34b37ef2636e20680accf399ea4a9332811
BSD-3-Clause
Qwen/Qwen-72B
1. YES
2. YES