## 1. Kalman Filter Tutorial (Cont'd...)

### 1.5 Simulation (cont'd...)

#### Simulation results (cont'd...)

The figure 4 shows the error of position velocity and acceleration estimation when the standard deviation
of measurement noise is considered as $\sigma=3 m/s^2$. From the figure 3 and 4 we see that less the measurement noise
covariance better the estimation.

Figure 4. Error of position velocity and acceleration estimation $\sigma=3$
Figure 5 shows the plot of test statistic when $\sigma=0.003$
and $\sigma=3$. This test statistic plot is also called as the universally most powerful test statistics (UMPTS),
which is computed from the Kalman filter innovation sequence. The average of the test statistics value for $\sigma=3$, and
$\sigma=0.003$ is 2.03 and 20.40 respectively. So we interpret that for $\sigma=3$, the Kalman filter is working whereas for
$\sigma=0.003$, the Kalman filter is not working satisfactorily. We see that for the input acceleration we assume the process model
with low noise could not describe the motion well leading to failure of Kalman filter algorithm.
It reflects that for

Figure 5. Plot of UMPTS at $\sigma=0.003$ and $\sigma=3$
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