Sensor Fusion Example
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## 1 Introduction to the Sensor Fusion Example

Sensor fusion is used when no single sensor can do the job. Sensors are what provides feedback to a closed loop system. In the aerospace industry it is not uncommon that no single sensor exists that can accomplish the task at hand.

When any one sensor cannot provide the necessary feedack then it is time for sensor fusion or sensor blending. The simplest form of sensor fusion is a matter of two or more sensors which are filtered so that their strengths (good responsivity and low noise) are used while their weaknesses are filtered out.

Often times sensor fusion is nothing more than simple second order low pass or high pass filters with their outputs added together. While sensors are often blended with simple filters and sometimes more complex Linear and Non-Linear Kalman filters are required.

## 2 Simple Example of Sensor Fusion

The most simple sensor fusion that I’ve come across is the combination of two angular rate gyroscopes. The low frequency gyro was good out to a frequency of approximately 20 Hz. The high frequency gyro was good between 1 and 1000 Hz. Unfortunately this system was sensitive to frequencies around 5 Hz.

Normally the blending frequency of the sensor fusion would have happened between 1 Hz and 20 Hz based on an analysis of each sensor’s noise and responsivity. This example system was sensitive to frequencies around 5 Hz which meant that we needed to avoid frequencies between 0.5 Hz and 50 Hz.

The main weakness of the high frequency sensor was phase loss below 1 Hz. So we designed a filter to extend the low end of the high frequency sensor down to 0.5 Hz. More difficult to implement than to conceptualize but it takes some practice to do it correctly.

### 2.1 Low Frequency Sensor

Figure 1: Bode Plot of Low Frequency Sensor

As stated in the description of the sensor fusion example the low pass sensors is a DC sensor with a bandwidth of 20 Hz and a damping of $LaTeX: \frac{1}{\sqrt{2}}$. Figure 1 shows the bode response of our low frequency sensor for blending.

### 2.2 High Frequency Sensor

Figure 2: Bode Plot of High Frequency Sensor

As stated in the description of the sensor fusion example the lhigh pass sensors is a high frequency sensor with a lower bandwidth of 1 Hz, an upper bandwidth of 1 kHz and a damping of $LaTeX: \frac{1}{\sqrt{2}}$. Figure 2 shows the bode response of our low frequency sensor for blending.

## 3 Blending Filters

Figure 3: Bode Plot of Filters

The blended sensor's response is the sum of the output of these two filters. The low pass filter (LPF) is connected in series with the low frequency sensor. The high pass filter (HPF) is connected in series with the high frequency sensor. The outputs are then added together.

The blended performance is discussed in the next section.

## 4 Blended Performance

Figure 4: Bode Plot of Blended Performance without LPF
Figure 5: Bode Plot of Blended Performance with LPF

Initially I assumed that the low frequency sensor would require an LPF to achieve the desired performance. The LPF bandwidth was initially set at 15 Hz. The high frequency sensor requires an HPF with a bandwidth of 15 Hz. Figure 4 shows the blended sensor's performance without the LPF. Figure 5 shows the blended sensor's performance with the LPF. Both blending schemes use the HPF.

## 5 Sensor Fusion Conclusions

The blended sensor's performance is good when the LPF is not used. I think it is also obvious that the blended performance could be improved with careful design of the filters. Proper filter design may even require higher order filters. Anyone who has attempted to design higher order filters - like say 5th order and higher - knows that this takes experience, skill, and a little luck.