1 Introduction to Sensor Fusion (or Sensor Blending)
Sensors are what provides feedback to a closed loop system. Sometimes you can’t get the sensor characteristics you need. This happens a lot in the aerospace industry.
Sensor fusion, or sensor blending, is used to create a better sensor by blending 2 or more sensors. Sensor fusion is accomplished by filtering the output of the individual sensors. Careful choice of both the sensors and the filters allows the designer to use individual sensors where they are strong while reducing their effect where they are weak.
- noise levels
- non-unity magnitude
When any one sensor cannot provide the necessary feedack then it is time for 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. This simple fusion allows for two sensors to provide the desired output.
2 Sensor Fusion to overcome sensor weakness
There are few, if any, true DC IMUs. I assume most sensors - position and accelerometers included - cannot go to true DC. There are few sensors that are both good at low frequency and high frequency. This is usually due to the underlying dynamics of the sensor.
So if the system being designed needs good performance across a larger frequency range than any single sensor can provide sensor fusion is used to overcome this weakness.
3 Simple Sensor Fusion
The simplest form of sensor fusion is to use sensors with overlapping bandwidths and blend them through simple first or second order filters. The low frequency sensor is blended using a high pass filter while the high frequency sensor is blended using a low pass filter. Typically the corner frequencies of the two sensor fusion filters are close if not the same.
3.1 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.
4 Ideal Sensor vs. Real Sensor
The ideal sensor is typically modeled with a second order system that has a natural frequency equal to the spec bandwidth and a damping of 0.707 or 1. I default to 0.707. This leads to a nice flat, unity response for the sensor below the bandwidth. Real sensors are non-unity below the bandwidth - i.e. the magnitude has some ripple to it. Sensor ripple around the blending frequency can be very problematic and must be assessed based on the system needs.