Today I decided to enhance US sensor output. Why? Sometimes I had the impression the car changed behaviour. I suspected this had something to do with faulty readings from the Ultrasonic sensor. I decided to make a low pass filter for the US sensor. This should eliminate random faulty readings. But first I had to understand low pass filters. Coding a low pass filter isn’t too hard. There is an explanation on Wikipedia. Basicly it’s just one line of code:
lowPassUS=lowPassUS+alpha*(SensorValue[sonar]-lowPassUS);
The filtered value is calculated from the raw value and the previous filtered value. There is one parameter, alpha, that controls the filter. I wanted to understand how the value of alpha changes the behaviour of the filter. That is why I did some experiments in Excel. Here is an example. The red line represents unfiltered values, the green filtered values. The horizontal axis represents time. 

The alpha factor does one thing, it controls how fast the filter adjusts to a new situation. The smaller the alpha, the quicker the filter reacts. In the plot it means that the green line follows the red line more closely. The downside is that less noise is filtered out.
There is one other thing that is important to realise. Alpha doesn’t control the time the filter takes to adjust, it controls the number of steps (iterations) the filter needs to adjust. This means that there is a relation between sample rate, how often the output from the US sensor is read, and alpha. With a higher sample rate and constant alpha, the filter adjusts quicker in real time. But also, if the sample rate is changes one also needs to consider to change the alpha.

The graph above shows four scenario’s. At t=1 the sampling starts, the filter needs time to adjust. One should give the filter time to settle, or, one should initialize the filtered value to the unfiltered value.
Around t=0,3 I tested another scenario. The reading of the Sensor changes because an object is in sight. In this example it takes about 0,1 second for the filter to adjust to the new situation. Is this quick enough, for me it is.
Around t=0,46 there is an faulty reading, the filter dampens the reading but for a short time (0,06 seconds) the objects seems further than it is.  In my case, The damping needs to be enough so that the filtered value  not exceeds treshhold. I need more real life testing to find out the damping is enough. Also I do know i get faulty 255 values sometimes, but I don’t know if I also get faulty zero values. These will affect behaviour more often, as they can influence collision detection.
Around t=0,6 the last scenario is shown.  Here an object at 60 cm dissappears and and a background object at 90 cm appears. But this time the objects doesn’t dissappear at once but during a short time it is sometimes sen and at other times it is not seen. Here the filter really smoothens out the jitter.

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