Sensor Filter Lab

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About This MicroSim

Real sensors are noisy. Even when your robot sits still, the ToF sensor might read 143 cm, then 145 cm, then 141 cm. Now and then it gives a wild reading, a spike, that is far from the truth. A filter combines several readings to get a better answer.

This lab runs the two filters from Chapter 8 on the same stream of readings:

• The moving average (orange) adds up the last few readings and divides by how many there are. This is filtered_distance().
• The median filter (blue) sorts the last few readings and picks the middle one. This is median_distance().

The gray dots are the raw readings. The dashed green line is the true distance. The shaded band on the right shows the window, which is the group of readings each filter is using right now.

The readout under the chart scores each filter. Error is how far, on average, the output is from the true distance over the last 100 readings. Lag is how many readings a filter needs to get within 10 cm of a new distance after the person walks in.

How to Use

1. Look at the chart before you press anything. Find a spike. What does the orange line do there? What does the blue line do?
2. Click Start to stream new readings, 10 per second. Click Pause any time to study the chart.
3. Raise Spike chance to 15%. Compare the average error and the median error.
4. Change Window size. The filters instantly recompute on the same readings, so you can compare fairly.
5. Click Person walks in. The true distance drops from 150 cm to 40 cm. Read the lag for each filter. Try again with a window of 3 and a window of 15.
6. Use Show average and Show median to look at one filter at a time.

Iframe Embed Code

You can add this MicroSim to any web page by adding this to your HTML:

<iframe src="https://dmccreary.github.io/stem-robots/sims/sensor-filter-lab/main.html"
        height="502px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

Grades 8–12

Duration

20–25 minutes

Learning Objective

Students will evaluate when a moving average or a median filter is the better choice for a robot's distance readings, and will justify a window size by explaining how it trades smoothness (low error) against lag (slow reaction).

Prerequisites

• Lists, append(), pop(), sum(), and sorted() from Chapter 5: Data Structures, Modular Programming, and Version Control
• Writing functions with parameters from Chapter 4: Control Flow, Functions, and Exception Handling
• ToF distance readings and the out-of-range value from the Time-of-Flight section of Chapter 8
• Mean and median from middle-school math

Activities

1. Warm-up by hand (4 min). Give students five readings: 148, 151, 149, 230, 150. They compute the mean (165.6) and the median (150) and discuss which one better describes the real distance.
2. Spikes (5 min). With window 5, students raise the spike chance from 0% to 15% in steps of 5% and record both errors. They should find that the median barely changes while the average error grows.
3. Lag (6 min). Students press Person walks in with windows 3, 7, and 15 and record the lag for each filter. They should find that lag grows with the window, and that the median reacts faster than the average for the same window.
4. Noise without spikes (3 min). With spike chance 0% and noise 8 cm, students compare the two filters again. The moving average is often a little smoother here, so neither filter wins every case.
5. Decide and defend (5 min). Each pair writes a recommendation for a robot that drives at 20 cm per second and must stop 30 cm from a wall: which filter and which window, with evidence from the lab.

Assessment

• Challenge: "Set the spike chance to 15% and the window to 5. Which filter stays closer to 150 cm?" (The median filter.) "Set the window to 15 and press Person walks in. What happens to the lag?" (It grows to about 7 readings for the median and about 13 for the average, so the robot reacts later.)
• Evaluate in writing: "A robot's ToF sometimes returns 8190 when it loses the target. Which filter would you use, and what window? Explain the cost of your choice."
• Rubric (4-point): Exemplary — recommends a filter and window using measured error and lag values, and names the trade-off and a case where the other filter wins. Proficient — picks the median for spiky data and explains that bigger windows add lag. Developing — picks a filter with evidence from only one measurement. Beginning — believes a bigger window is always better.

Simplifications to Mention

• Noise is spread evenly between plus and minus the noise setting. Real sensor noise is often bell-shaped.
• Real out-of-range readings such as 8190 are much larger than the 40 to 80 cm spikes used here; a median filter rejects them the same way.

References

1. Chapter 8: Sensors and Data Input — Sensor Data Filtering — the filtered_distance() and median_distance() functions used here.
2. Moving average (Wikipedia) — how a simple moving average smooths data and why it lags.
3. Median filter (Wikipedia) — why the median removes spikes while keeping sharp edges.
4. Steven W. Smith, The Scientist and Engineer's Guide to Digital Signal Processing, Chapter 15: Moving Average Filters — a free textbook chapter on noise reduction and step response.
5. Noise (signal processing) (Wikipedia) — where sensor noise comes from.
6. Chart.js line chart documentation — the charting library used to draw this MicroSim.