rasp5b_vid1.mp4

Motion Tracking with EMA Filtering

Real-time light tracking on a Raspberry Pi, with a first-order low-pass (exponential moving average) filter to stabilize noisy camera measurements. Built for the EECS 150 extra-credit project at UC Irvine.

A light is mounted on a double pendulum (chaotic, so the motion is unbiased) and tracked in the dark by a Raspberry Pi Camera Module 3. The same detection code runs with and without the filter, and the raw (red) and filtered (green) paths are compared frame by frame.

Results

Run	Setup	Raw jitter	Filtered jitter	Reduction	Mean lag
V1	30 fps, Pi 4, large light, slow swing	46 px/frame	17 px/frame	63%	153 px
V2	90 fps, Pi 5, small light, fast swing	23 px/frame	13 px/frame	44%	117 px

• Jitter drops 44-63% at alpha = 0.1. V2 starts from less noise (higher fps means smaller per-frame displacement), so there is less left to remove.
• The cost is lag. At 30 fps, tau = 0.314 s, so the filter trails the signal by about 9-10 frames; at 17 px/frame that is about 153 px, matching the measured value.
• Alpha trades smoothness for responsiveness (see the sweep below).

The alpha sweep re-filters the recorded raw coordinates offline, so it isolates alpha from everything else in the setup. More plots (X/Y over time, lag) are in results/.

How it works

Pipeline per frame (src/sensor_project_code.py):

1. Capture a 1280x720 frame with picamera2
2. Downsize to 160x90 for speed
3. Convert to grayscale
4. Threshold at brightness 220 to find the light
5. Morphological open (3x3 ellipse) to remove small noise blobs
6. Find external contours, take the largest, compute its centroid from image moments
7. Rescale the centroid back to full resolution
8. Apply the EMA filter: y[n] = a*x[n] + (1-a)*y[n-1]
9. Log timestamp, raw and filtered coordinates, and contour count to CSV
10. Draw the last 20 points of both traces on the frame and write it to video

See docs/filter-math.md for how the EMA relates to the continuous first-order filter and how tau and the cutoff frequency are derived.

Repo layout

src/sensor_project_code.py   capture, detect, filter, record (runs on the Pi)
analysis/analyze.py          jitter / lag / alpha-sweep analysis and plots
data/                        recorded tracking CSVs (V1 30 fps, V2 90 fps)
results/                     generated plots and summary tables
docs/filter-math.md          filter derivation and parameter notes

Usage

On the Raspberry Pi (camera module attached):

sudo apt install python3-picamera2 python3-opencv python3-numpy
python3 src/sensor_project_code.py     # Ctrl+C to stop

This writes tracking_comparison.avi and tracking_data.csv. Tunable constants are at the top of the file: ALPHA, VIDEO_FPS, BRIGHTNESS_THRESHOLD, MIN_CONTOUR_AREA. V2 was recorded with VIDEO_FPS = 90.

To reproduce the analysis (any machine):

pip install -r requirements.txt
python3 analysis/analyze.py

Parameters studied

FPS, resolution, alpha (filter weight), light brightness/size, and CPU (Pi 4 vs Pi 5).

Future work

• Dynamic alpha based on object velocity, to cut lag during fast motion while keeping smoothing when the light is slow
• Other filters (Kalman, higher-order low-pass) on the same setup
• Object detection model in place of brightness thresholding

Team

• Jeremiah Yong: custom detection model for light and objects
• Daniel Wong: low-pass filter, detection debugging, testing
• Michael Bakhtiar: double pendulum and light rig (3D printed), results analysis