Signal Through the Noise: Improving Radon Readings with a Kalman Filter

Transcript:

Hi, I'm Nolan. I'm standing in my basement and there's something in this room that you can't see. Radon. It's invisible and odorless and in Canada it's the leading cause of lung cancer in non-smokers. In Nova Scotia, about 37% of homes are above the safety guidelines. This $200 sensor can detect it, but its readings are a bit messy. Over 17 days, my sensor read anywhere from 7 to 112 in the same room. Radon does fluctuate, but most of the scatter is sensor noise from radioactive decay. So I applied a Kalman filter, the same math used in space navigation, to clean up the signal. It cut the noise by 29% and eliminated every random spike. And it does something no simple average can: a 95% confidence range with every reading. 20 lines of code could be the start to saving 3,000 Canadian lives a year. Thank you.

In Nova Scotia, 37% of homes exceed Health Canada's radon guideline of 200 Bq/m³ more than double the national average. (Government of Nova Scotia, 2024).

Radon is a naturally occurring radioactive gas produced by uranium decay in bedrock and soil. It enters homes through foundation cracks, accumulates in basements, and is completely odourless and invisible, requiring instrumental detection.

The health consequences are serious. Health Canada identifies radon as the leading cause of lung cancer among non-smokers, responsible for more than 3,000 deaths per year in Canada. Irvine et al. (2022) demonstrated that delayed mitigation raises lifetime lung cancer risk by 30 to 40%.

Affordable consumer sensors like the RadonEye RD200 (~$200) are the only realistic option for most families. Lemieux et al. (2025) found that high-performing consumer sensors had absolute mean differences below 22%, while low-performing devices showed errors from 28 to 238%. Irvine et al. (2022) found that 29% of homeowners who detected high radon cited economic barriers to mitigation. For families who cannot afford mitigation, an inaccurate sensor creates an impossible situation: they cannot confidently determine whether costly remediation is necessary, yet the consequences of delay are serious. Sensor inaccuracy is not a statistical abstraction but a direct obstacle to safe decision-making.

This project investigated whether a Kalman filter, a recursive estimation algorithm used in GPS navigation and spacecraft tracking, could improve consumer sensor reliability so families can trust their readings and make informed health decisions.

The filter assigned only 11.4% weight to the noisy sensor and 88.6% to its own prediction, because the sensor noise is much larger than the expected hour-to-hour radon drift.

A RadonEye RD200 sensor was placed in the basement of my home in Nova Scotia, where it recorded radon concentrations once per hour over 17 continuous days, producing a dataset of 412 measurements. The sensor remained in a fixed location throughout to control for spatial variation. Lemieux et al. (2025) independently classified the RadonEye RD200 as a conforming sensor with measurement error below 25%, confirming it was appropriate as a data source.

I developed a scalar Kalman filter in MATLAB using a random-walk process model, which assumes radon concentration changes gradually and unpredictably from one hour to the next. The filter requires two tuning parameters. R represents measurement noise variance, set to 342 Bq²/m⁶, derived from the manufacturer's minimum stated error of ±0.5 pCi/L (approximately ±18.5 Bq/m³), since 18.5² = 342 (Ecosense, 2024). Q represents expected real radon drift per hour, set to 5 Bq²/h.

Before applying the filter to real measurements, I validated it on synthetic data where the correct answer was known. I generated a simulated radon signal using a random-walk model, added Gaussian noise calibrated to the sensor's stated accuracy, and measured performance against the true signal using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). Testing on known ground truth is the most rigorous form of algorithm validation because it removes all ambiguity about whether the filter is actually improving accuracy.

Scalar Kalman Filter Equations

Predict step:

Kalman gain:

Update step:

Confidence band:

96.5% of the filter's corrections targeted random sensor noise. Only 3.5% affected genuine radon variation, the filter suppresses exactly what it should and preserves exactly what matters.

The Kalman filter reduced the standard deviation of the 412 hourly readings from 17.33 to 12.36 Bq/m³, a 28.7% reduction in measurement noise, and eliminated all large random spikes that exceeded three standard deviations. The mean shifted by only 0.14 Bq/m³, confirming the filter removed noise without distorting the underlying signal. This breakdown is visualized in the graphs above, confirming the filter's corrections are precisely targeted.

On synthetic data with known ground truth, the filter reduced RMSE from 20.22 to 10.21 Bq/m³, a 49.5% improvement, and reduced MAE from 15.82 to 8.54 Bq/m³. These results confirm the filter substantially improves sensor accuracy when the correct answer can be independently verified.

On the created synthetic data, the Kalman filter outperformed all moving average benchmarks: the 5-hour average scored 10.80 RMSE, the 10-hour 11.93, and the 24-hour 11.24, all higher than the Kalman filter's 10.21. On real data, the 5-hour moving average outperformed the Kalman filter on one-step-ahead prediction error, scoring 115 compared to 167. This is reported transparently as a genuine finding. The moving average's advantage reflects its stronger bias toward recent observations, which reduces short-term prediction error but provides no uncertainty quantification.

The Kalman filter produces a 95% confidence band alongside every estimate, calculated directly from its error covariance. After reaching steady state, it reported each estimate at ±12.5 Bq/m³. No moving average produces a comparable measure. Health Canada's Guide for Radon Measurements (2017) states that measurements should provide a reasonable estimate of a home's average annual radon level to support mitigation decisions. The Kalman filter's confidence band directly supports this goal by quantifying the reliability of each estimate, something no moving average can provide. Lemieux et al. (2025) showed that raw sensor uncertainty near the 200 Bq/m³ guideline can span nearly 100 Bq/m³; the filter's narrower band is a significant improvement for decisions near that threshold.

The filter's steady-state Kalman gain converged to K = 0.1138, exactly matching the discrete algebraic Riccati equation solution (DARE), confirming the MATLAB implementation is mathematically correct. Innovation sequence diagnostics validated the tuning: skewness 0.418, kurtosis 3.256, mean 0.197, all consistent with a well-calibrated filter.

Performance Metrics

RMSE:

Noise reduction:

MAE:

Moving average:

A raw sensor reading of 185 Bq/m³ leaves real uncertainty about whether a home is safe. A filtered estimate of 185 ±12.5 Bq/m³ shows both the radon level and how much to trust it, the filter makes the answer visible.

This project confirmed that a Kalman filter can meaningfully improve the reliability of a low-cost consumer radon sensor. Across synthetic and real datasets, the filter reduced noise, eliminated large measurement spikes, preserved the true signal mean, and automatically generated confidence estimates that no alternative method could provide. The research question is answered affirmatively.

The results also revealed a more layered finding: the Kalman filter and the moving average are not simply better or worse than each other, but are suited to different measurement objectives. The moving average converges reliably to a single long-term concentration estimate, aligning with Health Canada's recommended approach for deciding whether to mitigate. The Kalman filter is better suited to real-time monitoring, where responsiveness and uncertainty quantification matter more than long-run stability.

The confidence band is the filter's most important practical contribution. Lemieux et al. (2025) identified accessible uncertainty communication as a critical gap in consumer radon measurement guidance. The Kalman filter addresses this directly: rather than reporting a single number that conceals its own unreliability, it reports an estimate with a quantified measure of confidence. Near the 200 Bq/m³ decision threshold, this distinction is consequential, as shown in the image above.

Four extensions would strengthen and broaden this work. Hahn et al. (2023) found that higher barometric pressure was associated with lower indoor radon concentrations, suggesting pressure drops drive radon entry. Testing whether the filter's innovation sequence correlates with pressure changes would determine if the random-walk model is missing a physical driver and motivate a pressure-aware filter. Further extensions are outlined in the image above.

I would like to thank my parents for providing the RadonEye RD200 sensor, supporting 17 days of continuous data collection, and encouraging me throughout this project. I am grateful to my mother who reviewed this project text before submission. I extend my gratitude to the Strait Regional Science Fair for providing me with this incredible opportunity to present my research. A big shout out to Shannon MacLennan, Andrew Clarey, and Brandon MacKinnon from the SRCE for their support and encouragement leading up to the CWSF.

Thank you all!!

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