[Paper Review] Iterative Correction of Sensor Degradation and a Bayesian Multi-Sensor Data Fusion Method

Luka Kolar, Rok Sikonja+1 more|arXiv (Cornell University)|Sep 7, 2020

Gaussian Processes and Bayesian Inference7 references4 citations

TL;DR

This paper proposes a data-driven method for correcting sensor degradation in multi-sensor systems using iterative ratio-based correction and Bayesian Gaussian process fusion. By modeling degradation as a monotonic, continuous function and leveraging the ratio between two signals with differing exposure, the method iteratively estimates the ground-truth signal and fuses corrected signals using sparse Gaussian processes with sensor-specific noise modeling, achieving convergence to the true signal in noiseless conditions and robust estimation in noisy settings.

ABSTRACT

We present a novel method for inferring ground-truth signal from multiple degraded signals, affected by different amounts of sensor exposure. The algorithm learns a multiplicative degradation effect by performing iterative corrections of two signals solely from the ratio between them. The degradation function d should be continuous, satisfy monotonicity, and d(0) = 1. We use smoothed monotonic regression method, where we easily incorporate the aforementioned criteria to the fitting part. We include theoretical analysis and prove convergence to the ground-truth signal for the noiseless measurement model. Lastly, we present an approach to fuse the noisy corrected signals using Gaussian processes. We use sparse Gaussian processes that can be utilized for a large number of measurements together with a specialized kernel that enables the estimation of noise values of all sensors. The data fusion framework naturally handles data gaps and provides a simple and powerful method for observing the signal trends on multiple timescales(long-term and short-term signal properties). The viability of correction method is evaluated on a synthetic dataset with known ground-truth signal.

Motivation & Objective

• To develop a general, data-driven method for correcting sensor degradation caused by differential exposure in multi-sensor systems.
• To enable accurate reconstruction of the ground-truth signal from two or more degraded, noisy sensor measurements with varying exposure levels.
• To design a Bayesian data fusion framework that integrates corrected signals while estimating sensor-specific noise variances.
• To provide theoretical convergence guarantees for the iterative correction method under a noiseless model.
• To enable multi-timescale signal observation through scalable sparse Gaussian processes with adaptive inducing points.

Proposed method

• The method models sensor degradation as a continuous, monotonically decreasing function d(e) with d(0) = 1, where e is cumulative exposure.
• It performs iterative correction by exploiting the ratio between two sensor signals (a and b), assuming the ratio converges to a constant under correct estimation.
• A smoothed monotonic regression approach enforces continuity and monotonicity constraints during degradation function fitting.
• The corrected signals are fused using sparse variational Gaussian processes (SGP), with a specialized kernel that estimates sensor-specific noise variances.
• The SGP framework uses inducing points to scale to large datasets and enables multi-timescale signal analysis by varying the number of inducing points.
• The method is validated on synthetic data with known ground-truth, using Brownian motion for signal generation and sub-sampling to simulate exposure differences.

Experimental results

Research questions

• RQ1 Can iterative correction based on the ratio between two degraded signals converge to the ground-truth signal in the absence of noise?
• RQ2 How can sensor degradation be modeled and corrected without prior knowledge of the true signal, using only the relative behavior of two sensors?
• RQ3 Can a Bayesian data fusion framework effectively combine multiple corrected signals while estimating sensor-specific noise levels?
• RQ4 How does the choice of inducing point count in sparse Gaussian processes affect the fidelity and timescale resolution of the reconstructed signal?
• RQ5 What is the impact of noise amplification during iterative correction, and how can it be mitigated through subsequent fusion?

Key findings

• The iterative correction method converges to the ground-truth signal under the noiseless measurement model, as proven theoretically in the paper.
• In the presence of noise, the corrected signals converge toward the ground-truth, though noise amplification increases with time due to division by decreasing degradation values.
• The ratio between corrected signals converges to a constant unit function, confirming the consistency of the correction process.
• The sparse Gaussian process fusion framework successfully reconstructs the ground-truth signal with a 95% confidence interval that tightly envelopes the true signal when using m=500 inducing points.
• By varying the number of inducing points (m ∈ {100, 300, 500}), the method enables multi-timescale signal observation, with higher m values capturing finer temporal fluctuations.
• The convergence history shows that correction quality improves with each iteration, especially when the back-up sensor signal is well-estimated early on.