Machine Learning and Kalman Filtering for Nanomechanical Mass Spectrometry

TL;DR

This paper addresses the speed-accuracy trade-off in nanomechanical mass spectrometry by refining Kalman-filter-based event detection augmented with maximum-likelihood estimation. It introduces a confidence boosted thresholding scheme and evaluates two learning-based approaches: a black-box ML method operating on raw sensor data and an ML-aided KF method using likelihood histories for binary detection, followed by ML-guided location and size estimation via maximum-likelihood rules. The authors provide theoretical insights, synthetic data generation benchmarks, and extensive performance comparisons across architectures (RFNN, CNN, XGBoost, RUSBoost), demonstrating robust operation and practical considerations for real-time DSP/FPGA implementations. The work highlights that physics-informed, model-based methods offer robust detection with lower computational cost than end-to-end ML on raw data, while ML-aided approaches can match performance under appropriate data regimes; future work targets real-world validation and deployment in hardware systems.

Abstract

Nanomechanical resonant sensors are used in mass spectrometry via detection of resonance frequency jumps. There is a fundamental trade-off between detection speed and accuracy. Temporal and size resolution are limited by the resonator characteristics and noise. A Kalman filtering technique, augmented with maximum-likelihood estimation, was recently proposed as a Pareto optimal solution. We present enhancements and robust realizations for this technique, including a confidence boosted thresholding approach as well as machine learning for event detection. We describe learning techniques that are based on neural networks and boosted decision trees for temporal location and event size estimation. In the pure learning based approach that discards the Kalman filter, the raw data from the sensor are used in training a model for both location and size prediction. In the alternative approach that augments a Kalman filter, the event likelihood history is used in a binary classifier for event occurrence. Locations and sizes are predicted using maximum-likelihood, followed by a Kalman filter that continually improves the size estimate. We present detailed comparisons of the learning based schemes and the confidence boosted thresholding approach, and demonstrate robust performance for a practical realization.

Figures (9)

• Figure 1: Contour plot of False Detection + Miss with window size $M = 50$. Darkest (lightest) regions correspond to 0 (100)% False Detection + Miss. The minimum detectable event size $7.5\times 10^{-6}$, and the optimal threshold range are indicated where both false detection and miss are 0%.
• Figure 2: Kalman filtering and maximum likelihood based event detection, with either Confidence Boosted Thresholding (A), or ML based Classifier (B) for event classification.
• Figure 3: Black-box ML for event detection
• Figure 4: Event prediction with ML-aided Kalman filtering.
• Figure 5: Window size $M$ versus minimum detectable event size $\Delta{y}_\textsf{\tiny min}$. Plot generated with equations \ref{['eqn:varAKF']} and \ref{['eqn:minsize']}, and $M$ = $2\, t_e$.