13.4 Sensor fusion and data processing

Sensor fusion and data processing are crucial in embedded systems, combining data from multiple sensors to get more accurate readings. These techniques help overcome individual sensor limitations, reducing noise and improving overall system performance.

Kalman filters, complementary filters, and machine learning algorithms are key tools for sensor fusion. Data preprocessing, including calibration, filtering, and feature extraction, is essential for preparing sensor data for analysis and decision-making in embedded systems.

Sensor Fusion Algorithms

Kalman Filter for Optimal State Estimation

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• Recursive algorithm estimates the state of a dynamic system from a series of noisy measurements
• Consists of two main steps: prediction and update
  • Prediction step uses the system model to predict the current state based on the previous state estimate
  • Update step incorporates new measurements to refine the state estimate
• Widely used in applications such as navigation, tracking, and control systems (GPS, radar tracking)
• Handles uncertainties and noise in sensor data by maintaining a probabilistic representation of the system state

Complementary Filters for Sensor Data Integration

• Combines data from multiple sensors to obtain a more accurate and reliable estimate of the measured quantity
• Typically used to fuse data from sensors with complementary characteristics (accelerometer and gyroscope)
  • Accelerometer provides accurate long-term orientation but is sensitive to high-frequency noise
  • Gyroscope measures angular velocity and is less affected by external forces but suffers from drift over time
• Applies a high-pass filter to one sensor's data and a low-pass filter to the other sensor's data
• The filtered data is then combined to obtain a fused estimate that leverages the strengths of each sensor

Advanced Data Fusion Techniques

• Bayesian inference methods combine prior knowledge with sensor observations to estimate the system state
  • Particle filters represent the state probability distribution using a set of weighted samples (particles)
  • Unscented Kalman Filter (UKF) handles non-linear systems by using a deterministic sampling approach
• Dempster-Shafer theory allows for the representation of uncertainty and conflicting evidence from multiple sources
• Information fusion architectures organize and manage the flow of data and information in multi-sensor systems
  • Centralized architecture collects raw data from all sensors and performs fusion at a central node
  • Decentralized architecture distributes the fusion process among multiple nodes, each processing a subset of sensors

Machine Learning for Sensor Data Analysis

• Machine learning techniques can be applied to sensor data for pattern recognition, anomaly detection, and prediction
• Supervised learning algorithms learn from labeled training data to classify or predict outcomes
  • Support Vector Machines (SVM) find optimal decision boundaries for classification tasks
  • Neural networks, such as Convolutional Neural Networks (CNN), can learn hierarchical features from raw sensor data
• Unsupervised learning algorithms discover inherent structures or patterns in unlabeled data
  • Clustering methods group similar data points together (k-means, DBSCAN)
  • Dimensionality reduction techniques (PCA, t-SNE) help visualize and analyze high-dimensional sensor data
• Deep learning models, such as Long Short-Term Memory (LSTM) networks, can capture temporal dependencies in time-series sensor data

Data Preprocessing

Sensor Calibration Techniques

• Process of adjusting sensor parameters to ensure accurate and consistent measurements
• Offset calibration corrects for systematic biases in sensor readings
  • Determines the difference between the sensor output and a known reference value
  • Subtracts the offset from the sensor readings to obtain calibrated values
• Gain calibration adjusts the sensor's sensitivity to match the expected input-output relationship
  • Multiplies the sensor readings by a scaling factor to achieve the desired output range
• Non-linearity calibration compensates for non-linear sensor responses using lookup tables or polynomial regression

Signal Processing Methods

• Filtering techniques remove unwanted noise and extract relevant information from sensor signals
  • Low-pass filters attenuate high-frequency noise while preserving low-frequency components (moving average filter)
  • High-pass filters remove low-frequency drift and emphasize high-frequency components (differentiator)
  • Band-pass filters select a specific frequency range of interest and reject others (Butterworth filter)
• Resampling methods change the sampling rate of sensor data to match the desired temporal resolution
  • Downsampling reduces the sampling rate by keeping only a subset of the original samples (decimation)
  • Upsampling increases the sampling rate by interpolating new samples between existing ones (linear interpolation)
• Synchronization aligns sensor data from multiple sources based on timestamps or other temporal markers

Noise Reduction Techniques

• Averaging multiple sensor readings over time can reduce random noise and improve signal-to-noise ratio
• Median filtering replaces each sample with the median value of its neighboring samples, effectively removing outliers
• Kalman filtering recursively estimates the true signal by combining noisy measurements with a system model
• Wavelet denoising decomposes the signal into wavelet coefficients, thresholds the coefficients, and reconstructs the denoised signal

Feature Extraction and Selection

• Identifies and extracts informative features from preprocessed sensor data for further analysis or machine learning
• Time-domain features capture statistical properties of the signal (mean, variance, peak-to-peak amplitude)
• Frequency-domain features reveal the spectral content of the signal (Fourier transform, power spectral density)
• Time-frequency features analyze the signal's frequency content over time (short-time Fourier transform, wavelet transform)
• Feature selection methods identify the most relevant and discriminative features for a given task
  • Filter methods rank features based on statistical measures (correlation, mutual information)
  • Wrapper methods evaluate feature subsets using a machine learning model's performance
  • Embedded methods incorporate feature selection within the model training process (L1 regularization)