Sensor Fusion

From Capsil Wiki

Sensor fusion is the process of combining data provided by various sensors to better solve a problem than using the sources individually. Fusion can be at different levels, including the data level, the feature level and the decision level.

The use of multiple sensors with information fusion has the following main advantages compared to single sensor systems Thomopoulos 90:

• Improved signal to noise ratio
• Enhanced robustness and reliability in the event of sensor failure
• Extended parameter coverage
• Integration of independent features and prior knowledge
• Increased dimensionality of the measurement
• Improved resolution, precision, confidence and hypothesis discrimination
• Reduce uncertainty

Fundamental issues to be addressed in building a data fusion system for a particular application include Hall and Llinas 977:

1. what algorithms or techniques are appropriate and optimal for a particular application;
2. what architecture should be used (i.e., where in the processing flow should data be fused);
3. how should the individual sensor data be processed to extract the maximum amount of information;
4. what accuracy can realistically be achieved by a data fusion process;
5. how can the fusion process be optimized in a dynamic sense;
6. how does the data collection environment (i.e., signal propagation, target characteristics, etc.) affect the processing;
7. under what conditions does multi sensor data fusion improve system operation?

In this page, sensor fusion at the following levels will be explained:

• Direct data fusion
• Feature level fusion
• Dimensionality reduction
• Feature selection
• Decision-level fusion

Contents 1 Direct Data Fusion 2 Feature Level Fusion 3 Distance Metrics and Clustering 4 Dimensionality Reduction 5 Feature Selection 6 Decision Level Fusion

Direct Data Fusion

Sensor fusion at the data-level allows us in many cases to overcome some of the inherent limitations of single elements of the ensemble Yang 06. Another use could be self calibration of some sensors in a sensor array. Techniques of direct data fusion include the following:

• Optimal Averaging of sensor data Xiao et al. 05
• Sensor Data Imputation:
  • Multiple statistical imputation website
  • The multiple imputation faq website
  • A Data Imputation Model in Sensor Databases
  • A Data Analyst's perspective to multivariate missing data problems
  • The use of Gaussian Processes to predict missing data using correlation information.
  • Source recovery at the data level:
  • ICA: The original paper and a brief introduction . Also, ICA code in Matlab and C
  • Kernel ICA Bach and Jordan 03
  • Non-linear ICA webpage

Feature Level Fusion

Fusion at the feature level involves the integration of feature sets corresponding to different sensors. These feature vectors are often fused to form joint feature vectors from which the classification is made. The first feature towards feature level fusion is that of effective feature detection. Once features are selected, the role of feature-level fusion is to establish boundaries in feature space and separate patterns belonging to different classes. Thus two main issues are of importance: feature detection and the use of distance metrics for clustering. Feature Detection

In general, signal features can be classified into the following 3 categories:

• Time domain features describing waveform characteristics (slopes, amplitude values, maxima/minima and zero crossing rates) and statistics (mean, standard deviation, energy, kurtosis, etc)
• Frequency domain features (periodic structures, Fourier coefficients, spectral density)
• Hybrid features covering both time and frequency domains (Wavelet representations, Wigner-Ville distributions, etc...)

Distance Metrics and Clustering

Widely used distance metrics include the Mahalanobis distance and the Euclidean distance. Methods for distance-based clustering include the following:

• k-means clustering Kanungo et al. 02,MPIKmeans and Hamerly and Elkan 03
• ISODATA
• Agglomerative clustering
• Fuzzy c -means clustering

Dimensionality Reduction

The intrinsic dimensionality of a dataset is usually related to the number of independent variables that account for most variability within the data. Some of the techniques that address dimensionality reduction are:

• SVD (Singular value decomposition)
• PCA
• Non-linear PCA, probabilistic PCA
• Multi-dimensional scaling (MDS), comparison of algorithms for MDS
• Locally linear embedding (LLE)
• Isometric mapping (Isomap)
• Gaussian Process latent variable models (GPLVM)
• Self Organising Maps (SOM)

Feature Selection

The aim of feature selection is to reduce the complexity of an induction system by eliminating redundant and irrelevant features. Advantages of feature selection include reducing computational cost and storage as well as improving prediction accuracy. In machine learning, feature selection is normally divided into two groups: wrapper and filter methods. Wrapper methods use the estimated accuracy of an induction algorithm to evaluate candidate feature subsets. Filter methods, on the other hand, learn from data and operate independently of any induction algorithm.

Relevant links to feature selection include:

• NIPS 2003 Feature selection challenge, including datasets and a comparison of algorithms
• JMLR Special issue on variable and feature selection
• RELIEF
• A video lecture on Feature selection (link)
• Analysis of relevance and redundancy in feature selection algorithms
• Margin based feature selection

Decision Level Fusion

Decision level fusion is generally based on a joint declaration of multiple single source results (or decisions) to achieve an improved classification or event detection. At the decision level, prior knowledge and domain specific information can also be incorporated. Widely used methods for decision level fusion include the following:

• Bayesian inference (Information theory, inference and learning algorithms, book by David Mackay)
• Classical inference; computing a joint probability given an assumed hypothesis usually using Maximum aposteriori (MAP) or maximum likelihood decision rules.
• Dempster-Shafer's method