Decentralized Data Fusion Algorithm using Factor Analysis Model

S.A.Quadri and Othman Sidek Collaborative µ-electronic Design Excellence CentreUniversiti Sains Malaysia

The 2012 International Conference on Mechatronics and Control Engineering(ICMCE 2012)

Presentation overview

Introduction to data fusion

Decentralized data fusion

Inertial measurement unit (IMU)

Factor analysis

Decentralized data fusion algorithm

Conclusion and future work

DATA FUSION •Data-fusion is process of combining inputs from various sensors to provide a robust and complete description of an environment or process of interest.

•It is multilevel, multifaceted process dealing with the automatic detection, association, correlation , estimation, and combination of data and information from single and multiple sources.

•Data fusion plays a pivotal role to achieve reasonable accuracy and precision.

• An appropriate fusion process can reduce imprecision, uncertainties and

incompleteness, thus increasing the robustness and reliability of identification.

•To achieve the great benefits of fusion, one of the important steps is

Identification of the optimal fusion architecture. Basically, there are three

fusion architectures:

Independent (autonomous) fusion architecture

Centralized fusion architecture

Decentralized fusion architecture

Independent fusion architecture: It is the simplest fashion in which signal features are extracted and recognition (recognition is to establish the posterior consensus) is carried out independently by individual sensors.

Centralized fusion architecture:Extracts a generic set of features with commonness from pre-processed signals provided by individual sensors in parallel for subsequent recognition. This is distinct from other architectures where different sensors may provide uncorrelated or irrelevant features.

Decentralized fusion architecture:

•It executes feature extraction & selection for each sensor independently.

•The features can be in common or irrelevant from sensor to sensor. All the extracted features are then fused for recognition.

•A decentralized system is characterized by being modular, scalable and survivable.

• By the virtue of scalability and modularity, decentralized fusion algorithms have significant role in data fusion systems.

•Decentralised data fusion algorithms communicate information rather than states & probabilities.

Advantages of Decentralized fusion architecture

Decentralised algorithms offer a uniquely powerful method of mathematically modeling large-scale systems of systems.

Decentralised methods allow information gathering and decision making systems to be described in a mathematically rigorous and modular manner.

Decentralised methods provide an ability to analyze and reason about a system and its information gathering or decision making role.

Decentralised methods also provide a compelling ability to compose mathematical descriptions of larger systems from descriptions of component sub-systems. That is the inherent modularity and scalability of decentralized system algorithms.

Decentralised methods provide a natural and powerful ability to reason about composite systems and in particular to study, a priori, system pay-offs.

Here we presents fusion of estimates from gyroscope and accelerometer in an IMU

employing Factor analysis model.

Exploiting factor analysis as a tool, a Decentralized data fusion algorithm is proposed,

that extracts features (factors) from the raw data and fuse them to obtain global

estimates.

After a brief description of IMU and Factor analysis model , detail working of algorithm

is shown in following flow chart.

Decentralized Data Fusion Algorithm using Factor Analysis Model

Inertial measurement unit (IMU)An inertial measurement unit (IMU) is an electronic device that measures & reports on a craft's velocity, orientation, & gravitational forces, using a combination of accelerometers and gyroscopes [1]

IMU works by detecting changes in pitch, roll, and yaw.

[1] A.D. King: ‘Inertial Navigation-40 Years of Evolution’, GEC Review,13(3),(1998), p.140.

Factor analysis

•Factor analysis is a statistical method used to describe variability among observed,

correlated variables in terms of a potentially lower number of unobserved, uncorrelated

variables called factors.

•Factor analysis is a collection of methods used to examine how underlying constructs

influence the responses on a number of measured variables also used to assess the

reliability and validity of measurement scales.

•Factor analysis is used to uncover the latent structure (dimensions) of a set of variables.

•Mostly used when need to reduce a large number of variables to a smaller number of

factors for modeling purpose.

Factor analysis is related to principal component analysis (PCA), but the two are not identical.

The difference is:

• Diagonal of the relationships matrix is replaced with communalities in Factor analysis.

•The variance is accounted for more than one variable in Factor analysis.

Factor Analysis Equations:

Considering each object or record has p features, so Xij is the value of feature j for object i.

We will center all the observations (subtract off their mean).

We postulate that there are q factor variables, and each observation is a linear combination of

factor scores Fir plus noise:

Xij= εij + Firwrj (1)

The weights wrj are called the factor loadings of the observable features; how much feature j

changes, on average, in response to a one-unit change in factor score r.

Here εij is as usual the noise term for feature j on object i. We will assume this has mean zero

and variance ψj that is, different features has differently sized noise terms. The ψ j are known as

the specific variances, because they are specific to individual features. We will further assume

that E[εij εlm] = 0, unless i = l, j = m, that is, each object and each feature has uncorrelated noise.

With w being a q x p matrix. If we stack the vectors into a matrix, we get

X= ε + Fw (3) [2]

This is the factor analysis model.

In a factor analysis model, the measured variables depend on a smaller number of unobserved (latent) factors.

Because each factor might affect several variables in common, they are known as common factors.

Each variable is assumed dependent on a linear combination of the common factors, and the coefficients are known as

loadings.

Each measured variable also includes a component due to independent random variability, known as specific variance

because it is specific to one variable.

Specifically, factor analysis assumes that the covariance matrix of data is of the form

∑x = ΛΛT + Ψ (4)

Where Λ is the matrix of loadings and the elements of the diagonal matrix Ψ are the specific variances.

The function factoran fits the factor analysis model using maximum likelihood.

Where Λ is the matrix of loadings and the elements of the diagonal matrix Ψ are the specific variances.

Factor analysis assumes that the covariance matrix of data is of the form.

SigmaX = Lambda*Lambda' + Psi (5)

Where Lambda is the matrix of loadings and the elements of the diagonal matrix Psi are the specific variances.

We can also re-write the model in vector form,

(2)

[2] Jing, T , An Algorithm for estimating signals using factor analysis model, China 1991 Int. Con. Circuits and Systems, 1991, China , pp. 358-360

Decentralized Data Fusion Algorithm - Flowchart

Data is obtained from the SparkFun IMU that has noise variance of 0.07701688 for accelerometer & 0.00025556 for gyroscope [3].

Factor analysis is carried using the Matlab Statistics Toolbox™.

The flow of data and various steps of the algorithm are shown in flowchart.

Two set of maximum likelihood estimates are obtained:

Case1) With noise variance.

Case 2) Without noise variance.

In the final step of algorithm, Maximum likelihood estimates (MLE) incorporating noise in gyroscope and accelerometer (case1) and ML estimates without noise (case2) are fused and global estimates are obtained.

[3] http://home.comcast.net/~michael.p.thompson/kalman/kalman_test2.c

Simulation is carried on Matlab platform. The algorithm is executed by feeding raw data from gyroscope and accelerometer. The estimates of gyroscope and accelerometer incorporated with noise variance are fused, simultaneously estimates of the same with zero noise variance are also fused in order to obtain two set of global estimates.The output result of both cases are shown in graph.

The paper presents development of decentralized data fusion algorithm to fuse data in an IMU, utilizing factor analysis model.

One of the main concerns in data fusion technique is the risk of producing fused estimates that are worse and lead to discontentment. Noise variance could be one of the responsible factors for poor performance of data fusion system.

The decentralised architecture of algorithm allows studying exclusively effect of noise parameter associated with individual sensors.

The future work is to study and analyze estimation error and effect of noise variances and finally, comparison of the proposed method with other existing algorithms.

Conclusion and future work

Any Questions