Article
Time-Domain Data Fusion Using Weighted Evidence
and Dempster–Shafer Combination Rule: Application
in Object Classification
Nazmuzzaman Khan * and Sohel Anwar
Department of Mechanical and Energy Engineering, Indiana University—Purdue University Indianapolis,
Indianapolis, IN 46202, USA; soanwar@iupui.edu
* Correspondence: mdkhan@iupui.edu
Received: 26 October 2019; Accepted: 22 November 2019; Published: 26 November 2019
Abstract:
To apply data fusion in time-domain based on Dempster–Shafer (DS) combination rule,
an 8-step algorithm with novel entropy function is proposed. The 8-step algorithm is applied
to time-domain to achieve the sequential combination of time-domain data. Simulation results
showed that this method is successful in capturing the changes (dynamic behavior) in time-domain
object classification. This method also showed better anti-disturbing ability and transition property
compared to other methods available in the literature. As an example, a convolution neural network
(CNN) is trained to classify three different types of weeds. Precision and recall from confusion matrix
of the CNN are used to update basic probability assignment (BPA) which captures the classification
uncertainty. Real data of classified weeds from a single sensor is used test time-domain data fusion.
The proposed method is successful in filtering noise (reduce sudden changes—smoother curves) and
fusing conflicting information from the video feed. Performance of the algorithm can be adjusted
between robustness and fast-response using a tuning parameter which is number of time-steps(t
s
).
Keywords: evidence combination; time-domain data fusion; object classification; uncertainty
1. Introduction
Dempster–Shafer theory (DS theory), also called belief function theory, as introduced and
developed by Dempster and Shafer [
1
,
2
], has emerged from their works on statistical inference and
uncertain reasoning. As a tool to manipulate an uncertain environment, DS evidence theory established
a rounded system for uncertainty management and information fusion [
3
–
6
]. The research is mainly
focused on multi-sensor fusion in space-domain where multiple pieces of evidence are gathered from
multiple sensors and combined to achieve a decision-level fusion. However, for real-time application
of multi-sensor systems, time-domain evidence fusion is also needed. Due to noise and disturbances
from environment or wrong output from sensors in space-domain, noisy, distorted or even wrong
results can be obtained at a certain time-step. The goal of the time-domain evidence fusion is, by using
the information available at previous time-steps, to capture the dynamic behavior of the system and
reduce the disturbance of the final output.
Few studies considered the influence of time factor on time-domain evidence combination.
Hong and Lynch [
7
] showed multiple approaches of how original DS method can be applied to
time-domain, but no steps to improve the limitations of the original DS method [
8
] is mentioned. Song
et al. [
9
,
10
] proposed credibility decay model based on the idea that credibility of the evidence will
decay over time. However, his methods showed poor anti-disturbing ability when conflicting (noisy)
evidence is present in time-domain. Chengkun et al. [
11
] proposed an improved credibility decay
model using exponential smoothing and conflict degree between pieces of evidence. His method
Sensors 2019, 19, 5187; doi:10.3390/s19235187 www.mdpi.com/journal/sensors
