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HYBRID WAVELET-KALMAN FILTER MULTI-SCALE
SEQUENTIAL FUSION METHOD
Funa Zhou
1,2
and Tianhao Tang
1
1.
Department of Electrical & Control Engineering, Shanghai Marintime University, Shanghai, China
2.
Computer&Information Engineering School, Henan University, Kaifeng, Henan, China
Keywords: Hybrid wavelet-Kalman filter, Sequential fusion, Non-
n
2
sampling.
Abstract: With the development of automation, multi-scale data fusion has become a hot research topic, however,
limited by the constraint that signal to implement wavelet transform must have the length of
q
2
, multi-scale
data fusion problem involved with non-
n
2
sampled observation data still hasn’t been efficiently solved. In
this paper, we develop a hybrid wavelet-Kalman filter multiscale sequential fusion method. First, we
develop the hybrid wavelet-Kalman filter multiscale estimation method which combines the advantage of
wavelet and Kalman filter to obtain the real time, recursive, multiscale estimation of the dynamic system.
Then, a multiscale sequential fusion method is presented. Under the hybrid wavelet-Kalman filter multiscale
estimation frame, we can easily fuse information from multiple sensors sequentially without designing other
complex fusion algorithm. The multiscale sequential fusion method can fuse non-
n
2
sampled data just by
analyzing the possible observation structure to design the observation model of the stacked dynamic system.
Simulation result of three sensors with sampling interval 1, 2 and 3 shows the efficiency of this method.
1 INTRODUCTION
In many fields, such as, automatic control,
aerospace, communication, navigation and
production industry, more than one sensor is used to
gather complete information of the object or process.
According to the mechanism of each sensor, they
can be placed on different scales and the sampling
rate of these sensors may also be different. The
research of multi-sensor data fusion for dynamic
system is significant both in practice and
theoretically (Wen 2002a, Wen 2002b, Lang
Hong1994). Especially, in many cases, the sampling
interval may not equal to
n
2
, thus it is inconvenient
for us to fuse information provided by these sensors.
Therefore the tracking or estimation accuracy may
be strongly reduced.
The main technique used in multi-scale data
fusion is Kalman filter and wavelet analysis. Kalman
filter can result in real-time, recursive and optimal
estimate while it doesn’t take the multi-scale
character of the object into account. Wavelet
transform can implement multi-scale analysis and
estimation of the dynamic system, but the estimate is
neither real time nor recursive (Wen 2002a).
Using Kalman filter, data fusion algorithm for
multi-sensor sampling at same rate has been
successfully developed. Coporating with multi-scale
theory, multi-scale data fusion algorithm for multi-
sensor sampling at
n
2
interval has also been
developed. Limited by the fact that signals to
implement wavelet transform must have the length
of
q
2 , the method mentioned in (Wen 2002b, Lang
Hong1994) can’t solve the data fusion problem
when the sensors used are not sampling at
n
2
interval.
We find that once the dynamic system is stacked
in a given length
q
2
, sensors not sampled at interval
n
2
has different observation structure on each block,
that is, the length of the observation vector on each
block may be different, and the sampling rule on
each observation block is also different.
Based on the hybrid wavelet and Kalman filter
sequential fusion method developed in (Wen 2006a,
Zhou 2007), we are intend to develop a sequential
fusion scheme by designing the stacked observation
model to fuse the observation data coming from
those sensors sampling at non-
n
2
interval.
244
Zhou F. and Tang T. (2008).
HYBRID WAVELET-KALMAN FILTER MULTI-SCALE SEQUENTIAL FUSION METHOD.
In Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - SPSMC, pages 244-248
DOI: 10.5220/0001483702440248
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SciTePress