الفهرس 
Kalman Filter And Innovation Approach To Least-Squares Estimation.Only 14 pages are availabe for public view
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Abstract
In this thesis we consider the problem of estimating
the state noise covariance Q and the measurement noise covariance
R. One of the approaches used in the litrature
estimated one value of the Q and R matrices after a long
interval, i.e. after the Kalman filter reached the steady
state conditions.
In this thesis we mOdified the above approach to obtain
estimated values of the Q and R after a shorter interval,
i.e. estimation occurs during the transient period of the
Kalman filter; only a short non-estimation start-up period
is essential. As an example; estimating R can start after
3 sampling periods. Also the first estimated values of Q
matrix can be obtained beginning from sample number 5, and
at any sample after that.
Also the suggested approach can be modified to suit any
system having time varying parameters \ r
- 2 -
After that we checked this approach by solving two
examples, one for a first order system and the other is for
a second order system, to obtain the estimated values of R
and Q matrices.
Different computational tests were performed to observe
the effect of various parameters on the estimates of Rand
Q. The effect of the following parameters were considered
1) The number of delayed samples
The values of initial guesses for measurment noise cova-
riance (RE) , and state disturbance covariance (QE).
3) The value of assumed actual noise.
The thesis consists of six chapters. Chapter I is the
introduction. Cba.pter II presents both tne Kalman filter
and ru~ovatj.on approaches. Chapter III illustrates the
causes of divergence of l;;bE:Kalman filt9r and the methods
used to overcome this. Ohapter IV presents the approach used
to estimate the value of the Rand Q matrices. Chapter V,
indicates the results obtained from the different computational
tests Which were done by applying the suggested a?proach
to solve two examples.
Chapter VI is the conclusion.