Adaptative high-gain extended Kalman filter and applications

tel-00559107, version 1 - 24 Jan 2011
4.3 real-time Implementation
− the two last blocks are gain factors that adjust the measured signals to the appropriate
scale 23 .
The implementation of the two main blocks is done with the RTAICblock block that
appears in the RTAI-lib palette. It is an adaptation of the Cblock2 block of the palette
Others 24 .
Generally speaking, Scicos blocks are composed of two files: the interfacing function and
the computational function. The role of the interfacing function is to link the computational
function to Scicos. It defines how the computational function has to be interpreted and what
the appearance of the Scicos block actually is (number of entry points, size and name of the
block, etc.). The computational function is the core of the block. It defines what the block
does. Most of the time a flag parameter is used to specify which part of the computational
function has to be considered. As may be guessed from its name, the computational function
of this block has to be written in C code. The structure is similar to that of a Matlab
S-function (see [41], Chpt. 9, in particular Sec. 9.5.2).
The calculation of a solution for the Riccati equation requires several matrix multiplications.
We examined the two following approaches:
1. Scicos is embedded into Scilab, which deals pretty smoothly with the multiplication of
matrices. Scilab is built from several FORTRAN, C and C++ routines and is open
source. This means that the original files are serviceable from Scilab source code. In
order to use those routines in C, the header
#include
is required. The two routines we need are
(a) extern int C2F(dmmul)(); that takes the matrices A, B, C as input parameters
and outputs the matrix C = A × B,
(b) extern int C2F(dmmul)(); that takes the matrices A, B, C as input parameters
and outputs the matrix C = C + A × B,
Combinations of those two functions enable us to perform all the matrix multiplications
required. In addition, recall that the Ricatti matrix of Kalman-like filters is square
symmetric, i.e., for a dim(n × n) matrix, only n(n + 1)/2 integrations (or updates)
are required. A small program that transforms the square matrix into a corresponding
column vector and vice versa, must be developed.
2. the matrices used have particular shapes:
− A(u) is an upper diagonal matrix,
− Q and R are taken diagonal,
− b ∗ (z, u) is lower triangular.
23 The I/O card delivers a digital input positive signal on the range (0 − 5), while the maximum current
supported by the DC supply is 10 A. The scaling factor is therefore 2. The scaling factor for the voltage is 60.
24 The palette Others is a regular Scicos palette. Since those two functions need to interact with the real-time
routine of the operating system and have to be taken from the RTAI-lib palette.
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