bayesian filtering classes.html

良好的代码实现

						<TD WIDTH=342>
							<P>Represents only the Bayesian Likelihood of a state
							observation</TD>
					</TR>
					<TR VALIGN=TOP>
						<TD WIDTH=210>
							<P><STRONG>Functional_filter</STRONG></TD>
						<TD WIDTH=342>
							<P>Represents only the filter prediction by a simple
							functional (non-stochastic) model</TD>
					</TR>
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							<P><STRONG>State_filter</STRONG></TD>
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							<P>Represents only the filter state and an update on that
							state</TD>
					</TR>
					<TR VALIGN=TOP>
						<TD WIDTH=210>
							<P><STRONG>Kalman_state_filter</STRONG></TD>
						<TD WIDTH=342>
							<P>Kalman representation of state statistics.<BR>Represents a
							state vector and a covariance matrix. That is the 1st (mean)
							and 2nd (covariance) moments of a distribution.</TD>
					</TR>
					<TR VALIGN=TOP>
						<TD WIDTH=210>
							<P><B>Information_state_filter</B></TD>
						<TD WIDTH=342>
							<P>Information representation of state statistics.<BR>Effectively
							the inverse of the Kalman_state_filter representation.</TD>
					</TR>
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						<TD WIDTH=210>
							<P><STRONG>Linrz_filter</STRONG></TD>
						<TD WIDTH=342>
							<P>Model interface for a linear or gradient linearized Kalman
							filters.<BR>Specifies filter operation using predict and
							observe functions</TD>
					</TR>
					<TR VALIGN=TOP>
						<TD WIDTH=210>
							<P><STRONG>Sample_filter</STRONG></TD>
						<TD WIDTH=342>
							<P>Discreate reprensation of state statistic.<BR>Base class
							for filters representing state probability distribution by a
							discrete sampling</TD>
					</TR>
				</TABLE>
	</DD>
</DL>
<H2 ALIGN=LEFT>Model Hierarchy</H2>
<P ALIGN=LEFT>These two tables show some of the classes in the
hierarchy upon which models are built.</P><A NAME="predict models"></A>
<DL>
	<DD>
					<TABLE WIDTH=561 BORDER=3 CELLPADDING=2 CELLSPACING=0>
						<COL WIDTH=223>
						<COL WIDTH=324>
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							<TD WIDTH=223>
								<P><STRONG>Sampled_predict_model</STRONG></TD>
							<TD WIDTH=324>
								<P>Sampled stochastic prediction model</TD>
						</TR>
						<TR VALIGN=TOP>
							<TD WIDTH=223>
								<P><STRONG>Functional_predict_model</STRONG>
							</TD>
							<TD WIDTH=324>
								<P>Functional (non-stochastic) prediction model
							</TD>
						</TR>
						<TR VALIGN=TOP>
							<TD WIDTH=223>
								<P><STRONG>Addative_predict_model</STRONG></TD>
							<TD WIDTH=324>
								<P>Additive Gaussian noise prediction model.<BR>This
								fundamental model for linear/linearized filtering, with noise
								added to a functional prediction</TD>
						</TR>
						<TR VALIGN=TOP>
							<TD WIDTH=223>
								<P><STRONG>Linrz_predict_model</STRONG></TD>
							<TD WIDTH=324>
								<P>Linearized prediction model with Jacobian of non-linear
								functional part</TD>
						</TR>
						<TR VALIGN=TOP>
							<TD WIDTH=223>
								<P><STRONG>Linear_predict_model</STRONG></TD>
							<TD WIDTH=324>
								<P>Linear prediction model</TD>
						</TR>
						<TR VALIGN=TOP>
							<TD WIDTH=223>
								<P><STRONG>Linear_invertable_predict_model</STRONG></TD>
							<TD WIDTH=324>
								<P>Linear prediction model which is invertible</TD>
						</TR>
					</TABLE>
	</DD>
</DL>
<P>&nbsp;</P><A NAME="observe models"></A>
<DL>
	<DD>
					<TABLE WIDTH=558 BORDER=3 CELLPADDING=2 CELLSPACING=0>
						<COL WIDTH=222>
						<COL WIDTH=322>
						<TR VALIGN=TOP>
							<TD WIDTH=222 HEIGHT=39>
								<P><STRONG>Likelihood_observe_model</STRONG>
							</TD>
							<TD WIDTH=322>
								<P>Likelihood observation model<BR>The most fundamental
								Bayesian definition of an observation</TD>
						</TR>
						<TR VALIGN=TOP>
							<TD WIDTH=222>
								<P><STRONG>Functional_observe_model</STRONG></TD>
							<TD WIDTH=322>
								<P>Functional (non-stochastic) observation model</TD>
						</TR>
						<TR VALIGN=TOP>
							<TD WIDTH=222>
								<P><STRONG>Linrz_uncorrelated_observe_model</STRONG></TD>
							<TD WIDTH=322>
								<P>Linearized observation model with Jacobian of non-linear
								functional part and additive uncorrelated noise</TD>
						</TR>
						<TR VALIGN=TOP>
							<TD WIDTH=222 HEIGHT=23>
								<P><STRONG>Linrz_correlated_observe_model</STRONG></TD>
							<TD WIDTH=322>
								<P>as above, but with additive correlated noise</TD>
						</TR>
					</TABLE>
	</DD>
</DL>
<H1>Capabilities</H1>
<H2>Probabilistic representation of state</H2>
<P>Bayes rule is usually defined in term of Probability Density
Functions. However PDFs never appear in Bayes++. They are always
represented by their statistics.</P>
<P>This is for good reason, there is very little that can be done
algorithmically with a function. However the sufficient statistics,
given the assumptions of a filter, can be easily manipulated to
implement Bayes rule. Each filter class is derived from a base
classes that represent the statistics used. For example the
Kalman_filter and Sample_filter base classes.</P>
<P>It would be possible to use a common abstract base class for that
enforces the implementation of a PDF function; a function that maps
state to probability. This would provide a very weak method to view
the PDF of state. However such a function could not be efficiently
implemented by all schemes. Therefore to enforce this requirement in
the base class would be highly restrictive.</P>
<H2>Linear and Linearized models</H2>
<P>Many of the filters use classical linear estimation techniques,
such as the Kalman filter. To make them useful they are applied in
modified forms to cope with <U>linearized</U> models of some kind.
Commonly a gradient linearized model is used to update uncertainty,
while the state is directly propagated through the non-linear model.
This is the <I>Extended</I> form used by the Extended Kalman Filter.</P>
<P>However, some numerical schemes cannot be modified using the
<I>Extended</I> form. In particular, it is not always possible to use
the extended form with correlated noises. Where this is the case, the
linearized model is used for uncertainty and state.</P>
<P>There are also many Bayesian filters that work with non-Gaussian
noise and non-linear models - such as the <I>SIR_filter</I>. The SIR
scheme has been built so it works with Likelihood model.</P>
<P>The filters support discontinuous models such as those depending
on angles. In this case the model must be specifically formulated to
normalize the states. However, some schemes need to rely on an
additional normalization function. Normalization works well for
functions that are locally continuous after normalization (such as
angles). Non-linear functions that cannot be made into locally
continuous models are not appropriate for linear filters.</P>
<H2>Interface Regularity</H2>
<P>Where possible, the Schemes have been designed to all have the
same interface, providing for easy interchange. However, this is not
possible in all cases as the mathematical methods vary greatly. For
efficiency some schemes also implement additional functions. The
functions can be use to avoid inefficiencies where the general form
is not required.</P>
<P>Scheme class constructors are irregular (their parameter list
varies) and must be used with care. Each numerical scheme has
different requirements, and the representation size needs to be
parameterized. A template class Filter_scheme can be used to provide
a generic constructor interface. It provides provides specialization
for all the Schemes so they can be constructed with a common
parameter list.</P>
<H3>Open interface</H3>
<P>The design of the class hierarchy is deliberately open. Many of
the variables associated with schemes are exposed as <I>public
members</I>. For example the covariance filter&rsquo;s innovation
covariance is public. This is to allow efficient algorithms to be
implemented using the classes. In particular it is often the case
that subsequent computations reuse the values that have already been
computed by the numerical schemes. Each scheme defines a <I>public
state representation</I>.</P>
<P>Furthermore many temporaries are <I>protected members</I> to allow
derived classes to modify a scheme without requiring any additional
overhead to allocate its own temporaries.</P>
<P>Open interfaces are potentially hazardous. The danger is that
abuse could result in unnecessary dependencies on particular
implementation characteristics.
</P>
<H4>Public state representation Initialization and Update</H4>
<P>The two functions <B>init</B> and <B>update</B> are defined in the
filter class hierarchy for classes with names ending <B>_state_filter</B>.
They are very important in allowing the <I>public state
representation</I> to be managed.</P>
<BLOCKQUOTE><P><U>After</U> the public representation of a scheme is
changed (externally) the filter should be <I>initialized</I> with an
<B>init</B> function. The scheme may define additional init functions
that allow it to be initialized from alternative representations.
<B>init()</B> is defined for schemes derived from
<B>Kalman_state_filter</B>.</P></BLOCKQUOTE>
<BLOCKQUOTE><P><U>Before</U> the public representation of a scheme is
used the filter should be <I>updated</I> with an <B>update</B>
function. The scheme may define additional update functions that
allow it to update alternative representations. <B>update()</B> is
defined for schemes derived from <B>Kalman_state_filter</B>.</P></BLOCKQUOTE>
<H4>Sharing schemes state representation</H4>
<P>The filter hierarchy has been specifically designed to allow state
representation to be shared. Schemes state representations are
inherited using one or more <B>_state_filter</B> 's as virtual base
classes. It is therefore possible to combine multiple schemes (using
multiple inheritance) and only a single copy of each state
representation will exist.</P>
<P>The <B>init</B> and <B>update</B> functions should be used to
coordinate between the schemes and state representation. This allows
precise control numerical conversions necessary for different schemes
to share the state.</P>
<H4>Assignment and Copy Construction</H4>
<P>Filter classes can be assigned when they are of the same size. In
cases where the class includes members in addition to the public
representation this is optimized so that only public representation
is assigned. Assignment is equivalent to: <I>update</I>, assignment
of public representation and <I>initialization</I> from the new
state.</P>
<P>Copy Constructors are NOT defined. Generally the classes are
expensive to copy and so copies should be avoided. Instead references
or (smart) pointers should be combined with assignment to create
copies if necessary.</P>