Moved AHRS to gtsam_unstable

release/4.3a0
Frank Dellaert 2013-05-20 23:16:44 +00:00
parent 314b854ecb
commit 1d9000724d
7 changed files with 915 additions and 171 deletions

362
.cproject
View File

@ -1,5 +1,7 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<?fileVersion 4.0.0?><cproject storage_type_id="org.eclipse.cdt.core.XmlProjectDescriptionStorage">
<?fileVersion 4.0.0?>
<cproject storage_type_id="org.eclipse.cdt.core.XmlProjectDescriptionStorage">
<storageModule moduleId="org.eclipse.cdt.core.settings">
<cconfiguration id="cdt.managedbuild.toolchain.gnu.macosx.base.1359703544">
<storageModule buildSystemId="org.eclipse.cdt.managedbuilder.core.configurationDataProvider" id="cdt.managedbuild.toolchain.gnu.macosx.base.1359703544" moduleId="org.eclipse.cdt.core.settings" name="MacOSX GCC">
@ -307,14 +309,6 @@
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="testGaussianFactor.run" path="linear/tests" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>testGaussianFactor.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="all" path="inference" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
@ -341,6 +335,7 @@
</target>
<target name="tests/testBayesTree.run" path="inference" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments/>
<buildTarget>tests/testBayesTree.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>false</useDefaultCommand>
@ -348,6 +343,7 @@
</target>
<target name="testBinaryBayesNet.run" path="inference" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments/>
<buildTarget>testBinaryBayesNet.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>false</useDefaultCommand>
@ -395,6 +391,7 @@
</target>
<target name="testSymbolicBayesNet.run" path="inference" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments/>
<buildTarget>testSymbolicBayesNet.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>false</useDefaultCommand>
@ -402,6 +399,7 @@
</target>
<target name="tests/testSymbolicFactor.run" path="inference" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments/>
<buildTarget>tests/testSymbolicFactor.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>false</useDefaultCommand>
@ -409,6 +407,7 @@
</target>
<target name="testSymbolicFactorGraph.run" path="inference" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments/>
<buildTarget>testSymbolicFactorGraph.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>false</useDefaultCommand>
@ -424,11 +423,20 @@
</target>
<target name="tests/testBayesTree" path="inference" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments/>
<buildTarget>tests/testBayesTree</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>false</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="testGaussianFactor.run" path="linear/tests" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>testGaussianFactor.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="testPoseRTV.run" path="build/gtsam_unstable/dynamics" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j5</buildArguments>
@ -517,22 +525,6 @@
<useDefaultCommand>false</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="all" path="CppUnitLite" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>all</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="clean" path="CppUnitLite" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>clean</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="tests/testPose2.run" path="build_retract/gtsam/geometry" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
@ -549,6 +541,22 @@
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="all" path="CppUnitLite" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>all</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="clean" path="CppUnitLite" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>clean</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="all" path="spqr_mini" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
@ -573,34 +581,26 @@
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="testValues.run" path="build/gtsam/nonlinear" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<target name="all" path="build_wrap" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j5</buildArguments>
<buildTarget>testValues.run</buildTarget>
<buildArguments>-j2</buildArguments>
<buildTarget>all</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="testOrdering.run" path="build/gtsam/nonlinear" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<target name="check" path="build_wrap" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j5</buildArguments>
<buildTarget>testOrdering.run</buildTarget>
<buildArguments>-j2</buildArguments>
<buildTarget>check</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="testKey.run" path="build/gtsam/nonlinear" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<target name="clean" path="build_wrap" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j5</buildArguments>
<buildTarget>testKey.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="testLinearContainerFactor.run" path="build/gtsam/nonlinear" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j5</buildArguments>
<buildTarget>testLinearContainerFactor.run</buildTarget>
<buildArguments>-j2</buildArguments>
<buildTarget>clean</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
@ -685,26 +685,34 @@
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="all" path="build_wrap" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<target name="testValues.run" path="build/gtsam/nonlinear" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>all</buildTarget>
<buildArguments>-j5</buildArguments>
<buildTarget>testValues.run</buildTarget>
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<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="check" path="build_wrap" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<target name="testOrdering.run" path="build/gtsam/nonlinear" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>check</buildTarget>
<buildArguments>-j5</buildArguments>
<buildTarget>testOrdering.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="clean" path="build_wrap" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<target name="testKey.run" path="build/gtsam/nonlinear" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>clean</buildTarget>
<buildArguments>-j5</buildArguments>
<buildTarget>testKey.run</buildTarget>
<stopOnError>true</stopOnError>
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<runAllBuilders>true</runAllBuilders>
</target>
<target name="testLinearContainerFactor.run" path="build/gtsam/nonlinear" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j5</buildArguments>
<buildTarget>testLinearContainerFactor.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
@ -821,6 +829,14 @@
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="testAHRS.run" path="build/gtsam_unstable/slam" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j5</buildArguments>
<buildTarget>testAHRS.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="testDiscreteFactor.run" path="build/gtsam/discrete" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j5</buildArguments>
@ -1055,6 +1071,7 @@
</target>
<target name="testGraph.run" path="build/tests" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments/>
<buildTarget>testGraph.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>false</useDefaultCommand>
@ -1062,6 +1079,7 @@
</target>
<target name="testJunctionTree.run" path="build/tests" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments/>
<buildTarget>testJunctionTree.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>false</useDefaultCommand>
@ -1069,6 +1087,7 @@
</target>
<target name="testSymbolicBayesNetB.run" path="build/tests" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments/>
<buildTarget>testSymbolicBayesNetB.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>false</useDefaultCommand>
@ -1236,6 +1255,7 @@
</target>
<target name="testErrors.run" path="linear" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments/>
<buildTarget>testErrors.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>false</useDefaultCommand>
@ -1281,14 +1301,6 @@
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="testGaussianFactor.run" path="build/linear/tests" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>testGaussianFactor.run</buildTarget>
<stopOnError>true</stopOnError>
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<runAllBuilders>true</runAllBuilders>
</target>
<target name="check" path="base" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
@ -1369,6 +1381,14 @@
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="testGaussianFactor.run" path="build/linear/tests" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>testGaussianFactor.run</buildTarget>
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<target name="check" path="build/inference" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
@ -1675,7 +1695,6 @@
</target>
<target name="testSimulated2DOriented.run" path="slam" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments/>
<buildTarget>testSimulated2DOriented.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>false</useDefaultCommand>
@ -1715,7 +1734,6 @@
</target>
<target name="testSimulated2D.run" path="slam" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments/>
<buildTarget>testSimulated2D.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>false</useDefaultCommand>
@ -1723,7 +1741,6 @@
</target>
<target name="testSimulated3D.run" path="slam" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments/>
<buildTarget>testSimulated3D.run</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>false</useDefaultCommand>
@ -1923,7 +1940,6 @@
</target>
<target name="tests/testGaussianISAM2" path="build/slam" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments/>
<buildTarget>tests/testGaussianISAM2</buildTarget>
<stopOnError>true</stopOnError>
<useDefaultCommand>false</useDefaultCommand>
@ -1945,102 +1961,6 @@
<useDefaultCommand>true</useDefaultCommand>
<runAllBuilders>true</runAllBuilders>
</target>
<target name="testRot3.run" path="geometry" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>testRot3.run</buildTarget>
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</target>
<target name="testRot2.run" path="geometry" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
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</target>
<target name="testPose3.run" path="geometry" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>testPose3.run</buildTarget>
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</target>
<target name="timeRot3.run" path="geometry" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
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<target name="testPose2.run" path="geometry" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
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</target>
<target name="testCal3_S2.run" path="geometry" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>testCal3_S2.run</buildTarget>
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<runAllBuilders>true</runAllBuilders>
</target>
<target name="testSimpleCamera.run" path="geometry" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>testSimpleCamera.run</buildTarget>
<stopOnError>true</stopOnError>
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<runAllBuilders>true</runAllBuilders>
</target>
<target name="testHomography2.run" path="geometry" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>testHomography2.run</buildTarget>
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</target>
<target name="testCalibratedCamera.run" path="geometry" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j2</buildArguments>
<buildTarget>testCalibratedCamera.run</buildTarget>
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<target name="testPoint2.run" path="geometry" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
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</target>
<target name="install" path="" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>make</buildCommand>
<buildArguments>-j3</buildArguments>
@ -2242,6 +2162,7 @@
</target>
<target name="Generate DEB Package" path="" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
<buildCommand>cpack</buildCommand>
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<buildTarget>-G DEB</buildTarget>
<stopOnError>true</stopOnError>
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@ -2249,6 +2170,7 @@
</target>
<target name="Generate RPM Package" path="" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
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@ -2256,6 +2178,7 @@
</target>
<target name="Generate TGZ Package" path="" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
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@ -2263,6 +2186,7 @@
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<target name="Generate TGZ Source Package" path="" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
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@ -2404,34 +2328,98 @@
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<target name="testSimpleCamera.run" path="geometry" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
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/*
* @file AHRS.cpp
* @brief Attitude and Heading Reference System implementation
* Created on: Jan 26, 2012
* Author: cbeall3
*/
#include "AHRS.h"
#include <cmath>
using namespace std;
namespace gtsam {
Matrix cov(const Matrix& m) {
const double num_observations = m.cols();
const Vector mean = m.rowwise().sum() / num_observations;
Matrix D = m.colwise() - mean;
Matrix DDt = D * trans(D);
return DDt / (num_observations - 1);
}
Matrix I3 = eye(3);
Matrix Z3 = zeros(3, 3);
/* ************************************************************************* */
AHRS::AHRS(const Matrix& stationaryU, const Matrix& stationaryF, double g_e) :
KF_(9) {
// Initial state
mech0_ = Mechanization_bRn2::initialize(stationaryU, stationaryF, g_e);
size_t T = stationaryU.cols();
// estimate standard deviation on gyroscope readings
Pg_ = cov(stationaryU);
Vector sigmas_v_g = esqrt(Pg_.diagonal() * T);
// estimate standard deviation on accelerometer readings
Pa_ = cov(stationaryF);
// Quantities needed for integration
// dynamics, Chris' email September 23, 2011 3:38:05 PM EDT
double tau_g = 730; // correlation time for gyroscope
double tau_a = 730; // correlation time for accelerometer
F_g_ = -I3 / tau_g;
F_a_ = -I3 / tau_a;
Vector var_omega_w = 0 * ones(3); // TODO
Vector var_omega_g = (0.0034 * 0.0034) * ones(3);
Vector var_omega_a = (0.034 * 0.034) * ones(3);
Vector sigmas_v_g_sq = emul(sigmas_v_g, sigmas_v_g);
Vector vars = concatVectors(4, &var_omega_w, &var_omega_g, &sigmas_v_g_sq,
&var_omega_a);
var_w_ = diag(vars);
// Quantities needed for aiding
sigmas_v_a_ = esqrt(T * Pa_.diagonal());
// gravity in nav frame
n_g_ = Vector_(3, 0.0, 0.0, g_e);
n_g_cross_ = skewSymmetric(n_g_); // nav frame has Z down !!!
}
/* ************************************************************************* */
std::pair<Mechanization_bRn2, KalmanFilter::State> AHRS::initialize(double g_e) {
// Calculate Omega_T, formula 2.80 in Farrell08book
double cp = cos(mech0_.bRn().inverse().pitch());
double sp = sin(mech0_.bRn().inverse().pitch());
double cy = cos(0);
double sy = sin(0);
Matrix Omega_T = Matrix_(3, 3, cy * cp, -sy, 0.0, sy * cp, cy, 0.0, -sp, 0.0, 1.0);
// Calculate Jacobian of roll/pitch/yaw wrpt (g1,g2,g3), see doc/ypr.nb
Vector b_g = mech0_.b_g(g_e);
double g1 = b_g(0);
double g2 = b_g(1);
double g3 = b_g(2);
double g23 = g2 * g2 + g3 * g3;
double g123 = g1 * g1 + g23;
double f = 1 / (sqrt(g23) * g123);
Matrix H_g = Matrix_(3, 3,
0.0, g3 / g23, -(g2 / g23), // roll
sqrt(g23) / g123, -f * (g1 * g2), -f * (g1 * g3), // pitch
0.0, 0.0, 0.0); // we don't know anything on yaw
// Calculate the initial covariance matrix for the error state dx, Farrell08book eq. 10.66
Matrix Pa = 0.025 * 0.025 * eye(3);
Matrix P11 = Omega_T * (H_g * (Pa + Pa_) * trans(H_g)) * trans(Omega_T);
P11(2, 2) = 0.0001;
Matrix P12 = -Omega_T * H_g * Pa;
Matrix P_plus_k2 = Matrix(9, 9);
P_plus_k2.block(0, 0, 3, 3) = P11;
P_plus_k2.block(0, 3, 3, 3) = Z3;
P_plus_k2.block(0, 6, 3, 3) = P12;
P_plus_k2.block(3, 0, 3, 3) = Z3;
P_plus_k2.block(3, 3, 3, 3) = Pg_;
P_plus_k2.block(3, 6, 3, 3) = Z3;
P_plus_k2.block(6, 0, 3, 3) = trans(P12);
P_plus_k2.block(6, 3, 3, 3) = Z3;
P_plus_k2.block(6, 6, 3, 3) = Pa;
Vector dx = zero(9);
KalmanFilter::State state = KF_.init(dx, P_plus_k2);
return std::make_pair(mech0_, state);
}
/* ************************************************************************* */
std::pair<Mechanization_bRn2, KalmanFilter::State> AHRS::integrate(
const Mechanization_bRn2& mech, KalmanFilter::State state,
const Vector& u, double dt) {
// Integrate full state
Mechanization_bRn2 newMech = mech.integrate(u, dt);
// Integrate error state Kalman filter
// FIXME:
//if nargout>1
Matrix bRn = mech.bRn().matrix();
Matrix I3 = eye(3);
Matrix Z3 = zeros(3, 3);
Matrix F_k = zeros(9, 9);
F_k.block(0, 3, 3, 3) = -bRn;
F_k.block(3, 3, 3, 3) = F_g_;
F_k.block(6, 6, 3, 3) = F_a_;
Matrix G_k = zeros(9, 12);
G_k.block(0, 0, 3, 3) = -bRn;
G_k.block(0, 6, 3, 3) = -bRn;
G_k.block(3, 3, 3, 3) = I3;
G_k.block(6, 9, 3, 3) = I3;
Matrix Q_k = G_k * var_w_ * trans(G_k);
Matrix Psi_k = eye(9) + dt * F_k; // +dt*dt*F_k*F_k/2; // transition matrix
Matrix B = zeros(9, 9);
Vector u2 = zero(9);
KalmanFilter::State newState = KF_.predictQ(state, Psi_k,B,u2,dt*Q_k);
return make_pair(newMech, newState);
}
/* ************************************************************************* */
std::pair<Mechanization_bRn2, KalmanFilter::State> AHRS::aid(
const Mechanization_bRn2& mech, KalmanFilter::State state,
const Vector& f, bool Farrell) {
Matrix bRn = mech.bRn().matrix();
// get gravity in body from accelerometer
Vector measured_b_g = mech.x_a() - f;
Matrix R, H;
Vector z;
if (Farrell) {
// calculate residual gravity measurement
z = n_g_ - trans(bRn) * measured_b_g;
H = collect(3, &n_g_cross_, &Z3, &bRn);
R = trans(bRn) * diag(emul(sigmas_v_a_, sigmas_v_a_)) * bRn;
} else {
// my measurement prediction (in body frame):
// F(:,k) = bias - b_g
// F(:,k) = mech.x_a + dx_a - bRn*n_g;
// F(:,k) = mech.x_a + dx_a - bRn*(I+P)*n_g;
// F(:,k) = mech.x_a + dx_a - b_g - bRn*(rho x n_g); // P = [rho]_x
// b_g - (mech.x_a - F(:,k)) = dx_a + bRn*(n_g x rho);
z = bRn * n_g_ - measured_b_g;
Matrix b_g = bRn * n_g_cross_;
H = collect(3, &b_g, &Z3, &I3);
R = diag(emul(sigmas_v_a_, sigmas_v_a_));
}
// update the Kalman filter
KalmanFilter::State updatedState = KF_.updateQ(state, H, z, R);
// update full state (rotation and accelerometer bias)
Mechanization_bRn2 newMech = mech.correct(updatedState->mean());
// reset KF state
Vector dx = zeros(9, 1);
updatedState = KF_.init(dx, updatedState->covariance());
return make_pair(newMech, updatedState);
}
/* ************************************************************************* */
std::pair<Mechanization_bRn2, KalmanFilter::State> AHRS::aidGeneral(
const Mechanization_bRn2& mech, KalmanFilter::State state,
const Vector& f, const Vector& f_previous,
const Rot3& R_previous) {
Matrix increment = R_previous.between(mech.bRn()).matrix();
// expected - measured
Vector z = f - increment * f_previous;
//Vector z = increment * f_previous - f;
Matrix b_g = skewSymmetric(increment* f_previous);
Matrix H = collect(3, &b_g, &I3, &Z3);
// Matrix R = diag(emul(sigmas_v_a_, sigmas_v_a_));
// Matrix R = diag(Vector_(3, 1.0, 0.2, 1.0)); // good for L_twice
Matrix R = diag(Vector_(3, 0.01, 0.0001, 0.01));
// update the Kalman filter
KalmanFilter::State updatedState = KF_.updateQ(state, H, z, R);
// update full state (rotation and gyro bias)
Mechanization_bRn2 newMech = mech.correct(updatedState->mean());
// reset KF state
Vector dx = zeros(9, 1);
updatedState = KF_.init(dx, updatedState->covariance());
return make_pair(newMech, updatedState);
}
/* ************************************************************************* */
void AHRS::print(const std::string& s) const {
mech0_.print(s + ".mech0_");
gtsam::print(F_g_, s + ".F_g");
gtsam::print(F_a_, s + ".F_a");
gtsam::print(var_w_, s + ".var_w");
gtsam::print(sigmas_v_a_, s + ".sigmas_v_a");
gtsam::print(n_g_, s + ".n_g");
gtsam::print(n_g_cross_, s + ".n_g_cross");
gtsam::print(Pg_, s + ".P_g");
gtsam::print(Pa_, s + ".P_a");
}
/* ************************************************************************* */
AHRS::~AHRS() {
}
/* ************************************************************************* */
} /* namespace gtsam */

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@ -0,0 +1,68 @@
/*
* AHRS.h
*
* Created on: Jan 26, 2012
* Author: cbeall3
*/
#ifndef AHRS_H_
#define AHRS_H_
#include "Mechanization_bRn2.h"
#include <gtsam/linear/KalmanFilter.h>
namespace gtsam {
Matrix cov(const Matrix& m);
class AHRS {
private:
// Initial state
Mechanization_bRn2 mech0_; ///< Initial mechanization state
KalmanFilter KF_; ///< initial Kalman filter
// Quantities needed for integration
Matrix F_g_; ///< gyro bias dynamics
Matrix F_a_; ///< acc bias dynamics
Matrix var_w_; ///< dynamic noise variances
// Quantities needed for aiding
Vector sigmas_v_a_; ///< measurement sigma
Vector n_g_; ///< gravity in nav frame
Matrix n_g_cross_; ///< and its skew-symmetric matrix
Matrix Pg_, Pa_;
public:
/**
* AHRS constructor
* @param stationaryU initial interval of gyro measurements, 3xn matrix
* @param stationaryF initial interval of accelerator measurements, 3xn matrix
* @param g_e if given, initializes gravity with correct value g_e
*/
AHRS(const Matrix& stationaryU, const Matrix& stationaryF, double g_e);
std::pair<Mechanization_bRn2, KalmanFilter::State> initialize(double g_e);
std::pair<Mechanization_bRn2, KalmanFilter::State> integrate(
const Mechanization_bRn2& mech, KalmanFilter::State state,
const Vector& u, double dt);
std::pair<Mechanization_bRn2, KalmanFilter::State> aid(
const Mechanization_bRn2& mech, KalmanFilter::State state,
const Vector& f, bool Farrell=0);
std::pair<Mechanization_bRn2, KalmanFilter::State> aidGeneral(
const Mechanization_bRn2& mech, KalmanFilter::State state,
const Vector& f, const Vector& f_expected, const Rot3& R_previous);
/// print
void print(const std::string& s = "") const;
virtual ~AHRS();
};
} /* namespace gtsam */
#endif /* AHRS_H_ */

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@ -0,0 +1,101 @@
/**
* @file Mechanization_bRn.cpp
* @date Jan 25, 2012
* @author Chris Beall
* @author Frank Dellaert
*/
#include "Mechanization_bRn2.h"
#include <boost/foreach.hpp>
namespace gtsam {
/* ************************************************************************* */
Mechanization_bRn2 Mechanization_bRn2::initializeVector(const std::list<Vector>& U,
const std::list<Vector>& F, const double g_e) {
Matrix Umat = Matrix_(3,U.size(), concatVectors(U));
Matrix Fmat = Matrix_(3,F.size(), concatVectors(F));
return initialize(Umat, Fmat, g_e);
}
/* ************************************************************************* */
Mechanization_bRn2 Mechanization_bRn2::initialize(const Matrix& U,
const Matrix& F, const double g_e) {
// estimate gyro bias by averaging gyroscope readings (10.62)
Vector x_g = U.rowwise().mean();
Vector meanF = -F.rowwise().mean();
Vector b_g, x_a;
if(g_e == 0) {
// estimate gravity in body frame from accelerometer (10.13)
b_g = meanF;
// estimate accelerometer bias as zero (10.65)
x_a = zero(3);
} else {
// normalize b_g and attribute remainder to biases
b_g = g_e * meanF/meanF.norm();
x_a = -(meanF - b_g);
}
// initialize roll, pitch (eqns. 10.14, 10.15)
double g1=b_g(0);
double g2=b_g(1);
double g3=b_g(2);
// Farrell08book eqn. 10.14
double roll = atan2(g2, g3);
// Farrell08book eqn. 10.15
double pitch = atan2(-g1, sqrt(g2 * g2 + g3 * g3));
double yaw = 0;
// This returns body-to-nav nRb
Rot3 bRn = Rot3::ypr(yaw, pitch, roll).inverse();
return Mechanization_bRn2(bRn, x_g, x_a);
}
/* ************************************************************************* */
Mechanization_bRn2 Mechanization_bRn2::correct(const Vector& dx) const {
Vector rho = sub(dx, 0, 3);
Rot3 delta_nRn = Rot3::rodriguez(rho);
Rot3 bRn = bRn_ * delta_nRn;
Vector x_g = x_g_ + sub(dx, 3, 6);
Vector x_a = x_a_ + sub(dx, 6, 9);
return Mechanization_bRn2(bRn, x_g, x_a);
}
/* ************************************************************************* */
Mechanization_bRn2 Mechanization_bRn2::integrate(const Vector& u,
const double dt) const {
// integrate rotation nRb based on gyro measurement u and bias x_g
// get body to inertial (measured in b) from gyro, subtract bias
Vector b_omega_ib = u - x_g_;
// assume nav to inertial through movement is unknown
Vector b_omega_in = zero(3);
// get angular velocity on bRn measured in body frame
Vector b_omega_bn = b_omega_in - b_omega_ib;
// convert to navigation frame
Rot3 nRb = bRn_.inverse();
Vector n_omega_bn = (nRb*b_omega_bn).vector();
// integrate bRn using exponential map, assuming constant over dt
Rot3 delta_nRn = Rot3::rodriguez(n_omega_bn*dt);
Rot3 bRn = bRn_.compose(delta_nRn);
// implicit updating of biases (variables just do not change)
// x_g = x_g;
// x_a = x_a;
return Mechanization_bRn2(bRn, x_g_, x_a_);
}
} /* namespace gtsam */

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@ -0,0 +1,81 @@
/**
* @file Mechanization_bRn.h
* @date Jan 25, 2012
* @author Chris Beall
* @author Frank Dellaert
*/
#pragma once
#include <gtsam/geometry/Rot3.h>
#include <gtsam/base/Vector.h>
#include <list>
namespace gtsam {
class Mechanization_bRn2 {
private:
Rot3 bRn_; ///< rotation from nav to body
Vector x_g_; ///< gyroscope bias
Vector x_a_; ///< accelerometer bias
public:
/**
* Constructor
* @param initial_bRn initial rotation from nav to body frame
* @param initial_x_g initial gyro bias
* @param r3 Z-axis of rotated frame
*/
Mechanization_bRn2(const Rot3& initial_bRn = Rot3(),
const Vector& initial_x_g = zero(3), const Vector& initial_x_a = zero(3)) :
bRn_(initial_bRn), x_g_(initial_x_g), x_a_(initial_x_a) {
}
Vector b_g(double g_e) {
Vector n_g = Vector_(3, 0.0, 0.0, g_e);
return (bRn_ * n_g).vector();
}
Rot3 bRn() const {return bRn_; }
Vector x_g() const { return x_g_; }
Vector x_a() const { return x_a_; }
/**
* Initialize the first Mechanization state
* @param U a list of gyro measurement vectors
* @param F a list of accelerometer measurement vectors
*/
static Mechanization_bRn2 initializeVector(const std::list<Vector>& U,
const std::list<Vector>& F, const double g_e = 0);
static Mechanization_bRn2 initialize(const Matrix& U,
const Matrix& F, const double g_e = 0);
/**
* Correct AHRS full state given error state dx
* @param obj The current state
* @param dx The error used to correct and return a new state
*/
Mechanization_bRn2 correct(const Vector& dx) const;
/**
* Integrate to get new state
* @param obj The current state
* @param u gyro measurement to integrate
* @param dt time elapsed since previous state in seconds
*/
Mechanization_bRn2 integrate(const Vector& u, const double dt) const;
/// print
void print(const std::string& s = "") const {
bRn_.print(s + ".R");
gtsam::print(x_g_, s + ".x_g");
gtsam::print(x_a_, s + ".x_a");
}
};
} // namespace gtsam

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/*
* @file testAHRS.cpp
* @brief Test AHRS
* @author Frank Dellaert
* @author Chris Beall
*/
#include <list>
#include <gtsam/geometry/Rot3.h>
#include <gtsam/base/Vector.h>
#include "../AHRS.h"
#include <CppUnitLite/TestHarness.h>
using namespace std;
using namespace gtsam;
// stationary interval of gyro U and acc F
Matrix stationaryU = trans(Matrix_(3,3,-0.0004,-0.0002,-0.0014,0.0006,-0.0003,0.0007,0.0006,-0.0002,-0.0003));
Matrix stationaryF = trans(Matrix_(3,3,0.1152,-0.0188,9.7419,-0.0163,0.0146,9.7753,-0.0283,-0.0428,9.9021));
double g_e = 9.7963; // Atlanta
/* ************************************************************************* */
TEST (AHRS, cov) {
// samples stored by row
Matrix A = Matrix_(4, 3,
1.0, 2.0, 3.0,
5.0, 7.0, 0.0,
9.0, 4.0, 7.0,
6.0, 3.0, 2.0);
Matrix actual = cov(trans(A));
Matrix expected = Matrix_(3, 3,
10.9167, 2.3333, 5.0000,
2.3333, 4.6667, -2.6667,
5.0000, -2.6667, 8.6667);
EXPECT(assert_equal(expected, actual, 1e-4));
}
/* ************************************************************************* */
TEST (AHRS, covU) {
Matrix actual = cov(10000*stationaryU);
Matrix expected = Matrix_(3, 3,
33.3333333, -1.66666667, 53.3333333,
-1.66666667, 0.333333333, -5.16666667,
53.3333333, -5.16666667, 110.333333);
EXPECT(assert_equal(expected, actual, 1e-4));
}
/* ************************************************************************* */
TEST (AHRS, covF) {
Matrix actual = cov(100*stationaryF);
Matrix expected = Matrix_(3, 3,
63.3808333, -0.432166667, -48.1706667,
-0.432166667, 8.31053333, -16.6792667,
-48.1706667, -16.6792667, 71.4297333);
EXPECT(assert_equal(expected, actual, 1e-4));
}
/* ************************************************************************* */
TEST (AHRS, constructor) {
AHRS ahrs = AHRS(stationaryU,stationaryF,g_e);
}
/* ************************************************************************* */
/* TODO: currently fails because of problem with ill-conditioned system
TEST (AHRS, init) {
AHRS ahrs = AHRS(stationaryU,stationaryF,g_e);
std::pair<Mechanization_bRn2, KalmanFilter::State> result = ahrs.initialize(g_e);
}
*/
/* ************************************************************************* */
int main() {
TestResult tr;
return TestRegistry::runAllTests(tr);
}
/* ************************************************************************* */