forked from Archive/PX4-Autopilot
217 lines
7.1 KiB
C
217 lines
7.1 KiB
C
/****************************************************************************
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*
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* Copyright (C) 2012 PX4 Development Team. All rights reserved.
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* Author: Lorenz Meier <lm@inf.ethz.ch>
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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* 3. Neither the name PX4 nor the names of its contributors may be
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* used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
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* OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
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* AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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*
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****************************************************************************/
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/**
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* @file calibration_routines.c
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* Calibration routines implementations.
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*
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* @author Lorenz Meier <lm@inf.ethz.ch>
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*/
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#include <math.h>
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#include "calibration_routines.h"
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int sphere_fit_least_squares(const float x[], const float y[], const float z[],
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unsigned int size, unsigned int max_iterations, float delta, float *sphere_x, float *sphere_y, float *sphere_z, float *sphere_radius) {
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float x_sumplain = 0.0f;
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float x_sumsq = 0.0f;
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float x_sumcube = 0.0f;
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float y_sumplain = 0.0f;
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float y_sumsq = 0.0f;
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float y_sumcube = 0.0f;
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float z_sumplain = 0.0f;
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float z_sumsq = 0.0f;
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float z_sumcube = 0.0f;
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float xy_sum = 0.0f;
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float xz_sum = 0.0f;
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float yz_sum = 0.0f;
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float x2y_sum = 0.0f;
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float x2z_sum = 0.0f;
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float y2x_sum = 0.0f;
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float y2z_sum = 0.0f;
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float z2x_sum = 0.0f;
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float z2y_sum = 0.0f;
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for (unsigned int i = 0; i < size; i++) {
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float x2 = x[i] * x[i];
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float y2 = y[i] * y[i];
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float z2 = z[i] * z[i];
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x_sumplain += x[i];
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x_sumsq += x2;
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x_sumcube += x2 * x[i];
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y_sumplain += y[i];
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y_sumsq += y2;
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y_sumcube += y2 * y[i];
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z_sumplain += z[i];
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z_sumsq += z2;
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z_sumcube += z2 * z[i];
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xy_sum += x[i] * y[i];
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xz_sum += x[i] * z[i];
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yz_sum += y[i] * z[i];
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x2y_sum += x2 * y[i];
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x2z_sum += x2 * z[i];
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y2x_sum += y2 * x[i];
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y2z_sum += y2 * z[i];
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z2x_sum += z2 * x[i];
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z2y_sum += z2 * y[i];
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}
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//
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//Least Squares Fit a sphere A,B,C with radius squared Rsq to 3D data
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//
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// P is a structure that has been computed with the data earlier.
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// P.npoints is the number of elements; the length of X,Y,Z are identical.
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// P's members are logically named.
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//
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// X[n] is the x component of point n
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// Y[n] is the y component of point n
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// Z[n] is the z component of point n
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//
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// A is the x coordiante of the sphere
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// B is the y coordiante of the sphere
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// C is the z coordiante of the sphere
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// Rsq is the radius squared of the sphere.
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//
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//This method should converge; maybe 5-100 iterations or more.
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//
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float x_sum = x_sumplain / size; //sum( X[n] )
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float x_sum2 = x_sumsq / size; //sum( X[n]^2 )
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float x_sum3 = x_sumcube / size; //sum( X[n]^3 )
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float y_sum = y_sumplain / size; //sum( Y[n] )
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float y_sum2 = y_sumsq / size; //sum( Y[n]^2 )
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float y_sum3 = y_sumcube / size; //sum( Y[n]^3 )
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float z_sum = z_sumplain / size; //sum( Z[n] )
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float z_sum2 = z_sumsq / size; //sum( Z[n]^2 )
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float z_sum3 = z_sumcube / size; //sum( Z[n]^3 )
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float XY = xy_sum / size; //sum( X[n] * Y[n] )
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float XZ = xz_sum / size; //sum( X[n] * Z[n] )
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float YZ = yz_sum / size; //sum( Y[n] * Z[n] )
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float X2Y = x2y_sum / size; //sum( X[n]^2 * Y[n] )
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float X2Z = x2z_sum / size; //sum( X[n]^2 * Z[n] )
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float Y2X = y2x_sum / size; //sum( Y[n]^2 * X[n] )
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float Y2Z = y2z_sum / size; //sum( Y[n]^2 * Z[n] )
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float Z2X = z2x_sum / size; //sum( Z[n]^2 * X[n] )
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float Z2Y = z2y_sum / size; //sum( Z[n]^2 * Y[n] )
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//Reduction of multiplications
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float F0 = x_sum2 + y_sum2 + z_sum2;
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float F1 = 0.5f * F0;
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float F2 = -8.0f * (x_sum3 + Y2X + Z2X);
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float F3 = -8.0f * (X2Y + y_sum3 + Z2Y);
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float F4 = -8.0f * (X2Z + Y2Z + z_sum3);
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//Set initial conditions:
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float A = x_sum;
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float B = y_sum;
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float C = z_sum;
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//First iteration computation:
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float A2 = A*A;
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float B2 = B*B;
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float C2 = C*C;
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float QS = A2 + B2 + C2;
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float QB = -2.0f * (A*x_sum + B*y_sum + C*z_sum);
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//Set initial conditions:
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float Rsq = F0 + QB + QS;
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//First iteration computation:
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float Q0 = 0.5f * (QS - Rsq);
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float Q1 = F1 + Q0;
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float Q2 = 8.0f * ( QS - Rsq + QB + F0 );
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float aA,aB,aC,nA,nB,nC,dA,dB,dC;
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//Iterate N times, ignore stop condition.
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int n = 0;
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while( n < max_iterations ){
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n++;
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//Compute denominator:
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aA = Q2 + 16.0f * (A2 - 2.0f * A*x_sum + x_sum2);
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aB = Q2 + 16.0f *(B2 - 2.0f * B*y_sum + y_sum2);
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aC = Q2 + 16.0f *(C2 - 2.0f * C*z_sum + z_sum2);
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aA = (aA == 0.0f) ? 1.0f : aA;
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aB = (aB == 0.0f) ? 1.0f : aB;
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aC = (aC == 0.0f) ? 1.0f : aC;
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//Compute next iteration
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nA = A - ((F2 + 16.0f * ( B*XY + C*XZ + x_sum*(-A2 - Q0) + A*(x_sum2 + Q1 - C*z_sum - B*y_sum) ) )/aA);
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nB = B - ((F3 + 16.0f * ( A*XY + C*YZ + y_sum*(-B2 - Q0) + B*(y_sum2 + Q1 - A*x_sum - C*z_sum) ) )/aB);
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nC = C - ((F4 + 16.0f * ( A*XZ + B*YZ + z_sum*(-C2 - Q0) + C*(z_sum2 + Q1 - A*x_sum - B*y_sum) ) )/aC);
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//Check for stop condition
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dA = (nA - A);
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dB = (nB - B);
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dC = (nC - C);
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if( (dA*dA + dB*dB + dC*dC) <= delta ){ break; }
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//Compute next iteration's values
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A = nA;
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B = nB;
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C = nC;
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A2 = A*A;
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B2 = B*B;
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C2 = C*C;
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QS = A2 + B2 + C2;
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QB = -2.0f * (A*x_sum + B*y_sum + C*z_sum);
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Rsq = F0 + QB + QS;
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Q0 = 0.5f * (QS - Rsq);
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Q1 = F1 + Q0;
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Q2 = 8.0f * ( QS - Rsq + QB + F0 );
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}
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*sphere_x = A;
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*sphere_y = B;
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*sphere_z = C;
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*sphere_radius = sqrtf(Rsq);
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return 0;
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}
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