SLAM.Inertial.SchmidtCorrectRelativePose

Parameters, inputs, outputs, defaults and equations from the source file.

function SchmidtCorrectRelativePose
  import RGBDProperRotationValue = SLAM.Localization.RGBDProperRotationValue;
  import SLAMCovariancePSDCheck = SLAM.Inertial.SLAMCovariancePSDCheck;
  import SLAMRotationCoordinates = SLAM.Inertial.SLAMRotationCoordinates;
  import SchmidtCorrectionSolve = SLAM.Inertial.SchmidtCorrectionSolve;

  input Real position[spaceDimension] = zeros(spaceDimension);
  input Real velocity[spaceDimension] = zeros(spaceDimension);
  input Real rotation[spaceDimension,spaceDimension] = identity(spaceDimension);
  input Real accelBias[spaceDimension] = zeros(spaceDimension);
  input Real gyroBias[spaceDimension] = zeros(spaceDimension);
  input Real covariance[errorDimension,errorDimension] = identity(errorDimension);
  input Real referencePosition[spaceDimension] = zeros(spaceDimension);
  input Real referenceRotation[spaceDimension,spaceDimension] = identity(spaceDimension);
  input Real referenceCovariance[poseDimension,poseDimension] = identity(poseDimension);
  input Real crossCovariance[errorDimension,poseDimension] = zeros(errorDimension,poseDimension);
  input Real opticalToBody[spaceDimension,spaceDimension] = [0.0,0.0,1.0;-1.0,0.0,0.0;0.0,-1.0,0.0];
  input Real cameraOriginBody[spaceDimension] = {0.18,0.0,-0.04};
  input Real measuredRotation[spaceDimension,spaceDimension] = identity(spaceDimension);
  input Real measuredTranslation[spaceDimension] = zeros(spaceDimension);
  input Real relativeCovariance[poseDimension,poseDimension] = identity(poseDimension);
  input Real measurementEnabled = 0.0;
  input Real maximumNis = 22.46;
  input Real maximumAngularInnovation = 0.35;
  output Real accepted;
  output Real nis;
  output Real innovation[poseDimension];
  output Real measurementJacobian[poseDimension,augmentedDimension];
  output Real innovationCovariance[poseDimension,poseDimension];
  output Real nextPosition[spaceDimension];
  output Real nextVelocity[spaceDimension];
  output Real nextRotation[spaceDimension,spaceDimension];
  output Real nextAccelBias[spaceDimension];
  output Real nextGyroBias[spaceDimension];
  output Real nextCovariance[errorDimension,errorDimension];
  output Real nextCrossCovariance[errorDimension,poseDimension];
  output Real nextReferenceCovariance[poseDimension,poseDimension];
protected
  constant Integer spaceDimension = 3;
  constant Integer errorDimension = 15;
  constant Integer poseDimension = 2*spaceDimension;
  constant Integer augmentedDimension = errorDimension+poseDimension;
  Real currentCameraTranspose[spaceDimension,spaceDimension];
  Real displacementBody[spaceDimension];
  Real predictedRotation[spaceDimension,spaceDimension];
  Real predictedTranslation[spaceDimension];
  Real logarithmVector[spaceDimension]; Real logarithmAngle; Real logarithmValid; Real logarithmQuaternion[4];
  Real skewDisplacement[spaceDimension,spaceDimension];
  Real skewOrigin[spaceDimension,spaceDimension];
  Real skewInnovation[spaceDimension,spaceDimension];
  Real inverseLeft[spaceDimension,spaceDimension];
  Real inverseRight[spaceDimension,spaceDimension];
  Real jacobianCoefficient;
  Real currentTranslationAngle[spaceDimension,spaceDimension];
  Real referenceTranslationAngle[spaceDimension,spaceDimension];
  Real currentRotationAngle[spaceDimension,spaceDimension];
  Real referenceRotationAngle[spaceDimension,spaceDimension];
  Real noiseMap[poseDimension,poseDimension];
  Real noiseRotation[spaceDimension,spaceDimension];
  Real noise[poseDimension,poseDimension];
  Real prior[augmentedDimension,augmentedDimension];
  // The component's default dimension is exactly21. Rebinding it to an equal
  // constant would introduce an unnecessary parameter-initialization owner.
  Real priorCheckValid;
  Real noiseCheckValid; Real noiseSolution[poseDimension,errorDimension+1];
  Real cross[augmentedDimension,poseDimension];
  Real rhs[poseDimension,errorDimension+1];
  Real solveValid; Real solved[poseDimension,errorDimension+1];
  Real gain[augmentedDimension,poseDimension];
  Real correction[errorDimension];
  Real residualMap[augmentedDimension,augmentedDimension];
  Real joseph[augmentedDimension,augmentedDimension];
  Real reset[augmentedDimension,augmentedDimension];
  Real resetCovariance[augmentedDimension,augmentedDimension];
  Real injectedRotation[spaceDimension,spaceDimension];
  Real increment[spaceDimension,spaceDimension];
  Real skewCorrection[spaceDimension,spaceDimension];
  Real correctionAngle;
  Real sineCoefficient;
  Real cosineCoefficient;
  Real resetCoefficient;
  Real skewCorrectionSquared[spaceDimension,spaceDimension];
  Real finiteChecks[augmentedDimension,augmentedDimension];
  Real geometryChecks[spaceDimension];
  Real currentValid; Real referenceValid; Real extrinsicsValid; Real measuredValid;
algorithm
  currentValid := RGBDProperRotationValue(rotation);
  referenceValid := RGBDProperRotationValue(referenceRotation);
  extrinsicsValid := RGBDProperRotationValue(opticalToBody);
  measuredValid := RGBDProperRotationValue(measuredRotation);
  (noiseSolution,noiseCheckValid) := SchmidtCorrectionSolve(A=relativeCovariance,B=zeros(poseDimension,errorDimension+1));
  currentCameraTranspose := transpose(opticalToBody)*transpose(rotation);
  displacementBody := transpose(rotation)*(referencePosition-position+referenceRotation*cameraOriginBody);
  predictedRotation := currentCameraTranspose*referenceRotation*opticalToBody;
  predictedTranslation := transpose(opticalToBody)*(displacementBody-cameraOriginBody);
  (logarithmVector,logarithmAngle,logarithmValid,logarithmQuaternion) := SLAMRotationCoordinates(transpose(predictedRotation)*measuredRotation);
  innovation := cat(1,measuredTranslation-predictedTranslation,logarithmVector);
  skewDisplacement := [0.0,-displacementBody[3],displacementBody[2];displacementBody[3],0.0,-displacementBody[1];-displacementBody[2],displacementBody[1],0.0];
  skewOrigin := [0.0,-cameraOriginBody[3],cameraOriginBody[2];cameraOriginBody[3],0.0,-cameraOriginBody[1];-cameraOriginBody[2],cameraOriginBody[1],0.0];
  skewInnovation := [0.0,-innovation[6],innovation[5];innovation[6],0.0,-innovation[4];-innovation[5],innovation[4],0.0];
  jacobianCoefficient := if noEvent(logarithmAngle < 1e-4) then
      1.0/12.0+logarithmAngle^2/720.0
    else (1.0-0.5*logarithmAngle*cos(0.5*logarithmAngle)/max(sin(0.5*logarithmAngle),1e-12))/max(logarithmAngle^2,1e-12);
  inverseLeft := identity(spaceDimension)-0.5*skewInnovation+jacobianCoefficient*(skewInnovation*skewInnovation);
  inverseRight := identity(spaceDimension)+0.5*skewInnovation+jacobianCoefficient*(skewInnovation*skewInnovation);
  currentTranslationAngle := transpose(opticalToBody)*skewDisplacement;
  referenceTranslationAngle := -currentCameraTranspose*referenceRotation*skewOrigin;
  currentRotationAngle := -inverseLeft*transpose(predictedRotation)*transpose(opticalToBody);
  referenceRotationAngle := inverseLeft*transpose(opticalToBody);
  noiseRotation := inverseRight*transpose(measuredRotation);
  // Explicit blocks keep every coordinate valid even during structural projection.
  // H := -d(innovation)/d(error); columns are p,v,theta,ba,bg,p_ref,theta_ref.
  measurementJacobian := cat(1,
    cat(2,-currentCameraTranspose,zeros(3,3),currentTranslationAngle,
      zeros(3,6),currentCameraTranspose,referenceTranslationAngle),
    cat(2,zeros(3,6),currentRotationAngle,zeros(3,9),referenceRotationAngle));
  noiseMap := cat(1,cat(2,identity(3),zeros(3,3)),
    cat(2,zeros(3,3),noiseRotation));
  prior := cat(1,cat(2,covariance,crossCovariance),cat(2,transpose(crossCovariance),referenceCovariance));
  priorCheckValid := SLAMCovariancePSDCheck(prior,1e-12);
  cross := prior*transpose(measurementJacobian);
  noise := noiseMap*relativeCovariance*transpose(noiseMap);
  innovationCovariance := measurementJacobian*cross+noise;
  for i in 1:poseDimension loop
    for j in 1:errorDimension loop
      rhs[i,j] := cross[j,i];
    end for;
    rhs[i,errorDimension+1] := innovation[i];
  end for;
  (solved,solveValid) := SchmidtCorrectionSolve(A=innovationCovariance,B=rhs);
  // Schmidt gain: reference uncertainty enters S, but reference gain is zero.
  gain := cat(1,transpose(solved[:,1:errorDimension]),zeros(poseDimension,poseDimension));
  correction := gain[1:errorDimension,:]*innovation;
  nis := sum(innovation[i]*solved[i,errorDimension+1] for i in 1:poseDimension);
  residualMap := identity(augmentedDimension)-gain*measurementJacobian;
  joseph := residualMap*prior*transpose(residualMap)+gain*noise*transpose(gain);
  skewCorrection := [0.0,-correction[9],correction[8];correction[9],0.0,-correction[7];-correction[8],correction[7],0.0];
  correctionAngle := sqrt(sum(correction[i]^2 for i in 7:9));
  sineCoefficient := if noEvent(correctionAngle < 1e-7) then 1.0 else sin(correctionAngle)/max(correctionAngle,1e-12);
  cosineCoefficient := if noEvent(correctionAngle < 1e-7) then 0.5 else (1.0-cos(correctionAngle))/max(correctionAngle^2,1e-12);
  resetCoefficient := if noEvent(correctionAngle < 1e-6) then 1.0/6.0 else (correctionAngle-sin(correctionAngle))/max(correctionAngle^3,1e-18);
  skewCorrectionSquared := skewCorrection*skewCorrection;
  increment := identity(spaceDimension)+sineCoefficient*skewCorrection+cosineCoefficient*skewCorrectionSquared;
  injectedRotation := rotation*increment;
  // Only current right-local attitude is reset; frozen reference tangent is unchanged.
  reset := cat(1,
    cat(2,identity(6),zeros(6,15)),
    cat(2,zeros(3,6),identity(3)-cosineCoefficient*skewCorrection
      +resetCoefficient*skewCorrectionSquared,zeros(3,12)),
    cat(2,zeros(12,9),identity(12)));
  resetCovariance := reset*joseph*transpose(reset);
  for i in 1:augmentedDimension loop
    for j in 1:augmentedDimension loop
      finiteChecks[i,j] := if noEvent(abs(resetCovariance[i,j]) <= 1e12) then 0.0 else 1.0;
    end for;
  end for;
  for i in 1:spaceDimension loop
    geometryChecks[i] := if noEvent(abs(position[i]) <= 1e6 and abs(referencePosition[i]) <= 1e6
      and abs(velocity[i]) <= 1e6 and abs(cameraOriginBody[i]) <= 10.0
      and abs(measuredTranslation[i]) <= 1e6 and abs(correction[i]) <= 1e6
      and abs(correction[i+3]) <= 1e6
      and abs(accelBias[i]+correction[i+9]) <= 2.0
      and abs(gyroBias[i]+correction[i+12]) <= 0.3) then 0.0 else 1.0;
  end for;
  accepted := if noEvent(measurementEnabled >= 1.0 and measurementEnabled <= 1.0
    and maximumNis > 0.0 and maximumNis <= 1e6
    and maximumAngularInnovation > 0.0 and maximumAngularInnovation <= 1.0
    and currentValid > 0.5 and referenceValid > 0.5
    and extrinsicsValid > 0.5 and measuredValid > 0.5 and logarithmValid > 0.5
    and priorCheckValid > 0.5 and noiseCheckValid > 0.5 and solveValid > 0.5
    and nis >= 0.0 and nis <= maximumNis and logarithmAngle <= maximumAngularInnovation
    and sum(finiteChecks) < 0.5 and sum(geometryChecks) < 0.5) then 1.0 else 0.0;
  nextPosition := if noEvent(accepted > 0.5) then position+correction[1:3] else position;
  nextVelocity := if noEvent(accepted > 0.5) then velocity+correction[4:6] else velocity;
  nextRotation := if noEvent(accepted > 0.5) then injectedRotation else rotation;
  nextAccelBias := if noEvent(accepted > 0.5) then accelBias+correction[10:12] else accelBias;
  nextGyroBias := if noEvent(accepted > 0.5) then gyroBias+correction[13:15] else gyroBias;
  for i in 1:errorDimension loop
    for j in 1:errorDimension loop
      nextCovariance[i,j] := if noEvent(accepted > 0.5) then
        0.5*(resetCovariance[i,j]+resetCovariance[j,i]) else covariance[i,j];
    end for;
    for j in 1:poseDimension loop
      nextCrossCovariance[i,j] := if noEvent(accepted > 0.5) then
        resetCovariance[i,errorDimension+j] else crossCovariance[i,j];
    end for;
  end for;
  // Schmidt gain/reset leave this block and the retained reference pose unchanged.
  nextReferenceCovariance := referenceCovariance;
end SchmidtCorrectRelativePose;