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diff -up ./gazebo/sensors/GaussianNoiseModel.cc.gaussianstddev ./gazebo/sensors/GaussianNoiseModel.cc
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--- ./gazebo/sensors/GaussianNoiseModel.cc.gaussianstddev	2020-01-18 13:54:05.637290373 -0500
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+++ ./gazebo/sensors/GaussianNoiseModel.cc	2020-01-18 13:55:36.961532289 -0500
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@@ -193,8 +193,12 @@ double GaussianNoiseModel::GetBias() con
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 //////////////////////////////////////////////////
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 void GaussianNoiseModel::SampleBias()
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 {
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-  this->bias =
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+  if (this->biasStdDev > 0) {
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+    this->bias =
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       ignition::math::Rand::DblNormal(this->biasMean, this->biasStdDev);
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+  } else {
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+    this->bias = this->biasMean;
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+  }
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   // With equal probability, we pick a negative bias (by convention,
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   // rateBiasMean should be positive, though it would work fine if
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   // negative).