diff --git a/cartographer/mapping/internal/2d/pose_graph_2d_test.cc b/cartographer/mapping/internal/2d/pose_graph_2d_test.cc
index 965ff0a..924f36e 100644
--- a/cartographer/mapping/internal/2d/pose_graph_2d_test.cc
+++ b/cartographer/mapping/internal/2d/pose_graph_2d_test.cc
@@ -142,6 +142,9 @@ class PoseGraph2DTest : public ::testing::Test {
               odometry_rotation_weight = 0.,
               fixed_frame_pose_translation_weight = 1e1,
               fixed_frame_pose_rotation_weight = 1e2,
+              fixed_frame_pose_use_tolerant_loss = false,
+              fixed_frame_pose_tolerant_loss_param_a = 1,
+              fixed_frame_pose_tolerant_loss_param_b = 1,
               log_solver_summary = true,
               use_online_imu_extrinsics_in_3d = true,
               fix_z_in_3d = false,
diff --git a/cartographer/mapping/internal/optimization/optimization_problem_3d.cc b/cartographer/mapping/internal/optimization/optimization_problem_3d.cc
index 1b8f632..83d1777 100644
--- a/cartographer/mapping/internal/optimization/optimization_problem_3d.cc
+++ b/cartographer/mapping/internal/optimization/optimization_problem_3d.cc
@@ -548,7 +548,10 @@ void OptimizationProblem3D::Solve(
 
       problem.AddResidualBlock(
           SpaCostFunction3D::CreateAutoDiffCostFunction(constraint_pose),
-          nullptr /* loss function */,
+          options_.fixed_frame_pose_use_tolerant_loss() ?
+              new ceres::TolerantLoss(
+            options_.fixed_frame_pose_tolerant_loss_param_a(),
+            options_.fixed_frame_pose_tolerant_loss_param_b()) : nullptr,
           C_fixed_frames.at(trajectory_id).rotation(),
           C_fixed_frames.at(trajectory_id).translation(),
           C_nodes.at(node_id).rotation(), C_nodes.at(node_id).translation());
diff --git a/cartographer/mapping/internal/optimization/optimization_problem_3d_test.cc b/cartographer/mapping/internal/optimization/optimization_problem_3d_test.cc
index 4e3a129..05bfac5 100644
--- a/cartographer/mapping/internal/optimization/optimization_problem_3d_test.cc
+++ b/cartographer/mapping/internal/optimization/optimization_problem_3d_test.cc
@@ -48,6 +48,9 @@ class OptimizationProblem3DTest : public ::testing::Test {
           odometry_rotation_weight = 1e-2,
           fixed_frame_pose_translation_weight = 1e1,
           fixed_frame_pose_rotation_weight = 1e2,
+          fixed_frame_pose_use_tolerant_loss = false,
+          fixed_frame_pose_tolerant_loss_param_a = 1,
+          fixed_frame_pose_tolerant_loss_param_b = 1,
           log_solver_summary = true,
           use_online_imu_extrinsics_in_3d = true,
           fix_z_in_3d = false,
diff --git a/cartographer/mapping/internal/optimization/optimization_problem_options.cc b/cartographer/mapping/internal/optimization/optimization_problem_options.cc
index f329217..a17088a 100644
--- a/cartographer/mapping/internal/optimization/optimization_problem_options.cc
+++ b/cartographer/mapping/internal/optimization/optimization_problem_options.cc
@@ -42,6 +42,12 @@ proto::OptimizationProblemOptions CreateOptimizationProblemOptions(
       parameter_dictionary->GetDouble("fixed_frame_pose_translation_weight"));
   options.set_fixed_frame_pose_rotation_weight(
       parameter_dictionary->GetDouble("fixed_frame_pose_rotation_weight"));
+  options.set_fixed_frame_pose_use_tolerant_loss(
+      parameter_dictionary->GetBool("fixed_frame_pose_use_tolerant_loss"));
+  options.set_fixed_frame_pose_tolerant_loss_param_a(
+      parameter_dictionary->GetDouble("fixed_frame_pose_tolerant_loss_param_a"));
+  options.set_fixed_frame_pose_tolerant_loss_param_b(
+      parameter_dictionary->GetDouble("fixed_frame_pose_tolerant_loss_param_b"));
   options.set_log_solver_summary(
       parameter_dictionary->GetBool("log_solver_summary"));
   options.set_use_online_imu_extrinsics_in_3d(
diff --git a/cartographer/mapping/proto/pose_graph/optimization_problem_options.proto b/cartographer/mapping/proto/pose_graph/optimization_problem_options.proto
index 6374fb6..efc61c1 100644
--- a/cartographer/mapping/proto/pose_graph/optimization_problem_options.proto
+++ b/cartographer/mapping/proto/pose_graph/optimization_problem_options.proto
@@ -18,8 +18,9 @@ package cartographer.mapping.optimization.proto;
 
 import "cartographer/common/proto/ceres_solver_options.proto";
 
-// NEXT ID: 19
+// NEXT ID: 26
 message OptimizationProblemOptions {
+  reserved 20 to 22; // For visual constraints.
   // Scaling parameter for Huber loss function.
   double huber_scale = 1;
 
@@ -45,12 +46,20 @@ message OptimizationProblemOptions {
   // odometry.
   double odometry_rotation_weight = 17;
 
-  // Scaling parameter for the FixedFramePose translation.
+  // Scaling parameter for the FixedFramePose translation. Unit: 1/meters.
   double fixed_frame_pose_translation_weight = 11;
 
   // Scaling parameter for the FixedFramePose rotation.
   double fixed_frame_pose_rotation_weight = 12;
 
+  bool fixed_frame_pose_use_tolerant_loss = 23;
+  // The following parameters are used only if fixed_frame_pose_use_tolerant_loss is true.
+  // See http://ceres-solver.org/nnls_modeling.html.
+  // For large values of s, the tolerant loss function approaches a null loss
+  // with fixed_frame_pose_translation_weight.
+  double fixed_frame_pose_tolerant_loss_param_a = 24;
+  double fixed_frame_pose_tolerant_loss_param_b = 25;
+
   // 3D only: fix Z.
   bool fix_z_in_3d = 13;
 
diff --git a/configuration_files/pose_graph.lua b/configuration_files/pose_graph.lua
index 797e407..572cd1a 100644
--- a/configuration_files/pose_graph.lua
+++ b/configuration_files/pose_graph.lua
@@ -71,6 +71,9 @@ POSE_GRAPH = {
     odometry_rotation_weight = 1e5,
     fixed_frame_pose_translation_weight = 1e1,
     fixed_frame_pose_rotation_weight = 1e2,
+    fixed_frame_pose_use_tolerant_loss = false,
+    fixed_frame_pose_tolerant_loss_param_a = 1,
+    fixed_frame_pose_tolerant_loss_param_b = 1,
     log_solver_summary = false,
     use_online_imu_extrinsics_in_3d = true,
     fix_z_in_3d = false,