diff --git a/matlab/+gtsam/VisualISAMInitialize.m b/matlab/+gtsam/VisualISAMInitialize.m
index 29f8b3b46..9b834e3e1 100644
--- a/matlab/+gtsam/VisualISAMInitialize.m
+++ b/matlab/+gtsam/VisualISAMInitialize.m
@@ -12,11 +12,11 @@ end
 isam = ISAM2(params);
 
 %% Set Noise parameters
-noiseModels.pose = noiseModel.Diagonal.Sigmas([0.001 0.001 0.001 0.1 0.1 0.1]');
+noiseModels.pose = noiseModel.Diagonal.Sigmas([0.001 0.001 0.001 0.1 0.1 0.1]', true);
 %noiseModels.odometry = noiseModel.Diagonal.Sigmas([0.001 0.001 0.001 0.1 0.1 0.1]');
-noiseModels.odometry = noiseModel.Diagonal.Sigmas([0.05 0.05 0.05 0.2 0.2 0.2]');
-noiseModels.point = noiseModel.Isotropic.Sigma(3, 0.1);
-noiseModels.measurement = noiseModel.Isotropic.Sigma(2, 1.0);
+noiseModels.odometry = noiseModel.Diagonal.Sigmas([0.05 0.05 0.05 0.2 0.2 0.2]', true);
+noiseModels.point = noiseModel.Isotropic.Sigma(3, 0.1, true);
+noiseModels.measurement = noiseModel.Isotropic.Sigma(2, 1.0, true);
 
 %% Add constraints/priors
 % TODO: should not be from ground truth!
diff --git a/matlab/gtsam_tests/testJacobianFactor.m b/matlab/gtsam_tests/testJacobianFactor.m
index 1c214c3bc..7a2d344b1 100644
--- a/matlab/gtsam_tests/testJacobianFactor.m
+++ b/matlab/gtsam_tests/testJacobianFactor.m
@@ -32,7 +32,7 @@ x1 = 3;
 % the RHS
 b2=[-1;1.5;2;-1];
 sigmas = [1;1;1;1];
-model4 = noiseModel.Diagonal.Sigmas(sigmas);
+model4 = noiseModel.Diagonal.Sigmas(sigmas, true);
 combined = JacobianFactor(x2, Ax2,  l1, Al1, x1, Ax1, b2, model4);
 
 % eliminate the first variable (x2) in the combined factor, destructive !
@@ -74,7 +74,7 @@ Bx1 = [
 % the RHS
 b1= [0.0;0.894427];
 
-model2 = noiseModel.Diagonal.Sigmas([1;1]);
+model2 = noiseModel.Diagonal.Sigmas([1;1], true);
 expectedLF = JacobianFactor(l1, Bl1, x1, Bx1, b1, model2);
 
 % check if the result matches the combined (reduced) factor
diff --git a/matlab/gtsam_tests/testKalmanFilter.m b/matlab/gtsam_tests/testKalmanFilter.m
index 3564c6b7a..46846b8f7 100644
--- a/matlab/gtsam_tests/testKalmanFilter.m
+++ b/matlab/gtsam_tests/testKalmanFilter.m
@@ -23,13 +23,13 @@ import gtsam.*
 F = eye(2,2);
 B = eye(2,2);
 u = [1.0; 0.0];
-modelQ = noiseModel.Diagonal.Sigmas([0.1;0.1]);
+modelQ = noiseModel.Diagonal.Sigmas([0.1;0.1], true);
 Q = 0.01*eye(2,2);
 H = eye(2,2);
 z1 = [1.0, 0.0]';
 z2 = [2.0, 0.0]';
 z3 = [3.0, 0.0]';
-modelR = noiseModel.Diagonal.Sigmas([0.1;0.1]);
+modelR = noiseModel.Diagonal.Sigmas([0.1;0.1], true);
 R = 0.01*eye(2,2);
 
 %% Create the set of expected output TestValues
diff --git a/matlab/gtsam_tests/testLocalizationExample.m b/matlab/gtsam_tests/testLocalizationExample.m
index ed091ea71..6c79eada5 100644
--- a/matlab/gtsam_tests/testLocalizationExample.m
+++ b/matlab/gtsam_tests/testLocalizationExample.m
@@ -17,7 +17,7 @@ graph = NonlinearFactorGraph;
 
 %% Add two odometry factors
 odometry = Pose2(2.0, 0.0, 0.0); % create a measurement for both factors (the same in this case)
-odometryNoise = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1]); % 20cm std on x,y, 0.1 rad on theta
+odometryNoise = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1], true); % 20cm std on x,y, 0.1 rad on theta
 graph.add(BetweenFactorPose2(1, 2, odometry, odometryNoise));
 graph.add(BetweenFactorPose2(2, 3, odometry, odometryNoise));
 
@@ -27,7 +27,7 @@ groundTruth = Values;
 groundTruth.insert(1, Pose2(0.0, 0.0, 0.0));
 groundTruth.insert(2, Pose2(2.0, 0.0, 0.0));
 groundTruth.insert(3, Pose2(4.0, 0.0, 0.0));
-model = noiseModel.Diagonal.Sigmas([0.1; 0.1; 10]);
+model = noiseModel.Diagonal.Sigmas([0.1; 0.1; 10], true);
 for i=1:3
     graph.add(PriorFactorPose2(i, groundTruth.atPose2(i), model));
 end
diff --git a/matlab/gtsam_tests/testOdometryExample.m b/matlab/gtsam_tests/testOdometryExample.m
index 9bd4762a7..744d1af6e 100644
--- a/matlab/gtsam_tests/testOdometryExample.m
+++ b/matlab/gtsam_tests/testOdometryExample.m
@@ -17,12 +17,12 @@ graph = NonlinearFactorGraph;
 
 %% Add a Gaussian prior on pose x_1
 priorMean = Pose2(0.0, 0.0, 0.0); % prior mean is at origin
-priorNoise = noiseModel.Diagonal.Sigmas([0.3; 0.3; 0.1]); % 30cm std on x,y, 0.1 rad on theta
+priorNoise = noiseModel.Diagonal.Sigmas([0.3; 0.3; 0.1], true); % 30cm std on x,y, 0.1 rad on theta
 graph.add(PriorFactorPose2(1, priorMean, priorNoise)); % add directly to graph
 
 %% Add two odometry factors
 odometry = Pose2(2.0, 0.0, 0.0); % create a measurement for both factors (the same in this case)
-odometryNoise = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1]); % 20cm std on x,y, 0.1 rad on theta
+odometryNoise = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1], true); % 20cm std on x,y, 0.1 rad on theta
 graph.add(BetweenFactorPose2(1, 2, odometry, odometryNoise));
 graph.add(BetweenFactorPose2(2, 3, odometry, odometryNoise));
 
diff --git a/matlab/gtsam_tests/testPlanarSLAMExample.m b/matlab/gtsam_tests/testPlanarSLAMExample.m
index e0b4dbfc8..8cb2826fd 100644
--- a/matlab/gtsam_tests/testPlanarSLAMExample.m
+++ b/matlab/gtsam_tests/testPlanarSLAMExample.m
@@ -30,18 +30,18 @@ graph = NonlinearFactorGraph;
 
 %% Add prior
 priorMean = Pose2(0.0, 0.0, 0.0); % prior at origin
-priorNoise = noiseModel.Diagonal.Sigmas([0.3; 0.3; 0.1]);
+priorNoise = noiseModel.Diagonal.Sigmas([0.3; 0.3; 0.1], true);
 graph.add(PriorFactorPose2(i1, priorMean, priorNoise)); % add directly to graph
 
 %% Add odometry
 odometry = Pose2(2.0, 0.0, 0.0);
-odometryNoise = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1]);
+odometryNoise = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1], true);
 graph.add(BetweenFactorPose2(i1, i2, odometry, odometryNoise));
 graph.add(BetweenFactorPose2(i2, i3, odometry, odometryNoise));
 
 %% Add bearing/range measurement factors
 degrees = pi/180;
-brNoise = noiseModel.Diagonal.Sigmas([0.1; 0.2]);
+brNoise = noiseModel.Diagonal.Sigmas([0.1; 0.2], true);
 graph.add(BearingRangeFactor2D(i1, j1, Rot2(45*degrees), sqrt(4+4), brNoise));
 graph.add(BearingRangeFactor2D(i2, j1, Rot2(90*degrees), 2, brNoise));
 graph.add(BearingRangeFactor2D(i3, j2, Rot2(90*degrees), 2, brNoise));
diff --git a/matlab/gtsam_tests/testPose2SLAMExample.m b/matlab/gtsam_tests/testPose2SLAMExample.m
index 72e5331f2..17374c71b 100644
--- a/matlab/gtsam_tests/testPose2SLAMExample.m
+++ b/matlab/gtsam_tests/testPose2SLAMExample.m
@@ -26,19 +26,19 @@ graph = NonlinearFactorGraph;
 %% Add prior
 % gaussian for prior
 priorMean = Pose2(0.0, 0.0, 0.0); % prior at origin
-priorNoise = noiseModel.Diagonal.Sigmas([0.3; 0.3; 0.1]);
+priorNoise = noiseModel.Diagonal.Sigmas([0.3; 0.3; 0.1], true);
 graph.add(PriorFactorPose2(1, priorMean, priorNoise)); % add directly to graph
 
 %% Add odometry
 % general noisemodel for odometry
-odometryNoise = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1]);
+odometryNoise = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1], true);
 graph.add(BetweenFactorPose2(1, 2, Pose2(2.0, 0.0, 0.0 ), odometryNoise));
 graph.add(BetweenFactorPose2(2, 3, Pose2(2.0, 0.0, pi/2), odometryNoise));
 graph.add(BetweenFactorPose2(3, 4, Pose2(2.0, 0.0, pi/2), odometryNoise));
 graph.add(BetweenFactorPose2(4, 5, Pose2(2.0, 0.0, pi/2), odometryNoise));
 
 %% Add pose constraint
-model = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1]);
+model = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1], true);
 graph.add(BetweenFactorPose2(5, 2, Pose2(2.0, 0.0, pi/2), model));
 
 %% Initialize to noisy points
diff --git a/matlab/gtsam_tests/testPose3SLAMExample.m b/matlab/gtsam_tests/testPose3SLAMExample.m
index 51ba69240..d5e23ee77 100644
--- a/matlab/gtsam_tests/testPose3SLAMExample.m
+++ b/matlab/gtsam_tests/testPose3SLAMExample.m
@@ -21,7 +21,7 @@ p1 = hexagon.atPose3(1);
 fg = NonlinearFactorGraph;
 fg.add(NonlinearEqualityPose3(0, p0));
 delta = p0.between(p1);
-covariance = noiseModel.Diagonal.Sigmas([0.05; 0.05; 0.05; 5*pi/180; 5*pi/180; 5*pi/180]);
+covariance = noiseModel.Diagonal.Sigmas([0.05; 0.05; 0.05; 5*pi/180; 5*pi/180; 5*pi/180], true);
 fg.add(BetweenFactorPose3(0,1, delta, covariance));
 fg.add(BetweenFactorPose3(1,2, delta, covariance));
 fg.add(BetweenFactorPose3(2,3, delta, covariance));
diff --git a/matlab/gtsam_tests/testSFMExample.m b/matlab/gtsam_tests/testSFMExample.m
index a1f63c3a7..6ac41eedc 100644
--- a/matlab/gtsam_tests/testSFMExample.m
+++ b/matlab/gtsam_tests/testSFMExample.m
@@ -25,7 +25,7 @@ poseNoiseSigmas = [0.001 0.001 0.001 0.1 0.1 0.1]';
 graph = NonlinearFactorGraph;
 
 %% Add factors for all measurements
-measurementNoise = noiseModel.Isotropic.Sigma(2,measurementNoiseSigma);
+measurementNoise = noiseModel.Isotropic.Sigma(2,measurementNoiseSigma, true);
 for i=1:length(data.Z)
     for k=1:length(data.Z{i})
         j = data.J{i}{k};
@@ -33,9 +33,9 @@ for i=1:length(data.Z)
     end
 end
 
-posePriorNoise  = noiseModel.Diagonal.Sigmas(poseNoiseSigmas);
+posePriorNoise  = noiseModel.Diagonal.Sigmas(poseNoiseSigmas, true);
 graph.add(PriorFactorPose3(symbol('x',1), truth.cameras{1}.pose, posePriorNoise));
-pointPriorNoise  = noiseModel.Isotropic.Sigma(3,pointNoiseSigma);
+pointPriorNoise  = noiseModel.Isotropic.Sigma(3,pointNoiseSigma, true);
 graph.add(PriorFactorPoint3(symbol('p',1), truth.points{1}, pointPriorNoise));
 
 %% Initial estimate
diff --git a/matlab/gtsam_tests/testSerialization.m b/matlab/gtsam_tests/testSerialization.m
index e55822c1c..2f1d116e8 100644
--- a/matlab/gtsam_tests/testSerialization.m
+++ b/matlab/gtsam_tests/testSerialization.m
@@ -45,30 +45,30 @@ graph = NonlinearFactorGraph;
 
 % Prior factor
 priorMean = Pose2(0.0, 0.0, 0.0); % prior at origin
-priorNoise = noiseModel.Diagonal.Sigmas([0.3; 0.3; 0.1]);
+priorNoise = noiseModel.Diagonal.Sigmas([0.3; 0.3; 0.1], true);
 graph.add(PriorFactorPose2(i1, priorMean, priorNoise)); % add directly to graph
 
 % Between Factors
 odometry = Pose2(2.0, 0.0, 0.0);
-odometryNoise = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1]);
+odometryNoise = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1], true);
 graph.add(BetweenFactorPose2(i1, i2, odometry, odometryNoise));
 graph.add(BetweenFactorPose2(i2, i3, odometry, odometryNoise));
  
 % Range Factors
-rNoise = noiseModel.Diagonal.Sigmas([0.2]);
+rNoise = noiseModel.Diagonal.Sigmas([0.2], true);
 graph.add(RangeFactor2D(i1, j1, sqrt(4+4), rNoise));
 graph.add(RangeFactor2D(i2, j1, 2, rNoise));
 graph.add(RangeFactor2D(i3, j2, 2, rNoise));
 
 % Bearing Factors
 degrees = pi/180;
-bNoise = noiseModel.Diagonal.Sigmas([0.1]);
+bNoise = noiseModel.Diagonal.Sigmas([0.1], true);
 graph.add(BearingFactor2D(i1, j1, Rot2(45*degrees), bNoise));
 graph.add(BearingFactor2D(i2, j1, Rot2(90*degrees), bNoise));
 graph.add(BearingFactor2D(i3, j2, Rot2(90*degrees), bNoise));
 
 % BearingRange Factors
-brNoise = noiseModel.Diagonal.Sigmas([0.1; 0.2]);
+brNoise = noiseModel.Diagonal.Sigmas([0.1; 0.2], true);
 graph.add(BearingRangeFactor2D(i1, j1, Rot2(45*degrees), sqrt(4+4), brNoise));
 graph.add(BearingRangeFactor2D(i2, j1, Rot2(90*degrees), 2, brNoise));
 graph.add(BearingRangeFactor2D(i3, j2, Rot2(90*degrees), 2, brNoise));
diff --git a/matlab/gtsam_tests/testStereoVOExample.m b/matlab/gtsam_tests/testStereoVOExample.m
index c721244ba..8edbb1553 100644
--- a/matlab/gtsam_tests/testStereoVOExample.m
+++ b/matlab/gtsam_tests/testStereoVOExample.m
@@ -33,7 +33,7 @@ graph.add(NonlinearEqualityPose3(x1, first_pose));
 %% Create realistic calibration and measurement noise model
 % format: fx fy skew cx cy baseline
 K = Cal3_S2Stereo(1000, 1000, 0, 320, 240, 0.2);
-stereo_model = noiseModel.Diagonal.Sigmas([1.0; 1.0; 1.0]);
+stereo_model = noiseModel.Diagonal.Sigmas([1.0; 1.0; 1.0], true);
 
 %% Add measurements
 % pose 1