Thornton-Bierman-factorization.md

@@ -22,9 +22,9 @@ containing the diagonal coefficients.
 
 ### Initial decomposition
 
-Even that we always work with the factorized covariance, we still read
-the unfactorized initial covariance matrix from the configuration file.
-Therefore, we need to factorize this initial covariance matrix before
+Even though the factorized covariance is used for computation, the unfactorized 
+initial covariance matrix is read from the configuration file.
+Therefore, this initial covariance matrix needs to be factorized before
 beginning to filter. This is done by the `EKF::UDDecomp()` method. This
 factorization is a variant of the Cholewsky decomposition, and the
 implementation is largely inspired from the source of Eigen's `LDLT`
@@ -51,12 +51,12 @@ implementation is very close to the Matlab
 implementation, since it is not possible to use many block operations in
 this case. It is implemented in the `EKF::updateState` method.
 
-Since the algorithm only support single-dimensional updates, we have to
-compute each component of the measurement sequentially. This implies
-that we must recompute the residuals after every component update. Since
-the measurement model is non-linear, we recompute the h function after
+Since the algorithm only supports single-dimensional updates, each component of 
+the measurement has to be computed sequentially. This implies
+that the residuals must be computed after every component update. Since
+the measurement model is non-linear, the h function is reevaluated after
 every iteration, and the results differ significantly from the result of
 the standard Kalman filter algorithm. The difference can be greatly
-reduced by using a linearized version of the of the measurement model.
+reduced by using a linearized version of the measurement model.
 In the absence of ground truth, it is not possible to tell which results
 are closest to reality, and this would require further research.
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