Simulating Range Bearing Sensor with MATLAB with Gaussian Noise (Generating Gaussian Colored Random Vector)
Few notes:


First you should multiply the noise by the Standard Deviation (Root of the Variance for zero mean noise).
You can do that by multiplying the Lower Cholesky Decomposition of matrix by a column vector of Gaussian noise. Yet since you assume no correlation, you can do that by independent multiplication.


Something like:

vZ = vZ + [sigma_range; sigma_angle] .* randn([2, 1]);