A technique for determination of the signal subspace dimension K in direction of arrival estimation and in exponentially damped sinusoids modeling (where K represents respectively the number of detected objects and the model order) by using the ratios between the squared singular values of the processed data matrix and of its sum with an auxiliary matrix composed of random entries from a normal distribution. The disclosed noise addition technique (NAT) is computationally effective and thoroughly tuned for use in each one of the designated tasks, causes very few false alarms, operates accurately within or below the SNR limits attained by others techniques and downwards determines a steadily decreasing to zero dimension K of the signal subspace.