A system for tracking the trajectory (T) of an underwater vehicle moving in a monitoring area , comprising: - at least three separate sensors located in known positions (S1, S2, S3) in said monitoring area and configured to detect, at respective receiving times (t ik ), an acoustic signal transmitted by said underwater vehicle ; and - a processing unit operatively coupled to said sensors and configured to determine said trajectory (T) as a function of said receiving times (t ik ); characterized in that said processing unit is configured to: - implement a hyperbolic iterative algorithm based on differences between said receiving times (t ik ) and on said known positions (S1, S2, S3) of said sensors , to determine an approximate position (P̃ tk ) of said underwater vehicle and make an approximate estimate (t̃ k ) of a transmission time of said acoustic signal by said underwater vehicle ; and - process said approximate position (P̃ tk ) and said approximate estimate (t̃ k ) of a transmission time using a time-varying predictive filter, to estimate said position of said underwater vehicle and derive said trajectory (T); wherein said hyperbolic iterative algorithm receives at its input at least three receiving times (t 1k , t 2k , t 3k ) associated with the at least three separate sensors ; and wherein said hyperbolic iterative algorithm comprises the iterative determination of the approximate position (P̃ tk ) of the underwater vehicle through the use of the following equation: x ̃ y ̃ k , n + 1 = s 2 ⁢ y − s 1 ⁢ y − s 3 ⁢ y − s 1 ⁢ y − s x 2 − s 1 ⁢ x s 3x − s 1 ⁢ x ⋅ s 3 ⁢ x − s 1 ⁢ x s 2 ⁢ y − s 1 ⁢ y − s 2 ⁢ x − s 1 ⁢ x s 3 ⁢ y − s 1 ⁢ y − 1 ⋅ ⋅ 0,5 ⋅ s 3 ⁢ x 2 − s 1 ⁢ x 2 + s 3 ⁢ y 2 − s 1 ⁢ y 2 − m 31 2 − m 31 ⋅ r k , n 0,5 ⋅ s 2 ⁢ x 2 − s 1 ⁢ x 2 + s 2 ⁢ y 2 − s 1 ⁢ y 2 − m 21 2 − m 21 ⋅ r k , n where: m 31 = c ⋅ t 3 ⁢ k − t 1 ⁢ k ; m 21 = c ⋅ t 2 ⁢ k − t 1 ⁢ k r k , n = x ̃ k , n − s 1 ⁢ x 2 + y ̃ k , n − s 1 ⁢ y 2 and where t 1k , t 2k , t 3k are said receiving times; S 1x , S 2x , S 3x and s 1y , S 2y , S 3y are coordinates of said known positions (S1, S2, S3) in a plane (xy) of said trajectory; x̃ tk ,ỹ tk are coordinates of said approximate position (P̃ tk ) in said plane; t k is said transmission time; and c is the speed of sound. - at least three separate sensors located in known positions (S1, S2, S3) in said monitoring area and configured to detect, at respective receiving times (t ik ), an acoustic signal transmitted by said underwater vehicle ; and - a processing unit operatively coupled to said sensors and configured to determine said trajectory (T) as a function of said receiving times (t ik ); - implement a hyperbolic iterative algorithm based on differences between said receiving times (t ik ) and on said known positions (S1, S2, S3) of said sensors , to determine an approximate position (P̃ tk ) of said underwater vehicle and make an approximate estimate (t̃ k ) of a transmission time of said acoustic signal by said underwater vehicle ; and - process said approximate position (P̃ tk ) and said approximate estimate (t̃ k ) of a transmission time using a time-varying predictive filter, to estimate said position of said underwater vehicle and derive said trajectory (T); <EOS>