A method for box regularised particle filtering, to predict a state of a system by a set of state intervals with weights associated with said state intervals, so as to form a probability distribution that characterises the state of the system, said system being a land, air, marine or space vehicle which is provided with a navigation system using measurement correlation, the method comprising repeatedly applying a sequence of steps to the set of state intervals with the associated weights to update the state intervals and said associated weights, the sequence of steps comprising a step called smoothing step, which consists in changing at least one of the state intervals by applying random changes to a set of interval boundaries, or central values and interval lengths, which determine the state interval according to state coordinates of the system, characterised in that the random changes relating to each state interval to be changed, which is identified by an integer index i, are determined by performing the following steps: - generating a first random value, noted β i and comprised between 0 and 1, the values 0 and 1 being allowed, according to a statistical distribution beta law of first parameter equal to d and of second parameter equal to 2, where d is a number of the system state coordinates; - generating 2·d second random values, noted v k,i, each according to a normal statistical distribution law with zero mean value and standard deviation equal to the unit, where k is another integer index which varies from 1 to 2·d and marks the interval boundaries, or central values and interval lengths, for each state interval; - calculating a first number, noted ξ i, according to the first formula: ξ i = [Σ k=1 à 2 · d (ν k,i) 2] 1/2; - calculating a second number, noted α i, according to the second formula: α i = β i 1/2 /ξ i; and - calculating 2·d third numbers, noted ε k,i, according to the third formula: ε k,i = ν k,i ·α i, and in that the random changes which are applied to the state interval i are one-to-one proportional to the third numbers ε k,i, with a proportionality coefficient which is non-zero and common to said random changes. the method comprising repeatedly applying a sequence of steps to the set of state intervals with the associated weights to update the state intervals and said associated weights, the sequence of steps comprising a step called smoothing step, which consists in changing at least one of the state intervals by applying random changes to a set of interval boundaries, or central values and interval lengths, which determine the state interval according to state coordinates of the system, characterised in that the random changes relating to each state interval to be changed, which is identified by an integer index i, are determined by performing the following steps: - generating a first random value, noted β i and comprised between 0 and 1, the values 0 and 1 being allowed, according to a statistical distribution beta law of first parameter equal to d and of second parameter equal to 2, where d is a number of the system state coordinates; - generating 2·d second random values, noted v k,i, each according to a normal statistical distribution law with zero mean value and standard deviation equal to the unit, where k is another integer index which varies from 1 to 2·d and marks the interval boundaries, or central values and interval lengths, for each state interval; - calculating a first number, noted ξ i, according to the first formula: ξ i = [Σ k=1 à 2 · d (ν k,i) 2] 1/2; - calculating a second number, noted α i, according to the second formula: α i = β i 1/2 /ξ i; and - calculating 2·d third numbers, noted ε k,i, according to the third formula: ε k,i = ν k,i ·α i, and in that the random changes which are applied to the state interval i are one-to-one proportional to the third numbers ε k,i, with a proportionality coefficient which is non-zero and common to said random changes. - generating a first random value, noted β i and comprised between 0 and 1, the values 0 and 1 being allowed, according to a statistical distribution beta law of first parameter equal to d and of second parameter equal to 2, where d is a number of the system state coordinates; - generating 2·d second random values, noted v k,i, each according to a normal statistical distribution law with zero mean value and standard deviation equal to the unit, where k is another integer index which varies from 1 to 2·d and marks the interval boundaries, or central values and interval lengths, for each state interval; - calculating a first number, noted ξ i, according to the first formula: ξ i = [Σ k=1 à 2 · d (ν k,i) 2] 1/2; - calculating a second number, noted α i, according to the second formula: α i = β i 1/2 /ξ i; and - calculating 2·d third numbers, noted ε k,i, according to the third formula: ε k,i = ν k,i ·α i, and in that the random changes which are applied to the state interval i are one-to-one proportional to the third numbers ε k,i, with a proportionality coefficient which is non-zero and common to said random changes.