A method for box regularised particle filtering, to predict a state of a system, said system being a land, air, marine or space vehicle which is provided with a navigation system using measurement correlation, the method comprising at least one execution of a sequence which includes the following steps: /1/ a prediction step, comprising predicting subsequent state intervals, each subsequent state interval being obtained by applying at least one propagation rule to one of a plurality of previous state intervals; /2/ a step of measuring a true state of the system; /3/ a step of contracting at least one of the subsequent state intervals, depending on at least one measurement result of the true state which was obtained in step /2/; /4/ a weight updating step, comprising assigning a weight to each subsequent state interval depending on a size of said subsequent state interval as resulting from step /3/, a size of said subsequent state interval as resulting from step /1/ before step /3/, and a weight of the previous state interval from which said subsequent state interval resulted during step /1/; and /5/ a step of redistributing the subsequent state intervals, comprising replacing at least one of the subsequent state intervals i by n i sub-intervals originating from a division of the subsequent state interval i, i being an integer index for numbering the subsequent state intervals and n i being a number of the sub-intervals which replace said subsequent state interval i, each sub-interval being intended to constitute a previous state interval for a subsequent iteration of the sequence of steps /1/ to /5/, the method being characterised in that at least one of steps /1/, /3/ to /5/ comprises at least one calculation of an estimate of the value of X α, where X is a variable number for each execution of said step and α is a non-zero exponent value which is constant between different executions of said step, the number X being positive if the exponent α is not an integer and non-zero if the exponent α is negative, the calculation comprising the following steps: /a/ writing the number X in a form X = ± (1+m).2 ex, where ex is a negative, positive or zero integer, and m is a mantissa comprised between 0 and 1, the value 0 and being permissible, such that a binary representation of the number X is: I = L.(m + ex + B), where L=2 n with n which is a number of bits of a binary writing of the mantissa m, and B is a constant positive or zero number, called bias; /b/ calculating a binary representation of X α in the form: I(X α) = a.I + L.(1 - α).(B - σ), where σ is a constant number whose value is recorded; and /c/ obtaining the estimate of the value of X α from the binary representation I(X α). /1/ a prediction step, comprising predicting subsequent state intervals, each subsequent state interval being obtained by applying at least one propagation rule to one of a plurality of previous state intervals; /2/ a step of measuring a true state of the system; /3/ a step of contracting at least one of the subsequent state intervals, depending on at least one measurement result of the true state which was obtained in step /2/; /4/ a weight updating step, comprising assigning a weight to each subsequent state interval depending on a size of said subsequent state interval as resulting from step /3/, a size of said subsequent state interval as resulting from step /1/ before step /3/, and a weight of the previous state interval from which said subsequent state interval resulted during step /1/; and /5/ a step of redistributing the subsequent state intervals, comprising replacing at least one of the subsequent state intervals i by n i sub-intervals originating from a division of the subsequent state interval i, i being an integer index for numbering the subsequent state intervals and n i being a number of the sub-intervals which replace said subsequent state interval i, each sub-interval being intended to constitute a previous state interval for a subsequent iteration of the sequence of steps /1/ to /5/, /a/ writing the number X in a form X = ± (1+m).2 ex, where ex is a negative, positive or zero integer, and m is a mantissa comprised between 0 and 1, the value 0 and being permissible, such that a binary representation of the number X is: I = L.(m + ex + B), where L=2 n with n which is a number of bits of a binary writing of the mantissa m, and B is a constant positive or zero number, called bias; /b/ calculating a binary representation of X α in the form: I(X α) = a.I + L.(1 - α).(B - σ), where σ is a constant number whose value is recorded; and /c/ obtaining the estimate of the value of X α from the binary representation I(X α).