A system for observing a walking activity of a person comprises a device (DISP) adapted for delivering at output, for a footstep of the person, a first difference of angular speeds of the corresponding tibia between the instant at which the heel of the foot is planted and the instant at which the foot is laid flat, a second difference of angular speeds of the corresponding tibia between the instant at which the heel of the foot is planted and the instant at which the last toe of the foot is lifted, and an angular speed of the corresponding tibia at the instant at which the foot is laid flat. The system comprises analysis means (AN) for analyzing the signals delivered by the device and adapted for determining a type of walking of the user as a function of time by using a hidden Markov model with N states corresponding respectively to N types of walking
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A system for observing a walking activity of a person, comprising: a device (DISP) adapted for delivering at output, for a footstep of the person: a first difference of angular speeds of a corresponding tibia between an instant at which a heel of a foot is planted and an instant at which the foot is laid flat, a second difference of angular speeds of the corresponding tibia between the instant at which the heel of the foot is planted and an instant at which a last toe of the foot is lifted, and an angular speed of the corresponding tibia at the instant at which the foot is laid flat; said system further comprising an analysis module communicatively coupled to the device, the analysis module comprising a processor configured to analyze signals delivered by the device and to determine, only from an analysis of these signals, a type of walking of the user as a function of time by using a hidden Markov model with N states corresponding respectively to N types of walking. 2. The system as claimed in claim 1, wherein a probability density p x(x(n)) of correspondence between the signals delivered by the device and a state of the hidden Markov model representing a type of walking is defined by the following first expression: 1 2  π   ∑  ·  - ( x _  ( n ) - μ _ ) T  ∑ - 1  ( x _  ( n ) - μ _ ) 2 in which: x(n) represents a column vector with components the three signals transmitted by the device; μ represents a column vector with three components, representative of the state of the hidden Markov model corresponding to said type of walking; and |Σ| represents an absolute value of a determinant of a diagonal matrix Σ of dimension 3 representative of the state of the hidden Markov model corresponding to said type of walking. 3. The system as claimed in claim 2, wherein the probability density of correspondence between the signals delivered by the device and the state of the hidden Markov model representing the type of walking is defined by a linear combination of said first expressions for probability densities of the set of types of walking, a sum of the coefficients of said linear combination being equal to 1. 4. The system as in claim 3, wherein the analysis module is configured to determine the type of walking of the user from among a set of at least two types of walking comprising walking on a flat surface, walking down a descent, walking up a climb, climbing a staircase, and descending a staircase. 5. The system as claimed in claim 3, wherein probabilities P, of said hidden Markov model, of switching between two states representing respectively one of said types of walking are such that: P(statei,statej)∈[0.5;0.9999], when i is different from j; and P(statei,statej)∈[0;0.5], when i is equal to j. 6. The system as claimed in claim 1, wherein said analysis module is fastened or remote with respect to the device, and the device comprises wired or wireless transmission means for transmitting its measurements to said analysis means. 7. The system as claimed in claim 1, further comprising a display fastened to the device or a remote display. 8. The system as claimed in claim 1, in which said device (DISP) comprises one or more of a magnetometer, an accelerometer, and a gyrometer for delivering its output signals. 9. A method for observing a walking activity of a person, based on, during a footstep, signals representing a first difference of angular speeds of a corresponding tibia between an instant at which a heel of a foot is planted and an instant at which the foot is laid flat, a second difference of angular speeds of the corresponding tibia between the instant at which the heel of the foot is planted and an instant at which a last toe of the foot is lifted, and an angular speed of the corresponding tibia at the instant at which the foot is laid flat, wherein said signals are analysed to determine a type of walking of the user as a function of time by using a hidden Markov model with N states corresponding respectively to N types of walking.