Hi guys, I approximately measure 3D acceleration of the center of mass of an athlete by means of a triaxial inertial measurement unit placed on the sacrum during a 100m sprint running. Accelerations are then expressed with respect to an earth-fixed global reference frame (vertical axis is defined by gravity). I have a problem: during the flight phase, the skin has a wobbling movement and it accelerates the accelerometer in the space. Thus, I have accelerometric data which do not “respect” the gravitational field: the two horizontal accelerations are not zero!!! And because of the inertia of the sismic mass of the accelerometer, the vertical acceleration only oscillates around -g (-9.81 m/s^2) but it is not exactly -g. Assuming I can identify on the accelerometric signal when the flight phases occur, and since during the fligth phase the motion of the center of mass is well known (ballistic motion), I would like to run a kalman filter to recursively adjust the accelerations in the way to obtain zero and -g for the horizontal and vertical accelerations respectively by imposing during the fligth phases the equation of the ballistic motion. I use matlab for calculations but I’ve never implemented a kalman filter in my life. Can anyone of you help me in defying the problem in terms of kalman filtering? I will be very grateful to you for you precious help. Cheers, Pietro
a kalman filter to correct 3D accelerometer data during running
Started by ●March 28, 2008
Reply by ●March 29, 20082008-03-29
On Fri, 28 Mar 2008 14:42:33 -0500, "Pietro" <pietro.picerno@tiscali.it> wrote:>Hi guys, >I approximately measure 3D acceleration of the center of mass of an >athlete by means of a triaxial inertial measurement unit placed on the >sacrum during a 100m sprint running. Accelerations are then expressed with >respect to an earth-fixed global reference frame (vertical axis is defined >by gravity). I have a problem: during the flight phase, the skin has a >wobbling movement and it accelerates the accelerometer in the space. Thus, >I have accelerometric data which do not “respect�? the gravitational >field: the two horizontal accelerations are not zero!!! And because of the >inertia of the sismic mass of the accelerometer, the vertical acceleration >only oscillates around -g (-9.81 m/s^2) but it is not exactly -g. Assuming >I can identify on the accelerometric signal when the flight phases occur, >and since during the fligth phase the motion of the center of mass is well >known (ballistic motion), I would like to run a kalman filter to >recursively adjust the accelerations in the way to obtain zero and -g for >the horizontal and vertical accelerations respectively by imposing during >the fligth phases the equation of the ballistic motion. I use matlab for >calculations but I’ve never implemented a kalman filter in my life. Can >anyone of you help me in defying the problem in terms of kalman >filtering?I can't help with your filtering problem, but I have a question. If by "flight phase" you mean when no part of the athlete is touching the ground, isn't the entire system in free fall then (vertically), and wouldn't you read zero acceleration on the vertical axis, rather than -g? And would the axis of the direction of running show deceleration due to air resistance, rather than zero? Sorry if these questions miss the point. -- John
Reply by ●March 29, 20082008-03-29
On Fri, 28 Mar 2008 22:32:57 -0500, John O'Flaherty wrote:> On Fri, 28 Mar 2008 14:42:33 -0500, "Pietro" <pietro.picerno@tiscali.it> > wrote: > >>Hi guys, >>I approximately measure 3D acceleration of the center of mass of an >>athlete by means of a triaxial inertial measurement unit placed on the >>sacrum during a 100m sprint running. Accelerations are then expressed >>with respect to an earth-fixed global reference frame (vertical axis is >>defined by gravity). I have a problem: during the flight phase, the skin >>has a wobbling movement and it accelerates the accelerometer in the >>space. Thus, I have accelerometric data which do not “respect�the>>gravitational field: the two horizontal accelerations are not zero!!! >>And because of the inertia of the sismic mass of the accelerometer, the >>vertical acceleration only oscillates around -g (-9.81 m/s^2) but it is >>not exactly -g. Assuming I can identify on the accelerometric signal >>when the flight phases occur, and since during the fligth phase the >>motion of the center of mass is well known (ballistic motion), I would >>like to run a kalman filter to recursively adjust the accelerations in >>the way to obtain zero and -g for the horizontal and vertical >>accelerations respectively by imposing during the fligth phases the >>equation of the ballistic motion. I use matlab for calculations but >>I’ve never implemented a kalman filter in my life. Can anyone of you >>help me in defying the problem in terms of kalman filtering? > > I can't help with your filtering problem, but I have a question. If by > "flight phase" you mean when no part of the athlete is touching the > ground, isn't the entire system in free fall then (vertically), and > wouldn't you read zero acceleration on the vertical axis, rather than > -g? And would the axis of the direction of running show deceleration due > to air resistance, rather than zero? Sorry if these questions miss the > point.The athlete-and-accelerometer system as a whole will be (approximately) in free fall. The accelerometer itself will get yanked around. -- Tim Wescott Control systems and communications consulting http://www.wescottdesign.com Need to learn how to apply control theory in your embedded system? "Applied Control Theory for Embedded Systems" by Tim Wescott Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
Reply by ●March 29, 20082008-03-29
On Fri, 28 Mar 2008 14:42:33 -0500, Pietro wrote:> Hi guys, > I approximately measure 3D acceleration of the center of mass of an > athlete by means of a triaxial inertial measurement unit placed on the > sacrum during a 100m sprint running. Accelerations are then expressed > with respect to an earth-fixed global reference frame (vertical axis is > defined by gravity). I have a problem: during the flight phase, the skin > has a wobbling movement and it accelerates the accelerometer in the > space. Thus, I have accelerometric data which do not “respect” the > gravitational field: the two horizontal accelerations are not zero!!! > And because of the inertia of the sismic mass of the accelerometer, the > vertical acceleration only oscillates around -g (-9.81 m/s^2) but it is > not exactly -g. Assuming I can identify on the accelerometric signal > when the flight phases occur, and since during the fligth phase the > motion of the center of mass is well known (ballistic motion), I would > like to run a kalman filter to recursively adjust the accelerations in > the way to obtain zero and -g for the horizontal and vertical > accelerations respectively by imposing during the fligth phases the > equation of the ballistic motion. I use matlab for calculations but I’ve > never implemented a kalman filter in my life. Can anyone of you help me > in defying the problem in terms of kalman filtering? > I will be very grateful to you for you precious help. Cheers, > PietroSo, how often do you walk up to folk and say "stand still while I tape an accelerometer to your butt"? While a Kalman filter may be the right choice given enough input data, I'm not sure that you have enough -- and since you haven't said what you're actually doing I can't tell. If you're just trying to figure out when a runner is in the air vs. when they're on the ground, low-pass filtering may be enough. I'd like to suggest a notch filter, but I'm willing to bet that skin doesn't make a very linear spring. Double-integrating the data with leaky integrators and displaying the resultant track may prove to be very informative. Using a 6-axis IMU could well make the difference between totally useless and very useful data, even if your gyro channels aren't that good -- at the least you'll be able to distinguish between tipping and lateral acceleration. -- Tim Wescott Control systems and communications consulting http://www.wescottdesign.com Need to learn how to apply control theory in your embedded system? "Applied Control Theory for Embedded Systems" by Tim Wescott Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
Reply by ●March 29, 20082008-03-29
On Sat, 29 Mar 2008 01:51:37 -0500, Tim Wescott <tim@seemywebsite.com> wrote:>On Fri, 28 Mar 2008 22:32:57 -0500, John O'Flaherty wrote: > >> On Fri, 28 Mar 2008 14:42:33 -0500, "Pietro" <pietro.picerno@tiscali.it> >> wrote: >> >>>Hi guys, >>>I approximately measure 3D acceleration of the center of mass of an >>>athlete by means of a triaxial inertial measurement unit placed on the >>>sacrum during a 100m sprint running. Accelerations are then expressed >>>with respect to an earth-fixed global reference frame (vertical axis is >>>defined by gravity). I have a problem: during the flight phase, the skin >>>has a wobbling movement and it accelerates the accelerometer in the >>>space. Thus, I have accelerometric data which do not �??respect�?? >the >>>gravitational field: the two horizontal accelerations are not zero!!! >>>And because of the inertia of the sismic mass of the accelerometer, the >>>vertical acceleration only oscillates around -g (-9.81 m/s^2) but it is >>>not exactly -g. Assuming I can identify on the accelerometric signal >>>when the flight phases occur, and since during the fligth phase the >>>motion of the center of mass is well known (ballistic motion), I would >>>like to run a kalman filter to recursively adjust the accelerations in >>>the way to obtain zero and -g for the horizontal and vertical >>>accelerations respectively by imposing during the fligth phases the >>>equation of the ballistic motion. I use matlab for calculations but >>>I�??ve never implemented a kalman filter in my life. Can anyone of you >>>help me in defying the problem in terms of kalman filtering? >> >> I can't help with your filtering problem, but I have a question. If by >> "flight phase" you mean when no part of the athlete is touching the >> ground, isn't the entire system in free fall then (vertically), and >> wouldn't you read zero acceleration on the vertical axis, rather than >> -g? And would the axis of the direction of running show deceleration due >> to air resistance, rather than zero? Sorry if these questions miss the >> point. > >The athlete-and-accelerometer system as a whole will be (approximately) >in free fall. The accelerometer itself will get yanked around.Nevetheless, the vertical axis will on average sense zero, and not -g during "flight phase", right? And since sprinters get to a considerable forward speed, the air drag will make the forward acceleration negative, proportional to forward speed, and variable with the angles of the parts of the body. -- John
Reply by ●March 29, 20082008-03-29
On Mar 29, 7:33 am, John O'Flaherty <quias...@yeeha.com> wrote:> On Sat, 29 Mar 2008 01:51:37 -0500, Tim Wescott <t...@seemywebsite.com> > wrote: > > > > >On Fri, 28 Mar 2008 22:32:57 -0500, John O'Flaherty wrote: > > >> On Fri, 28 Mar 2008 14:42:33 -0500, "Pietro" <pietro.pice...@tiscali.it> > >> wrote: > > >>>Hi guys, > >>>I approximately measure 3D acceleration of the center of mass of an > >>>athlete by means of a triaxial inertial measurement unit placed on the > >>>sacrum during a 100m sprint running. Accelerations are then expressed > >>>with respect to an earth-fixed global reference frame (vertical axis is > >>>defined by gravity). I have a problem: during the flight phase, the skin > >>>has a wobbling movement and it accelerates the accelerometer in the > >>>space. Thus, I have accelerometric data which do not �??respect�?? > >the > >>>gravitational field: the two horizontal accelerations are not zero!!! > >>>And because of the inertia of the sismic mass of the accelerometer, the > >>>vertical acceleration only oscillates around -g (-9.81 m/s^2) but it is > >>>not exactly -g. Assuming I can identify on the accelerometric signal > >>>when the flight phases occur, and since during the fligth phase the > >>>motion of the center of mass is well known (ballistic motion), I would > >>>like to run a kalman filter to recursively adjust the accelerations in > >>>the way to obtain zero and -g for the horizontal and vertical > >>>accelerations respectively by imposing during the fligth phases the > >>>equation of the ballistic motion. I use matlab for calculations but > >>>I�??ve never implemented a kalman filter in my life. Can anyone of you > >>>help me in defying the problem in terms of kalman filtering? > > >> I can't help with your filtering problem, but I have a question. If by > >> "flight phase" you mean when no part of the athlete is touching the > >> ground, isn't the entire system in free fall then (vertically), and > >> wouldn't you read zero acceleration on the vertical axis, rather than > >> -g? And would the axis of the direction of running show deceleration due > >> to air resistance, rather than zero? Sorry if these questions miss the > >> point. > > >The athlete-and-accelerometer system as a whole will be (approximately) > >in free fall. The accelerometer itself will get yanked around. > > Nevetheless, the vertical axis will on average sense zero, > and not -g during "flight phase", right?One has to differentiate between resting C.G. and dynamic C.G. Since the body has several degrees of freedom, these points can move relative to one another (e.g. in a pike position, the actual dynamic C.G. will move upwards relative to a fixed point marked on the body at the standing C.G. location. That is how divers and cats can shift their center of rotation, relative to their torso, in mid-air.) In a runners flight phase, the dynamic C.G. is in parabolic free fall, but any fixed point on the body can temporarily not be accelerating downwards, or possibly even be accelerating upwards if the limbs are driven downwards with enough force. IMHO. YMMV.
Reply by ●March 29, 20082008-03-29
On Sat, 29 Mar 2008 09:45:00 -0700 (PDT), "Ron N." <rhnlogic@yahoo.com> wrote:>On Mar 29, 7:33 am, John O'Flaherty <quias...@yeeha.com> wrote: >> On Sat, 29 Mar 2008 01:51:37 -0500, Tim Wescott <t...@seemywebsite.com> >> wrote: >> >> >> >> >On Fri, 28 Mar 2008 22:32:57 -0500, John O'Flaherty wrote: >> >> >> On Fri, 28 Mar 2008 14:42:33 -0500, "Pietro" <pietro.pice...@tiscali.it> >> >> wrote: >> >> >>>Hi guys, >> >>>I approximately measure 3D acceleration of the center of mass of an >> >>>athlete by means of a triaxial inertial measurement unit placed on the >> >>>sacrum during a 100m sprint running. Accelerations are then expressed >> >>>with respect to an earth-fixed global reference frame (vertical axis is >> >>>defined by gravity). I have a problem: during the flight phase, the skin >> >>>has a wobbling movement and it accelerates the accelerometer in the >> >>>space. Thus, I have accelerometric data which do not �??respect�?? >> >the >> >>>gravitational field: the two horizontal accelerations are not zero!!! >> >>>And because of the inertia of the sismic mass of the accelerometer, the >> >>>vertical acceleration only oscillates around -g (-9.81 m/s^2) but it is >> >>>not exactly -g. Assuming I can identify on the accelerometric signal >> >>>when the flight phases occur, and since during the fligth phase the >> >>>motion of the center of mass is well known (ballistic motion), I would >> >>>like to run a kalman filter to recursively adjust the accelerations in >> >>>the way to obtain zero and -g for the horizontal and vertical >> >>>accelerations respectively by imposing during the fligth phases the >> >>>equation of the ballistic motion. I use matlab for calculations but >> >>>I�??ve never implemented a kalman filter in my life. Can anyone of you >> >>>help me in defying the problem in terms of kalman filtering? >> >> >> I can't help with your filtering problem, but I have a question. If by >> >> "flight phase" you mean when no part of the athlete is touching the >> >> ground, isn't the entire system in free fall then (vertically), and >> >> wouldn't you read zero acceleration on the vertical axis, rather than >> >> -g? And would the axis of the direction of running show deceleration due >> >> to air resistance, rather than zero? Sorry if these questions miss the >> >> point. >> >> >The athlete-and-accelerometer system as a whole will be (approximately) >> >in free fall. The accelerometer itself will get yanked around. >> >> Nevetheless, the vertical axis will on average sense zero, >> and not -g during "flight phase", right? > >One has to differentiate between resting C.G. and dynamic >C.G. Since the body has several degrees of freedom, these >points can move relative to one another (e.g. in a pike >position, the actual dynamic C.G. will move upwards relative >to a fixed point marked on the body at the standing C.G. >location. That is how divers and cats can shift their center >of rotation, relative to their torso, in mid-air.) > >In a runners flight phase, the dynamic C.G. is in parabolic >free fall, but any fixed point on the body can temporarily >not be accelerating downwards, or possibly even be accelerating >upwards if the limbs are driven downwards with enough force.So you couldn't even get a zero for vertical during this phase, much less a -g point, since the point of attachment of the accelerometer could be doing most anything. Would the cumulative vertical acceleration over an entire gait period (terminology?) have to be -g, since any decrease in sensed gravity during free-fall would be compensated by an increase over -g during the deceleration of the body while landing? Would all the up-downs of the shaking accelerometer have to balance out if the runner is running on the level? -- John
Reply by ●March 30, 20082008-03-30
On Sat, 29 Mar 2008 13:02:10 -0500, John O'Flaherty wrote:> On Sat, 29 Mar 2008 09:45:00 -0700 (PDT), "Ron N." <rhnlogic@yahoo.com> > wrote: > >>On Mar 29, 7:33 am, John O'Flaherty <quias...@yeeha.com> wrote: >>> On Sat, 29 Mar 2008 01:51:37 -0500, Tim Wescott >>> <t...@seemywebsite.com> wrote: >>> >>> >>> >>> >On Fri, 28 Mar 2008 22:32:57 -0500, John O'Flaherty wrote: >>> >>> >> On Fri, 28 Mar 2008 14:42:33 -0500, "Pietro" >>> >> <pietro.pice...@tiscali.it> wrote: >>> >>> >>>Hi guys, >>> >>>I approximately measure 3D acceleration of the center of mass of an >>> >>>athlete by means of a triaxial inertial measurement unit placed on >>> >>>the sacrum during a 100m sprint running. Accelerations are then >>> >>>expressed with respect to an earth-fixed global reference frame >>> >>>(vertical axis is defined by gravity). I have a problem: during the >>> >>>flight phase, the skin has a wobbling movement and it accelerates >>> >>>the accelerometer in the space. Thus, I have accelerometric data >>> >>>which do not â??respectâ?? >>> >the >>> >>>gravitational field: the two horizontal accelerations are not >>> >>>zero!!! And because of the inertia of the sismic mass of the >>> >>>accelerometer, the vertical acceleration only oscillates around -g >>> >>>(-9.81 m/s^2) but it is not exactly -g. Assuming I can identify on >>> >>>the accelerometric signal when the flight phases occur, and since >>> >>>during the fligth phase the motion of the center of mass is well >>> >>>known (ballistic motion), I would like to run a kalman filter to >>> >>>recursively adjust the accelerations in the way to obtain zero and >>> >>>-g for the horizontal and vertical accelerations respectively by >>> >>>imposing during the fligth phases the equation of the ballistic >>> >>>motion. I use matlab for calculations but Iâ??ve never implemented >>> >>>a kalman filter in my life. Can anyone of you help me in defying >>> >>>the problem in terms of kalman filtering? >>> >>> >> I can't help with your filtering problem, but I have a question. If >>> >> by "flight phase" you mean when no part of the athlete is touching >>> >> the ground, isn't the entire system in free fall then (vertically), >>> >> and wouldn't you read zero acceleration on the vertical axis, >>> >> rather than -g? And would the axis of the direction of running show >>> >> deceleration due to air resistance, rather than zero? Sorry if >>> >> these questions miss the point. >>> >>> >The athlete-and-accelerometer system as a whole will be >>> >(approximately) in free fall. The accelerometer itself will get >>> >yanked around. >>> >>> Nevetheless, the vertical axis will on average sense zero, and not -g >>> during "flight phase", right? >> >>One has to differentiate between resting C.G. and dynamic C.G. Since >>the body has several degrees of freedom, these points can move relative >>to one another (e.g. in a pike position, the actual dynamic C.G. will >>move upwards relative to a fixed point marked on the body at the >>standing C.G. location. That is how divers and cats can shift their >>center of rotation, relative to their torso, in mid-air.) >> >>In a runners flight phase, the dynamic C.G. is in parabolic free fall, >>but any fixed point on the body can temporarily not be accelerating >>downwards, or possibly even be accelerating upwards if the limbs are >>driven downwards with enough force. > > So you couldn't even get a zero for vertical during this phase, much > less a -g point, since the point of attachment of the accelerometer > could be doing most anything. Would the cumulative vertical acceleration > over an entire gait period (terminology?) have to be -g, since any > decrease in sensed gravity during free-fall would be compensated by an > increase over -g during the deceleration of the body while landing? > Would all the up-downs of the shaking accelerometer have to balance out > if the runner is running on the level?If you could keep the accelerometer vertical, yes. Keeping track of which direction is "down" when you don't have gyros will be a challenge, though. -- Tim Wescott Control systems and communications consulting http://www.wescottdesign.com Need to learn how to apply control theory in your embedded system? "Applied Control Theory for Embedded Systems" by Tim Wescott Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
Reply by ●March 31, 20082008-03-31
>On Fri, 28 Mar 2008 14:42:33 -0500, "Pietro" ><pietro.picerno@tiscali.it> wrote: > >>Hi guys, >>I approximately measure 3D acceleration of the center of mass of an >>athlete by means of a triaxial inertial measurement unit placed on the >>sacrum during a 100m sprint running. Accelerations are then expressedwith>>respect to an earth-fixed global reference frame (vertical axis isdefined>>by gravity). I have a problem: during the flight phase, the skin has a >>wobbling movement and it accelerates the accelerometer in the space.Thus,>>I have accelerometric data which do not “respect‿ the gravitational >>field: the two horizontal accelerations are not zero!!! And because ofthe>>inertia of the sismic mass of the accelerometer, the verticalacceleration>>only oscillates around -g (-9.81 m/s^2) but it is not exactly -g.Assuming>>I can identify on the accelerometric signal when the flight phasesoccur,>>and since during the fligth phase the motion of the center of mass iswell>>known (ballistic motion), I would like to run a kalman filter to >>recursively adjust the accelerations in the way to obtain zero and -gfor>>the horizontal and vertical accelerations respectively by imposingduring>>the fligth phases the equation of the ballistic motion. I use matlabfor>>calculations but I’ve never implemented a kalman filter in my life.Can>>anyone of you help me in defying the problem in terms of kalman >>filtering? > >I can't help with your filtering problem, but I have a question. If by >"flight phase" you mean when no part of the athlete is touching the >ground, isn't the entire system in free fall then (vertically), and >wouldn't you read zero acceleration on the vertical axis, rather than >-g? And would the axis of the direction of running show deceleration >due to air resistance, rather than zero? Sorry if these questions miss >the point. >-- >John >Hi Jhon, thanks for replying. In an inertial reference frame, an arbitrarly tilted triaxial accelerometer in "free-fall" (flight phase in this case) measures indeed zero along the vertical axis of the inertial frame (gravity). In my case is -g just because I've intentionally subtracted gravity during quite standing of the subject to observe only accelerations due to external forces. Cheers, Pietro
Reply by ●March 31, 20082008-03-31
>On Fri, 28 Mar 2008 14:42:33 -0500, Pietro wrote: > >> Hi guys, >> I approximately measure 3D acceleration of the center of mass of an >> athlete by means of a triaxial inertial measurement unit placed on the >> sacrum during a 100m sprint running. Accelerations are then expressed >> with respect to an earth-fixed global reference frame (vertical axisis>> defined by gravity). I have a problem: during the flight phase, theskin>> has a wobbling movement and it accelerates the accelerometer in the >> space. Thus, I have accelerometric data which do not “respect” the >> gravitational field: the two horizontal accelerations are not zero!!! >> And because of the inertia of the sismic mass of the accelerometer,the>> vertical acceleration only oscillates around -g (-9.81 m/s^2) but itis>> not exactly -g. Assuming I can identify on the accelerometric signal >> when the flight phases occur, and since during the fligth phase the >> motion of the center of mass is well known (ballistic motion), I would >> like to run a kalman filter to recursively adjust the accelerations in >> the way to obtain zero and -g for the horizontal and vertical >> accelerations respectively by imposing during the fligth phases the >> equation of the ballistic motion. I use matlab for calculations butI’ve>> never implemented a kalman filter in my life. Can anyone of you helpme>> in defying the problem in terms of kalman filtering? >> I will be very grateful to you for you precious help. Cheers, >> Pietro > >So, how often do you walk up to folk and say "stand still while I tape an>accelerometer to your butt"? > >While a Kalman filter may be the right choice given enough input data, >I'm not sure that you have enough -- and since you haven't said what >you're actually doing I can't tell. > >If you're just trying to figure out when a runner is in the air vs. when>they're on the ground, low-pass filtering may be enough. I'd like to >suggest a notch filter, but I'm willing to bet that skin doesn't make a >very linear spring. > >Double-integrating the data with leaky integrators and displaying the >resultant track may prove to be very informative. > >Using a 6-axis IMU could well make the difference between totally useless>and very useful data, even if your gyro channels aren't that good -- at >the least you'll be able to distinguish between tipping and lateral >acceleration. > >-- >Tim Wescott >Control systems and communications consulting >http://www.wescottdesign.com > >Need to learn how to apply control theory in your embedded system? >"Applied Control Theory for Embedded Systems" by Tim Wescott >Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html >Hi T&im, thanks for replying. About: ">While a Kalman filter may be the right choice given enough input data,>I'm not sure that you have enough -- and since you haven't said what >you're actually doing I can't tell."I have a 3D accelerometer fixed on the sacrum of an athlete while running. I just want to get at least velocity from these data (beacuse a double integration is too much for a MEMS sensor). The problem is that during the fligth phases, because of skin artifact, the accelerometer is not axactly in free-fall but measures some accelerations which should not measure. Because of this, the first numerical integration of the signal is not the velocity of a point accelerated only by gravity and errors accumulate during time. So I used some switches on the feet synchronized with the accelerometer to check when the stance phases occur. So I can identify on the accelerometer's signal where the fligth phases are. What I would do is to use these informations to correct accelerometer signal in order to force it to respect the laws of ballistic motion during fligth phases. To do this, I would like to use a kalman filter. Cheers, Pietro