A method for determining both right and left SL during level walking using a single IMU to be used either indoor or outdoor, without space limitations and for prolonged periods of time, was presented and validated.

SL estimates were obtained directly from the IMU displacement between two consecutive HS, by employing an original method (the KOSE method) which double integrates the IMU acceleration along the DoP obtained after applying a Kalman filter. The KOSE method includes an adaptation to gait of an optimal integration technique originally proposed by Zok and colleagues [19] to reduce the errors caused by the drift affecting the dynamometric signals.

The method was tested on healthy subjects while they were walking increasing and decreasing their speed, five times along 30 m. The algorithm for the identification of left and right HS never failed in all the subjects analyzed. Both right and left HS were detected with an average time delay corresponding to 1.7 samples and 2.7 samples, respectively (sample frequency 100 frames/s). These errors implied that the right step duration was on average two samples shorter than the left one. Despite the shorter estimated step duration, the *rSL* resulted, over the different subjects, overestimated by 1.2%. The maximum mean error in estimating the SL was overestimated by 2.9% for the *rSL* and underestimated by 2.6% for the *lSL*. The main explanation for the side to side differences, is probably that the effect of the pelvic rotation, associated to the asymmetrical IMU positioning, was not completely compensated for by the correction term *d* sin(*θ*_{
j
} ). In fact, in this regard, several assumptions were not completely satisfied: being attached to the belt of the subject, the IMU was not rigidly moving with the pelvis and *d*, which is taken as the inter-ASIS distance may differ from the distance between the LF origin to the pelvis vertical axis of rotation. As expected, the maximum percent error on the total traversed distance was to 1.7% and therefore smaller than the maximum SL percent error. It is worth noticing that the estimate of the traversed distance was never consistently either an overestimate or an underestimate (average over subjects equal to 0.1%).

Several methods to estimate *rSL* and *lSL*, using a single IMU, have been proposed in the literature [16–18, 24]. A common feature of these methods is that the SL estimates were derived using indirect methodologies, either based on inverted pendulum models for level human walking representation [25, 26] or based on general regressive equation in which SL is expressed as function of the step frequency and accelerometric signal variations. Unfortunately, no data on the accuracy of the *rSL* and *lSL* estimates were provided in abovementioned studies. Therefore, a straightforward comparison among methods is not possible. However, Zijlstra and Hof (2003) [16] reported a consistent SL underestimation. As a consequence, also the mean speed (mean SL divided mean step time) was underestimated and to correct it, they introduced a coefficient of 1.25 heuristically determined. It could then be inferred that the SL estimations were affected by errors of about 20-30%. In Gonzales and colleagues (2007) [17], the performance of their method was evaluated by assessing the errors of the distance traversed in each acquisition. Across subjects, errors ranged from -6.5% to +6.0%. Shin and Park [18] tested their method on a single subject walking at a constant speed for a 70 m straight trajectory. Three data set were recorded (slow, normal and fast). Across trials, errors for the traversed distance varied between 1% to 3% with an accuracy error of 3.7% in the worst case.

In our study the errors in estimating the traversed distance ranged from -1.6% to +1.7% across subjects.

The smaller estimation errors compared to previously publish methods, confirm our initial hypothesis that the KOSE method improves the accuracy with respect to indirect methods based on the use of general models, which may not always take into account subject specificity in gait.

In this study, the IMU was attached to the subject's belt on the right side. This location was chosen to reduce subject discomfort and because it is a practical solution for monitoring daily life motor activities. However, it can be hypothesized that attaching the IMU centrally in the back (S2 or L3 vertebral level) similarly to Zijlstra and Hof (2003) [16], Gonzales and colleagues (2007) [17] and Shin and Park [18], the residual errors related to the pelvic rotation correction would be reduced and it would not be necessary to correct for the pelvic rotation effects.

In this study we presented results relative to gait event timings and SL estimations. Additional gait parameters can be easily calculated from the estimated parameters. Therefore, using a single IMU, we were able to provide excellent estimates of both temporal and spatial gait parameters bilaterally.

It is important to stress that the KOSE method was tested on experimental conditions fairly similar to those which can be encountered in the real life: different gait speeds (three gait speed levels), numerous velocity transients (five velocity transients on 30 m). It is reasonable to expect that, in healthy subjects, errors in traversed distance estimation during daily monitoring activity would be of the same order of magnitude of those presented.

The data set, derived from the experiments carried out in the present study, referred to a straight level walking. For this specific method validation, the GF was therefore defined, at the beginning of each acquisition with the *Y*_{
G
} axis coinciding with the DoP. The IMU acceleration component along the DoP, was then calculated by projecting the accelerometric signal, after having removed the gravitational contribution, on the GF. In general, if during the acquisition, the subject varies the DoP more than once, it would be necessary to define for every different DoP, an auxiliary GF with the *Y*_{
G
} axis aligned to the relevant DoP. However, the solution of the latter issue is out of the scope of the present study.

There are some limitations to the current proof of concept which need to be addressed before using the presented methodology to estimate gait spatial and temporal parameters in clinical contexts. One issue is related to the algorithm used to identify the gait events, which is normally based on IMU signal features. Such features may change or even disappear in pathologic subjects. Another issue is related to the assumption that the pelvis displacement along the DoP between HS equals the SL. It is certainly true in a symmetric gait, but in some gait disorders the pelvis displacement may not be in phase with the feet displacement as much as in healthy subjects. Future studies need to be performed to test the method performance on pathological gait [27].

In conclusion, the method proposed allows for an accurate estimate of right and left step length using a minimal invasive experimental set up through an optimal integration procedure of the accelerometric signals.