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where K is the total number of noise eigenvectors. In comparison to the conventional

MUSIC algorithm described above, smoothed MUSIC performs an additional step before it

computes the correlation matrix. It partitions each array h of size w into overlapping sub-

arrays of size w! < w. It then computes the correlation matrices for each of these sub-arrays.

Finally, it combines the different correlation matrices by summing them up before performing

the eigen decomposition. The additional step performed by smoothed MUSIC is intended to

de-correlate signals arriving from spatially different entities. Specifically, by taking different

shifts for the same antenna array, reflections from different bodies get shifted by different

amounts depending on the distance and orientation of the reflector, which helps de-

correlating them .Fig. 4 shows the result of applying smoothed MUSIC on the signal captured

from two moving humans. Similar to Fig. 3(b), the y-axis corresponds to the angle, and the x-

axis corresponds to time. As before, the zero line corresponds to DC. At any point in time, we

see significant energy at two angles (besides the DC). For example, at time n = 0.5s, both

humans have negative angles and, hence, are moving away from Wi-Vi. Between n = 1s and

n = 2s, only one angle is present. This may be because the other human is not moving or

he/she is too far inside the room. Again, from n = 2s to n = 3s, we see both humans, one

moving towards the device and the other moving away (since one has a positive angle while

the other has a negative angle). One point is worth emphasizing: the smoothed MUSIC

algorithm is conceptually similar to the standard antenna array beam forming; both

approaches aim at identifying the spatial angle of the signal. However, by projecting on the

null space and taking the inverse norm, MUSIC achieves sharper peaks, and hence is often

termed a super-resolution technique. Because smoothed MUSIC is similar to antenna array

beamforming, it can be used even to detect a single moving object, i.e., the presence of a

single person. In fact, Fig. 4.1.1 was generated by the smoothed MUSIC algorithm.. Any

human can be only at one location at any point in time. Thus, at any point in time, the larger

the number of humans, the higher the spatial variance. The spatial variance is computed as

follows. First, Wi-Vi computes the spatial centroid as a function of time:

It then computes the spatial variance as:

where K is the total number of noise eigenvectors. In comparison to the conventional

MUSIC algorithm described above, smoothed MUSIC performs an additional step before it

computes the correlation matrix. It partitions each array h of size w into overlapping sub-

arrays of size w! < w. It then computes the correlation matrices for each of these sub-arrays.

Finally, it combines the different correlation matrices by summing them up before performing

the eigen decomposition. The additional step performed by smoothed MUSIC is intended to

de-correlate signals arriving from spatially different entities. Specifically, by taking different

shifts for the same antenna array, reflections from different bodies get shifted by different

amounts depending on the distance and orientation of the reflector, which helps de-

correlating them .Fig. 4 shows the result of applying smoothed MUSIC on the signal captured

from two moving humans. Similar to Fig. 3(b), the y-axis corresponds to the angle, and the x-

axis corresponds to time. As before, the zero line corresponds to DC. At any point in time, we

see significant energy at two angles (besides the DC). For example, at time n = 0.5s, both

humans have negative angles and, hence, are moving away from Wi-Vi. Between n = 1s and

n = 2s, only one angle is present. This may be because the other human is not moving or

he/she is too far inside the room. Again, from n = 2s to n = 3s, we see both humans, one

moving towards the device and the other moving away (since one has a positive angle while

the other has a negative angle). One point is worth emphasizing: the smoothed MUSIC

algorithm is conceptually similar to the standard antenna array beam forming; both

approaches aim at identifying the spatial angle of the signal. However, by projecting on the

null space and taking the inverse norm, MUSIC achieves sharper peaks, and hence is often

termed a super-resolution technique. Because smoothed MUSIC is similar to antenna array

beamforming, it can be used even to detect a single moving object, i.e., the presence of a

single person. In fact, Fig. 4.1.1 was generated by the smoothed MUSIC algorithm.. Any

human can be only at one location at any point in time. Thus, at any point in time, the larger

the number of humans, the higher the spatial variance. The spatial variance is computed as

follows. First, Wi-Vi computes the spatial centroid as a function of time:

It then computes the spatial variance as: