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I'm developing a device for tracking pets in a room with several motion detectors. I use a Kalman filter to estimate the position, which is based on the active outputs of the motion detectors. If an motion detector is active the center of the detection region is the measurement value (position). In some cases the filter estimates the position to be outside the room.

How can I restrict the Kalman filter, should I restart and reinitialise the filter when the estimated position is not in the predefined area (of the room)?

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  • $\begingroup$ i had a similar problem with pedestrian tracking within the FOV of a camera with fixed position. In my case I was using Python and defined a class Pedestrian which would hold state for each pedestrian: if the Kalman prediction was outside the FOV, i destroyed the pedestrian (the same pedestrian would get a new ID if he/she returned in the FOV). $\endgroup$ Aug 26, 2015 at 13:58
  • $\begingroup$ Particle filters are more suitable for this $\endgroup$
    – gsmafra
    Aug 26, 2015 at 19:49
  • $\begingroup$ An e.g. assume we have 3 motion sensors, and the movement is started in the FOV of the first, then continued through the FOV of the second and finishing the movement of in the FOV of the third. So the estimated position of the Kalman filter is the centre of the first sensor, moving towards the centre of the second and finally moving towards the centre of the third sensor. But there is a slight overshooting so the estimated position goes beyond the centre of the third sensor, resulting in 'leaving' the room and then coming back to the centre of the third sensor. $\endgroup$ Aug 28, 2015 at 10:02

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The simplest solution in terms of computational resources as much as simplicity, I guess, is the Unscented Kalman Filter (UKF). There, the clipping might easily be added to the calculation of the sigma-points, in a way that they remain in certain boundary. I recommend that you take a look at this article, for example (working in 2016.04.22, Constrained State Estimation Using the Unscented Kalman Filter, Rambabu Kandepu, Lars Imsland and Bjarne A. Foss)

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