Negative-free approximation of probability density function for nonlinear projection filter

Abstract

Abstract-Several approaches have been developed to estimate probability density function (pdf). The pdf has two important properties: the integration of pdf over whole sampling space is equal to 1 and the value of pdf in the sampling space is greater than or equal to zero. The first constraint can be easily achieved by the normalisation. On the other hand, it is very hard to impose the non-negativeness in the sampling space. In the pdf estimation, some areas in the sampling space might have negative pdf values. It produces unreasonable moment values such as negative probability or variance. A transformation to guarantee the negative-free pdf over a chosen sampling space is presented and it is applied to the nonlinear projection filter. The filter approximates the pdf to solve nonlinear estimation problems. For simplicity, one-dimensional nonlinear system is used as an example to show the derivations and it can be readily generalised for higher dimensional systems. The efficiency of the proposed method is demonstrated by numerical simulations. The simulations also show that to achieve the same level of approximation error in the filter the required number of basis functions with the transformation is a lot smaller compared to the ones without transformation. This will be hugely benefited when the filter is used for high dimensional systems, which requires significantly less computational cost.

Position prediction using disturbance observer for planar pushing

“…For adapting to complex situations, machine vision information could be used with the machine learning algorithms as in [3]. Also, instead of predicting a single trajectory, an ensemble of trajectories distribution described by a probability density function would be predicted using nonlinear estimation algorithms such as the particle filter [11] or the nonlinear projection filter [12]. There is also possibility to plan the robot tip movements better for the identification phase in order to maximise information extraction about various physical properties of object, surface, stochastic characteristics, etc.…”