Lowering computational cost of estimating probability density functions

Image of a city

Lowering computational cost of estimating probability density functions

Dec 29 2016

Several approaches have been developed to estimate probability density functions (pdfs). 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 hard to impose the non-negativeness in the sampling space. In a 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, for the same level of approximation error in the filter, the required number of basis functions with the transformation is a lot smaller than the ones without transformation. This would largely benefit the computational cost reduction.

Kim, J and Richardson, R (2016) Negative-free approximation of probability density function for nonlinear projection filter. In: 2016 IEEE 55th Conference on Decision and Control (CDC). 55th IEEE Conference on Decision and Control, 12-14 Dec 2016, Las Vegas, Nevada, United States. IEEE , pp. 3738-3743. ISBN 978-1-5090-1837-6. Read publication.

Perch & Repair icon

Perch & Repair

Perceive & Patch icon

Perceive & Patch

Fire & Forget icon

Fire & Forget

City & Society icon

City & Society

The Latest

Self Repairing Cities Logo

Get Involved

Find out more about the project, get in touch today.