Roos' Matrix Permanent Approximation Bounds for Data Association Probabilities

TL;DR

This paper introduces a simple, error-bounded approximation algorithm for the matrix permanent, which is crucial in data association probability calculations, offering a practical alternative to complex existing methods.

Contribution

It presents a new, straightforward approximation algorithm for the matrix permanent with proven error bounds, tailored for data association in tracking.

Findings

The algorithm provides reliable approximations with known error bounds.

It is simpler and potentially more efficient than existing complex schemes.

Demonstrates practical use in estimating data association probabilities.

Abstract

Matrix permanent plays a key role in data association probability calculations. Exact algorithms (such as Ryser's) scale exponentially with matrix size. Fully polynomial time randomized approximation schemes exist but are quite complex. This letter introduces to the tracking community a simple approximation algorithm with error bounds, recently developed by Bero Roos, and illustrates its potential use for estimating probabilities of data association hypotheses.