# A linear programming approach to the tracking of partials

## TL;DR

This paper introduces a linear programming method for tracking sinusoidal chirps that outperforms classical algorithms in noisy conditions and has lower complexity than existing approaches.

## Contribution

It presents a novel LP formulation for sinusoidal partial tracking that improves efficiency and accuracy over traditional greedy and Viterbi-based methods.

## Key findings

- LP approach outperforms classical algorithm in noisy environments
- Complexity of LP method is less than previous approaches
- LP method effectively tracks sinusoidal chirps in high noise levels

## Abstract

A new approach to the tracking of sinusoidal chirps using linear programming is proposed. It is demonstrated that the classical algorithm of McAulay and Quatieri is greedy and exhibits exponential complexity for long searches, while approaches based on the Viterbi algorithm exhibit factorial complexity. A linear programming (LP) formulation to find the best $L$ paths in a lattice is described and its complexity is shown to be less than previous approaches. Finally it is demonstrated that the new LP formulation outperforms the classical algorithm in the tracking of sinusoidal chirps in high levels of noise.