arXiv subjects

Svyatoslav Covanov

Publications and source records attributed to Svyatoslav Covanov.

5 recordsLinked to original sources

arXiv2026

Validation methodology on real data of reversible Kalman Filter for state estimation with Manifold

This work extends a previous study that introduced an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its objective is to address the limitations of the earlier approach. The reversible Kalman filter was designed to provide a methodology for evaluating the accuracy of existing Kalman filter variants with arbitrary precision on synthetic data. It has favorable numerical properties on synthetic data, achieving arbitrary precision without relying on the small-velocity assumption and depending only on sensor noise. However, its application to real data encountered difficulties related to measurement noise, which was mitigated using a heuristic. In particular, the heuristic involved an event detection step switching between reversible Kalman filter and classical Kalman variant at chosen moments. In the present work, we propose a study of this detection step and propose a methodology to prove at which moment the reversible Kalman approach improves on classical multiplicative variant.

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arXiv2025

Reversible Kalman Filter for state estimation with Manifold

This work introduces an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its primary objective is to provide a methodology enabling the evaluation of the precision of existing Kalman filter variants with arbitrary accuracy on synthetic data, something that, to the best of our knowledge, has not been addressed in prior work. To this end, we develop a new filter that exhibits favorable numerical properties, thereby correcting the divergences observed in previous Kalman filter variants. In this formulation, the achievable precision is no longer constrained by the small-velocity assumption and is determined solely by sensor noise. In addition, this new filter assumes high precision on the sensors, which, in real scenarios require a detection step that we define heuristically, allowing one to extend this approach to scenarios, using either a 9-axis IMU or a combination of odometry, accelerometer, and pressure sensors. The latter configuration is designed for the reconstruction of trajectories in underwater environments.

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arXiv2018

Improved method for finding optimal formulae for bilinear maps in a finite field

In 2012, Barbulescu, Detrey, Estibals and Zimmermann proposed a new framework to exhaustively search for optimal formulae for evaluating bilinear maps, such as Strassen or Karatsuba formulae. The main contribution of this work is a new criterion to aggressively prune useless branches in the exhaustive search, thus leading to the computation of new optimal formulae, in particular for the short product modulo X 5 and the circulant product modulo (X 5 -- 1). Moreover , we are able to prove that there is essentially only one optimal decomposition of the product of 3 x 2 by 2 x 3 matrices up to the action of some group of automorphisms.

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arXiv2018

Fast integer multiplication using generalized Fermat primes

For almost 35 years, Sch{ö}nhage-Strassen's algorithm has been the fastest algorithm known for multiplying integers, with a time complexity O(n $\times$ log n $\times$ log log n) for multiplying n-bit inputs. In 2007, F{ü}rer proved that there exists K > 1 and an algorithm performing this operation in O(n $\times$ log n $\times$ K log n). Recent work by Harvey, van der Hoeven, and Lecerf showed that this complexity estimate can be improved in order to get K = 8, and conjecturally K = 4. Using an alternative algorithm, which relies on arithmetic modulo generalized Fermat primes, we obtain conjecturally the same result K = 4 via a careful complexity analysis in the deterministic multitape Turing model.

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arXiv2016

Parallel Integer Polynomial Multiplication

We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantages of this new approach.

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