Chapter 17
Modified Continuous-Time Particle Filter
Algorithm Without Overflow Errors
Irina A. Kudryavtseva and Konstantin A. Rybakov
Abstract The modification for the continuous-time particle filter algorithm is
offered. The developed modification that is based on the well-known strategy such as
modeling trajectories to numerically solve stochastic differential equations provides
the lack of overflow errors during the calculation of particle weights. To implement
such an idea practically particle weights should be expressed in terms of logarithms
with an additional customization of exponents. The effectiveness of the modified
algorithm is demonstrated when solving the tracking problem to find coordinates
and velocities of an aircraft executing a maneuver in the horizontal plane.
17.1 Introduction
The filtering problem for continuous-time stochastic systems given by two Stochastic
Differential Equations (SDEs) describing an unobservable Markov random process
and its measurements (two diffusion processes) is considered. The desired outcome
is to estimate a system state vector from given measurements in accordance with
some quality criterion [1–4]. Quality criteria can be chosen differently. For instance,
one can take the following criteria: the Minimum Mean Squared Error (MMSE)
criterion, the Maximum A Posteriori (MAP) criterion. Filtering problems arise in
many fields among which we would like to highlight motion control and navigation
data processing [5–16].
The goal of the paper is to develop the modification of the continuous-time particle
filter algorithm [3]. This modification is rooted in the probability representation of
I. A. Kudryavtseva · K. A. Rybakov (B)
Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow
125993, Russian Federation
e-mail: rkoffice@mail.ru
I. A. Kudryavtseva
e-mail: kudryavtseva.irina.a@gmail.com
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
L. C. Jain et al. (eds.), Applied Mathematics and Computational Mechanics for Smart
Applications, Smart Innovation, Systems and Technologies 217,
https://doi.org/10.1007/978-981-33-4826-4_17
245
Modified Continuous-Time Particle Filter
Algorithm Without Overflow Errors
Irina A. Kudryavtseva and Konstantin A. Rybakov
Abstract The modification for the continuous-time particle filter algorithm is
offered. The developed modification that is based on the well-known strategy such as
modeling trajectories to numerically solve stochastic differential equations provides
the lack of overflow errors during the calculation of particle weights. To implement
such an idea practically particle weights should be expressed in terms of logarithms
with an additional customization of exponents. The effectiveness of the modified
algorithm is demonstrated when solving the tracking problem to find coordinates
and velocities of an aircraft executing a maneuver in the horizontal plane.
17.1 Introduction
The filtering problem for continuous-time stochastic systems given by two Stochastic
Differential Equations (SDEs) describing an unobservable Markov random process
and its measurements (two diffusion processes) is considered. The desired outcome
is to estimate a system state vector from given measurements in accordance with
some quality criterion [1–4]. Quality criteria can be chosen differently. For instance,
one can take the following criteria: the Minimum Mean Squared Error (MMSE)
criterion, the Maximum A Posteriori (MAP) criterion. Filtering problems arise in
many fields among which we would like to highlight motion control and navigation
data processing [5–16].
The goal of the paper is to develop the modification of the continuous-time particle
filter algorithm [3]. This modification is rooted in the probability representation of
I. A. Kudryavtseva · K. A. Rybakov (B)
Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow
125993, Russian Federation
e-mail: rkoffice@mail.ru
I. A. Kudryavtseva
e-mail: kudryavtseva.irina.a@gmail.com
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
L. C. Jain et al. (eds.), Applied Mathematics and Computational Mechanics for Smart
Applications, Smart Innovation, Systems and Technologies 217,
https://doi.org/10.1007/978-981-33-4826-4_17
245