  Solar radio bursts (SRBs), are emitted by electrons propagating through the
corona and interplanetary space. Tracking such bursts is key to understanding
the properties of accelerated electrons and radio wave propagation as well as
the local plasma environment that they propagate through. Here, we present a
novel multilateration algorithm called BayEsian LocaLisation Algorithm (BELLA).
In addition, apparent SRB positions from BELLA are compared with comparable
localisation methods and the predictions of solar wind models. BELLA uses
Bayesian inference to create probabilistic distributions of source positions
and their uncertainties. This facilitates the estimation of algorithmic,
instrumental, and physical uncertainties in a quantitative manner. We validated
BELLA using simulations and a Type III SRB observed by STEREO A/B and Wind.
BELLA tracked the Type III source from $\sim$ 10--150 $R_{sun}$ (2-0.15 MHz)
along a spiral trajectory. This allowed for an estimate of an apparent solar
wind speed of $v_{sw} \sim$ 400 km s$^{-1}$ and a source longitude of $\phi_0
\sim$ 30deg. We compared these results with well-established methods of
positioning: Goniopolarimetric (GP), analytical time-difference-of-arrival
(TDOA), and Solar radio burst Electron Motion Tracker (SEMP). We found them to
be in agreement with the results obtained by BELLA. Additionally, the results
aligned with solar wind properties assimilated by the Heliospheric Upwind
Extrapolation with time dependence (HUXt) model. We have validated BELLA and
used it to identify apparent source positions as well as velocities and
densities of the solar wind. Furthermore, we identified higher than expected
electron densities, suggesting that the true emission sources were at lower
altitudes than those identified by BELLA, an effect that may be due to
appreciable scattering of electromagnetic waves by electrons in interplanetary
space.
