Abstract
We introduce the antiparticle filter, AF, a new type of recursive Bayesian estimator that is unlike either the extended Kalman Filter, EKF, unscented Kalman Filter, UKF or the particle filter PF. We show that for a classic problem of robot localization the AF can substantially outperform these other filters in some situations. The AF estimates the posterior distribution as an auxiliary variable Gaussian which gives an analytic formula using no random samples. It adaptively changes the complexity of the posterior distribution as the uncertainty changes. It is equivalent to the EKF when the uncertainty is low while being able to represent non-Gaussian distributions as the uncertainty increases. The computation time can be much faster than a particle filter for the same accuracy. We have simulated comparisons of two types of AF to the EKF, the iterative EKF, the UKF, an iterative UKF, and the PF demonstrating that AF can reduce the error to a consistent accurate value.
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Notes
- 1.
The iterative UKF is an iterative version of the UKF similar to the IEKF.
- 2.
We use the threshold 0.01 in our simulations.
- 3.
We use 1.0 for this threshold.
- 4.
We used N = 21.
- 5.
Λ is a matrix from the λ → x spaces and x vector Γ is a symmetric matrix wrt λ.
- 6.
α and β are matrices from the λ → x spaces.
- 7.
As in Thrun pp. 220–228 (UKF), 250–252 (PF) and 110 (low variance sampling).
- 8.
Q was 10−5, 10−4, or 10−3 along the diagonal.
- 9.
The simulated distance units are arbitrary but can be thought of as meters while the angles are in radians.
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This work was supported by the SSF through its Centre for Autonomous Systems (CAS).
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Folkesson, J. (2017). The Antiparticle Filter—An Adaptive Nonlinear Estimator. In: Christensen, H., Khatib, O. (eds) Robotics Research . Springer Tracts in Advanced Robotics, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-319-29363-9_13
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