  Object-level SLAM introduces semantic meaningful and compact object landmarks
that help both indoor robot applications and outdoor autonomous driving tasks.
However, the back end of object-level SLAM suffers from singularity problems
because existing methods parameterize object landmark separately by their
scales and poses. Under that parameterization method, the same abstract object
can be represented by rotating the object coordinate frame by 90 deg and
swapping its length with width value, making the pose of the same object
landmark not globally consistent. To avoid the singularity problem, we first
introduce the symmetric positive-definite (SPD) matrix manifold as an improved
object-level landmark representation and further improve the cost functions in
the back end to make them compatible with the representation. Our method
demonstrates a faster convergence rate and more robustness in simulation
experiments. Experiments on real datasets also reveal that using the same
front-end data, our strategy improves the mapping accuracy by 22% on average.
