ABSTRACT
Due to the uncertain origin o f the sensor data and uncertainty regarding the underlying system dynamics model, naively applied data processing according to the previous formalism leads to memory explosions: the number o f components in the mixture densities p(x* + i\Zk) and p {x k + J Zk+ l ) exponen tially grow at each prediction and filtering step. Thus, suboptimal approximation techniques are inevitable for any practical realization. Fortunately, the densities resulting from Equation 8.39 and 8.47 are characterized by a finite number o f modes that may be large and fluctuating, but do not explosively grow. This is the rationale for adaptive approximation methods that keep the number of mixture components under control without disturbing the density iteration too seriously. In other words, the densities can often be approximated by mixtures with (far) less components. Provided the relevant features o f the densities are preserved, the resulting suboptimal algorithms are expected to be close to optimal Bayesian filtering.
