Accelerating Particle Filter Using Randomized Multiscale and Fast Multipole Type Methods

Abstract

Abstract-Particle filter is a powerful method that tracks the state of a target based on non-linear observations. We present a multiscale based method that accelerates the computation of particle filters. Unlike the conventional way, which calculates weights over all particles in each cycle of the algorithm, we sample a small subset from the source particles using matrix decomposition methods. Then, we apply a function extension algorithm that uses a particle subset to recover the density function for all the rest of the particles not included in the chosen subset. The computational effort is substantial especially when multiple objects are tracked concurrently. The proposed algorithm reduces significantly the computational load. By using the Fast Gaussian Transform, the complexity of the particle selection step is reduced to a linear time in n and k , where n is the number of particles and k is the number of particles in the selected subset. We demonstrate our method on both simulated and on real data such as objects tracking in videos sequences.

Randomized LU decomposition

“…Efficient matrix decomposition serves as a basis for many studies and algorithms design for data analysis and applications. Fast randomized matrix decomposition algorithms are used for tracking objects in videos [39], multiscale extensions for data [4] and detecting anomalies in network traffic for finding cyber attacks [13], to name some. There are randomized versions for many different matrix factorization algorithms [24], compressed sensing [16] and least squares [3].…”

“…As the size of the data grows exponentially, feasible methods for the analysis of large datasets has gained an increasing interest. Such an analysis can involve a factorization step of the input data given as a large sample-by-feature matrix or given by a sample affinity matrix [45,12,39]. High memory consumption and the computational complexity of the factorization step are two main reasons for the difficulties in analyzing huge data structures.…”

Visual tracking via crossing-bin histogram Bhattacharyya similarity

“…The core idea of particle filter (Wang et al , 2014; Shabat et al , 2015) is to use a cluster of weighted random samples true{bold-italicnormalXbold-italicnormalkbold-italicnormali,wkitrue}i=1N (also known as particles) to approximate the target posterior probability distribution p ( X k | Z 1:k ), and then the target state is extracted as that: where X k represents the target state at time k , bold-italicnormalXbold-italicnormalkbold-italicnormali represents the target state of the i -th particle, Z 1:k represents the observation from the initial time to the current time k , N is the number of particles and wki is the weight of the particle at the time k , which can be computed as that: where ptrue(bold-italicnormalXbold-italicnormalkbold-italicnormali|bold-italicnormalXk-1bold-italicnormalitrue) is the target translation model. If the target state translation follows the Markov process, the above equation can be deformed as: where bold-italicnormalZbold-italicnormalkbold-italicnormali is the observation of the i -th the particle at the time k and ptrue(bold-italicnormalZbold-italicnormalkbold-italicnormali|bold-i...…”

Multi-scale Activity Estimation with Spatial Abstractions

“…Other ways to factoring computation exist, e.g. [6,10], and a hierarchy of feature encodings can be used [13]. However, to the best of our knowledge, no prior method allows tracking a process on multiple scales at once and accepts evidence with variable resolutions.…”