Harmonic Mean Density Fusion in Distributed Tracking: Performance and Comparison

A distributed sensor fusion architecture is preferred in a real target-tracking scenario as compared to a centralized scheme since it provides many practical advantages in terms of computation load, communication bandwidth, fault-tolerance, and scalability. In multi-sensor target-tracking literature, such systems are better known by the pseudonym - track fusion, since processed tracks are fused instead of raw measurements. A fundamental problem, however, in such systems is the presence of unknown correlations between the tracks, which renders a standard Kalman filter (naive fusion) useless. A widely accepted solution is covariance intersection (CI) which provides near-optimal estimates but at the cost of a conservative covariance. Thus, the estimates are pessimistic, which might result in a delayed error convergence. Also, fusion of Gaussian mixture densities is an active area of research where standard methods of track fusion cannot be used. In this article, harmonic mean density (HMD) based fusion is discussed, which seems to handle both of these issues. We present insights on HMD fusion and prove that the method is a result of minimizing average Pearson divergence. This article also provides an alternative and easy implementation based on an importance-sampling-like method without the requirement of a proposal density. Similarity of HMD with inverse covariance intersection is an interesting find, and has been discussed in detail. Results based on a real-world multi-target multi-sensor scenario show that the proposed approach converges quickly than existing track fusion algorithms while also being consistent, as evident from the normalized estimation-error squared (NEES) plots.

On Pooling-Based Track Fusion Strategies : Harmonic Mean Density

In a distributed sensor fusion architecture, using standard Kalman filter (naive fusion) can lead to degraded results as track correlations are ignored and conservative fusion strategies are employed as a sub-optimal alternative to the problem. Since, Gaussian mixtures provide a flexible means of modeling any density, therefore fusion strategies suitable for use with Gaussian mixtures are needed. While the generalized covariance intersection (CI) provides a means to fuse Gaussian mixtures, the procedure is cumbersome and requires evaluating a non-integer power of the mixture density. In this paper, we develop a pooling-based fusion strategy using the harmonic mean density (HMD) interpolation of local densities and show that the proposed method can handle both Gaussian and mixture densities without much changes to the framework. Mathematical properties of the proposed fusion strategy are studied and simulated on 2D and 3D maneuvering target tracking scenarios. The simulations suggest that the proposed HMD fusion performs better than other conservative strategies in terms of root-mean-squared error while being consistent.