Computing the Observed Information Matrix for Dynamic Mixture Models
Abstract
The observed information matrix for an important class of finite mixture models, called dynamic mixture models, is derived in this report. Dynamic mixture models are useful probability models for random data originating from a number of distinct moving sources. The multiple-target tracking problem is one application of these models. For these models, the inverse of the observed information matrix is a consistent estimate of the error-covariance matrix for the mixture parameters. Measurement-to-source assignment uncertainty is unavoidable in these problems, and increases as the distance between sources in the sample space decreases. The observed information matrix computations presented here account for this uncertainty by subtracting the information in the unobserved assignments, treated as missing data, from the information in the expected complete data sample. Two target tracking examples are given that demonstrate these computations for the linear Gauss-Markov mixture model for multiple target tracking. In each case, the consistency of the resulting error-covariance matrices is examined.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 25, 2006
- Accession Number
- ADA457101
Entities
People
- Michael J. Walsh
Organizations
- Naval Undersea Warfare Center