Journal of the Franklin Institute 337 (2000) 923–928 Brief communication Reduced-order filtering of jump Markov systems with noise-free measurements Edwin Engin Yaz a, *, Yvonne Ilke Yaz b a Department of Electrical Engineering, University of Arkansas, Fayetteville, AR 72701, USA b Department of Mathematics, Centenary College, Shreveport, LA 71134, USA Received 27 January 2000; received in revised form 25 July 2000 Abstract In continuous-time Kalman filtering for jump Markov systems, it is required that the measurement noise covariance be nonsingular. In this work, the case of noise-free measurements is considered and it is proposed that a reduced-order filter be used to overcome this singularity problem. This filter is optimal in the minimum variance sense and is of dimension ðn  pÞ where n and p are the state and measurement vector dimensions, respectively. After the optimal filter equations are derived for the finite-time case, we focus on the infinite-time case and characterize the set of all assignable estimation error covariances and parametrize the set of all estimator gains. The conditions for the existence of the optimal steady-state filter are obtained in terms of the system theoretic properties of the original signal model. # 2000 The Franklin Institute. Published by Elsevier Science Ltd. All rights reserved. 1. Introduction Dynamic system models with jump Markov parameters have been used to represent phenomena where there are sudden and gross changes in the operation mode (parameter matrices) with applications to economic, power, aerospace, thermal, and manufacturing problems [1]. The most common model for such situations involves a system state vector that takes on a continuum of values in either continuous or discrete time and system parameters that belong to a discrete set. The most thorough account of the analysis, control, and estimation theories of such systems are given in [1]. This work presents a reduced-order filtering approach to *Corresponding author. Tel.: +1-501-575-6580; fax: +1-501-575-7967. E-mail address: eyaz@comp.uark.edu (E.E. Yaz). 0016-0032/00/$ 20.00 # 2000 The Franklin Institute. Published by Elsevier Science Ltd. All rights reserved. PII:S0016-0032(00)00054-5