Recursive joint Cramér‐Rao lower bound for parametric systems with two‐adjacent‐states dependent measurements

Abstract

Joint Cramér-Rao lower bound ( JCRLB) is very useful for the performance evaluation of joint state and parameter estimation ( JSPE) of non-linear systems, in which the current measurement only depends on the current state. However, in reality, the non-linear systems with two-adjacent-states dependent (TASD) measurements, that is, the current measurement is dependent on the current state as well as the most recent previous state, are also common. First, the recursive JCRLB for the general form of such non-linear systems with unknown deterministic parameters is developed. Its relationships with the posterior CRLB for systems with TASD measurements and the hybrid CRLB for regular parametric systems are also provided. Then, the recursive JCRLBs for two special forms of parametric systems with TASD measurements, in which the measurement noises are autocorrelated or cross-correlated with the process noises at one time step apart, are presented, respectively. Illustrative examples in radar target tracking show the effectiveness of the JCRLB for the performance evaluation of parametric TASD systems.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Bayesian Cramér-Rao Lower Bounds for Prediction and Smoothing of Nonlinear TASD Systems

“…To initialize the recursion for FIMs of prediction and smoothing, the recursion of the FIM J k|k for filtering is required. This can be obtained from Corollary 3 of [51], as shown in the following lemma.…”

“…In practice, the TASD systems sometimes may incorporate some unknown nonrandom parameters. For the performance evaluation of joint state and parameter estimation for nonlinear parametric TASD systems, a recursive joint CRLB (JCRLB) was studied in [51].…”

“…As a result of this, BCRLBs can be computed offline. The BCRLB for the filtering of the general form of TASD systems has been obtained as a special case of the JCRLB in [51] when the parameter belongs to the empty set. However, the BCRLBs for the prediction and smoothing of the general form of TASD systems have not been studied yet.…”

Layout of Detection Array Based on Multi-Strategy Fusion Improved Adaptive Mayfly Algorithm in Bearing-Only Sensor Network

“…The determinant of the Fisher Information Matrix (FIM) is used to represent the observability measurement of the system, thereby providing a usable optimization index for the detection system [ 10 , 11 , 12 ]. Further research found that CRLB is equal to the inverse of FIM [ 13 , 14 ], which unified the positioning accuracy index and the observability index.…”