Noise identification and its influence on Kalman filter divergence (Q2737604)

The authors consider a discrete-time dynamic system with the state vector \(X\) and measurement vector \(Y\): NEWLINE\[NEWLINEX_{k+1}= FX_k+ Gw_k,\quad Y_{k+1}= HX_k+ v_k.NEWLINE\]NEWLINE Both \(w_k\) and \(v_k\) are assumed to be uncorrelated zero-mean Gaussian white noise sequences with covariances \(Q\) and \(R\) whose true values are assumed to be unknown. The proposal is based on statistical properties of the innovation matrix of the Kalman filter, and a weighted least squares scheme is used.NEWLINENEWLINEFor the entire collection see [Zbl 0955.00046].