Adaptive Noise Covariance Estimation under Colored Noise using Dynamic Expectation Maximization

A wide variety of NCM estimation methods have been proposed within the control community [1]. These methods Identifying the noise associated with a process, i.e., estimating can be classified into two categories: i) feedback free the Noise Covariance Matrix (NCM) is crucial for methods where the estimation is done by processing the state estimation and control of a dynamic system [1]. An entire data sequence offline and ii) feedback methods where incorrect NCM results in suboptimal gains (e.g., Kalman estimation is done online and. The feedback free methods are gain), significantly decreasing the quality of state estimation of two types: i) the correlation methods that are based on the and tracking. Hence, accurate NCM estimation has a wide analysis of the measurement error sequence, such as Indirect scope of applications that include robotics, signal processing, Correlation (ICM) [9], Input-Output Correlation (IOCM) fault detection, optimal controller design, system identification, [10], Weighted Correlation (WCM) [11], Measurement Average etc. However, most of the NCM estimation algorithms Correlation (MACM) [12], Direct Correlation (DCM) assume a white noise condition, which may not be true in [13] and Measurement Difference Correlation (MDCM) [14], practice. In many real-world applications the noise is colored and ii) the Maximum-Likelihood Methods (MLM) [15] that (e.g., there are temporal autocorrelations). This makes NCM maximises the likelihood function over the data.