State Space Recursive Least Squares Research Articles

Extended Kalman Filter-Based Power Line Interference Canceller for Electrocardiogram Signal.

Cardiac diseases constitute a major root of global mortality and they are likely to persist. Electrocardiogram (ECG) is widely opted in clinics to detect countless heart illnesses. Numerous artifacts interfere with the ECG signal, and their elimination is vital to allow medical specialists to acquire valuable statistics from the ECG. The utmost artifact that is added to the ECG signal is power line interference (PLI). Numerous filtering methods have been employed in the literature to eliminate PLI from noisy ECG. This article proposes an extended Kalman filter (EKF)-based adaptive noise canceller (ANC) that comprises PLI frequency as a distinct model parameter. Thus, it is capable of tracking PLI with drifting frequency. The proposed canceller's performance is compared with state-space recursive least squares (SSRLSs) filter-based PLI canceling. The evaluation is carried out for four cases of PLI, that is, PLI with known amplitude and frequency, PLI with unknown amplitude and frequency, PLI with drifting amplitude and frequency, and PLI removal from a real-time ECG recording. The samples of the Massachusetts Institude of Technology (MIT)-Boston's Beth Israel Hospital (BIH) arrhythmia database are considered for the first three cases, whereas, for the fourth case, real ECG signal is taken from armed forces institude of cardiology, the national institude of heart diseases (AFIC/NIHD), Pakistan. Mean square error, frequency spectrum, and noise reduction are selected as performance metrics for comparison. Simulation results depict that the presented EKF-based ANC system outperforms the SSRLS-based ANC system and effectively eliminates PLI from ECG under all four investigated scenarios.

State space least p-power filter

As a new addition to the recursive least squares (RLS) family filters, the state space recursive least squares (SSRLS) filter can achieve desirable performance by conquering some limitations of the standard RLS filter. However, when the system is contaminated by some non-Gaussian noises, the performance of SSRLS will get worse. The main reason for this is that the SSRLS is developed under the well-known minimum mean square error (MMSE) criterion, which is not very suitable for non-Gaussian situations. To address this issue, in this paper, we propose a new state space based linear filter, called the state space least p-power (SSLP) filter, which is derived under the least mean p-power error (LMP) criterion instead of the MMSE. With a proper p value, the SSLP can outperform the SSRLS substantially especially in non-Gaussian noises. Two illustrative examples are presented to show the satisfactory results of the new algorithm.

State space maximum correntropy filter

The state space recursive least squares (SSRLS) filter is a new addition to the well-known recursive least squares (RLS) family filters, which can achieve an excellent tracking performance by overcoming some limitations of the standard RLS algorithm. However, when the underlying system is disturbed by some heavy-tailed non-Gaussian impulsive noises, the performance of SSRLS will deteriorate significantly. The main reason for this is that the SSRLS is derived under the minimum mean square error (MMSE) criterion, which is not well-suited to estimation problems under non-Gaussian noises. To overcome this issue, we propose in this paper a novel linear filter, called the state space maximum correntropy (SSMC) filter, which is derived under the maximum correntropy criterion (MCC) instead of the MMSE. Since MCC is very suited to non-Gaussian signal processing, the SSMC performs very well in non-Gaussian noises especially when the signals are corrupted by impulsive noises. A simple illustrative example is presented to demonstrate the desirable performance of the new algorithm.

Extended state space recursive least squares

A new extended state space recursive least squares (ESSRLS) algorithm is proposed for state estimation of nonlinear systems. It is based on state space recursive least squares (SSRLS) approach and uses first order linearization of the system. It inherits the capability of obtaining state estimate without knowledge of process and measurement noise covariance matrices (Q and R respectively). The proposed approach is considered to provide new design option for scenarios where noise statistics and system dynamics vary. ESSRLS is initialized using delayed recursion method and a forgetting factor λ is employed to optimize the performance. The selection of λ can be problem specific as shown through experimental validations. However a value closer to and less than unity is generally recommended. Theoretical bases are validated by applying this algorithm to problems of tracking a non-conservative oscillator, a damped system with amplitude death and a signal modeled by mixture of Gaussian kernels. Simulation results show an MSE performance gain of 20 dB and 23 dB over extended Kalman filter (EKF) and unscented Kalman filter (UKF) while tracking van der Pol oscillator without knowledge about noise variances. The computational complexity of ESSRLS falls within that of EKF and UKF.

Comparative Analysis of SSRLS and SSRLS with Adaptive Memory for Wireless Channel Equalization

Wireless radio channels cause severe distortion in the signals. These distortions can be reduced by using different channel equalization techniques. In this paper, we compare the equalization performance of state-space recursive least squares (SSRLS) and state-space recursive least squares with adaptive memory (SSRLSWAM) to offset the effect of a linear dispersive channel. These adaptive filters are well-suited for the estimation of deterministic signals corrupted by the observation noise. We consider the equalization of both the linear time invariant and linear time varying systems to compare the performance of these filters. The performance is affected by the observation noise variance, choice of the forgetting factor and the model mismatch. We present simulation results to compare these cases by tracking a deterministic signal. It has been shown that SSRLSWAM outperforms SSRLS in both the time invariant and time varying channels.

State-space recursive least-squares with adaptive memory

State-space recursive least-squares (SSRLS) enhances the tracking ability of the standard recursive least-squares (RLS) by incorporating the underlying model of the environment. Its overall performance, however, depends on model uncertainty, presence of external disturbances, time-varying nature of the observed signal or nonstationary behavior of the observation noise. It turns out that the forgetting factor plays an important role in this context. However, depending on the problem, it may be difficult or even impossible to have a prior estimate of the best value of forgetting factor. As a logical approach to such situations, SSRLS with adaptive memory (SSRLSWAM) is developed in this paper. This in turn has been achieved by stochastic gradient tuning of the forgetting factor. An approximation based on steady-state SSRLS is also derived. The resultant filter alleviates the computational burden of the full-fledged algorithm. An example of tracking a noisy chirp demonstrates the overall capability and power of the new algorithm. It is expected that this new filter will be able to track and estimate time-varying signals that are difficult to handle with the available tools.

State-space recursive least squares: Part II

This paper is a sequel of our earlier development of state-space recursive least squares (SSRLS). Stability and convergence analysis of SSRLS and its steady-state counterpart complete the theoretical framework of this new powerful algorithm. Upper bounds on the forgetting factor that ensure stability of the filter have been derived. Properties like unbiasedness, convergence in mean, mean-square deviation and learning curves have been investigated. The results prove that SSRLS with infinite memory is optimal linear estimator for deterministic signals. The expressions and derivations show that different convergence properties of SSRLS are related to some forms of discrete Riccati or Lyapunov equations. The analysis done in this work would help understand the intricate details and behavior of SSRLS, which could subsequently aid in advanced applications and any further development.

State-space recursive least-squares: Part I

In this paper we present state-space recursive least-squares (SSRLS) filter. This algorithm is a new addition to the family of RLS filters. We cover core topics like batch processing, recursive updates, initialization and steady state solution, etc. SSRLS is very well-suited to estimate a wide class of deterministic signals corrupted by observation noise. This new filter exhibits excellent tracking performance by overcoming some of the limitations of the standard RLS algorithm. With its state-space formulation and sound mathematical basis, SSRLS is expected to become an important tool in estimation theory, adaptive filtering and control systems.