Discrete Time $q$-Lag Maximum Likelihood FIR Smoothing and Iterative Recursive Algorithm

FIR filters and recursive forms for discrete-time state-space models

In this paper, Rauch-Tung-Striebel(RTS) optimal smoothing algorithm is applied to improving off-line satellite attitude determination accuracy. The measurements are first processed by the forward filter, and then, a separate backward smoothing pass is used for obtaining the smoothing solution. The performances between RTS and extended Kalman filter(EKF) in gyro/star-sensor integrated system are compared. RTS smoother exhibits better accuracy and robustness than EKF under the situation of lower sensors precision, different length of data and larger initial attitude error. The results verify the effectiveness and practicability of RTS smoothing algorithm in satellite attitude determination.

The problem of uplink communications is considered where multiple mobile terminals equipped with multiple antennas are communicating with one base station also having multiple antennas. A theory for jointly optimizing the transmitter and receiver finite impulse response (FIR) multiple-input multiple-output (MIMO) filters is developed. The signals from the individual users are assumed to be uncorrelated with each other and the additive channel noise is uncorrelated with the original signals. The FIR MIMO channel filters are assumed to be known for both the mobile terminals and the base station. All the input signals to the FIR MIMO channels are assumed to be power-constrained. For given FIR MIMO channels with maximum allowable average input powers, the transmitter and receiver FIR MIMO filters are jointly optimized such that the mean square error (MSE) between the desired and reconstructed signals is minimized. An iterative numerical optimization algorithm is proposed. Numerical simulation results show that the proposed method has substantially better performance than a code division multiple access (CDMA) based system using minimum MSE receiver filters.

Application of ARIMA-RTS optimal smoothing algorithm in gas well production prediction

High computational complexity is a major problem encountered in the optimal design of two-dimensional (2-D) finite impulse response (FIR) filters. In this paper, we present an iterative matrix solution with very low complexity to the weighted least square (WLS) design of 2-D quadrantally symmetric FIR filters with two-valued weighting functions. Firstly, a necessary and sufficient condition for the WLS design of 2-D quadrantally symmetric filters with general nonnegative weighting functions is obtained. Then, based on this optimality condition, a novel iterative algorithm is derived for the WLS design problem with a two-valued weighting function. Because the filter parameters are arranged in their natural 2-D form and the transition band is not sampled, the computation amount of the proposed algorithm is reduced significantly, especially for high-order filters. The exponential convergence of the algorithm is established, and its computational complexity is estimated. Design examples demonstrating the convergence rate and solution accuracy of the algorithm, as well as the relation between the iteration number of the algorithm and the size and transition-band width of the filter are given.

Strictly nonwhite measurement noise (NMN) is observed in many industrial processes. Therefore, effective smoothing is often required to extract useful information about the process state with maximum accuracy. This article proposes a batch <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> -lag optimal finite impulse response (OFIR) smoother, operating under NMN with full block covariance matrices. It is shown that the OFIR smoother significantly outperforms the Rauch–Tung–Striebel (RTS) smoother and the unbiased FIR (UFIR) smoother. Testing is provided based on object tracking. The results are validated by a practical example of a three degree-of-freedom helicopter system, which confirms that OFIR smoothing provides better noise reduction than UFIR smoothing, RTS smoothing, and modified RTS smoothing using state augmentation and measurement differencing.

A novel procedure that makes use of the maximum entropy method (MEM) for the design of linear-phase FIR (finite impulse response) digital filters is described. It is shown that, by applying MEM to the inverse of the desired gain function or its square root function, it is possible to generate linear-phase FIR filters that match the given gain function to any desired degree of accuracy. Moreover, an iterative algorithm makes the design procedure very efficient, since the higher-order filters can be recursively generated from the lower-order ones. To minimize the effect of any residual passband distortion, a final averaging scheme on the lower-order filters generates a class of passband distortion-free linear-phase FIR filters. The new filters are seen to be more robust to changes in transition bandwidth as well as stopband level. Simulation results that compare the present procedure with other well-known methods are also presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Multiple Comparison Procedures with Modeling Techniques (MCP-Mod) framework has been recently approved by the U.S. Food, Administration, and European Medicines Agency as fit-for-purpose for phase II studies. Nonetheless, this approach relies on the asymptotic properties of Maximum Likelihood (ML) estimators, which might not be reasonable for small sample sizes. In this paper, we derived improved ML estimators and correction for their covariance matrices in the censored Weibull regression model based on the corrective and preventive approaches. We performed two simulation studies to evaluate ML and improved ML estimators with their covariance matrices in (i) a regression framework (ii) the Multiple Comparison Procedures with Modeling Techniques framework. We have shown that improved ML estimators are less biased than ML estimators yielding Wald-type statistics that controls type I error without loss of power in both frameworks. Therefore, we recommend the use of improved ML estimators in the MCP-Mod approach to control type I error at nominal value for sample sizes ranging from 5 to 25 subjects per dose.

This paper investigates the identification of FIR (finite impulse response) systems with quantized input and binary-valued observations. First, we obtain the ML (maximum likelihood) function of the available data, and construct an estimation algorithm of the unknown parameters when solving the maximum likelihood solution by transforming it into the solution to a set of linear equations. Secondly, based on the weighted least squares optimization technique, we establish the corresponding estimation algorithms in the case that the unknown parameters respectively satisfy a priori equality constraint and inequality constraint. Then, the AIC criterion is designed for estimating the order of the system. Finally, a numerical simulation example is employed to verify the effectiveness of the theoretical results obtained.

The authors examine the estimation of steady-state amplitude and phase using short, noisy records of the transient response of systems excited by a stepped sinusoid close to a resonance. Linear prediction estimation strategies are tested, and near maximum-likelihood (ML) performance is obtained by combining FIR (finite-impulse response) cancellation of the excitation poles with the truncated singular-value decomposition approach of R. Kumaresan and D.W. Tufts (1982). For the model tested, this excitation constrained estimation strategy departs from ML performance at a threshold signal-to-noise ratio that depends on the separation between the excitation and resonant frequencies. >

A localization and tracking algorithm for an early-warning tracking system based on the information fusion of Infrared (IR) sensor and Laser Detection and Ranging (LADAR) is proposed. The proposed Kalman filter scheme incorporates Out-of-Sequence Measurements (OOSMs) to address long-range, high-speed incoming targets to be tracked by networked Remote Observation Sites (ROS) in cluttered environments. The Rauch–Tung–Striebel (RTS) fixed lag smoothing algorithm is employed in the proposed technique to further improve tracking accuracy, which, in turn, is used for target profiling and efficient filter initialization at the targeted platform. This efficient initialization increases the probability of target engagement by increasing the distance at which it can be effectively engaged. The increased target engagement range also reduces risk of any damage from debris of the engaged target. Performance of the proposed target localization algorithm with OOSM and RTS smoothing is evaluated in terms of root mean square error (RMSE) for both position and velocity, which accurately depicts the improved performance of the proposed algorithm in comparison with existing retrodiction-based OOSM filtering algorithms. The effects of assisted target state initialization at the targeted platform are also evaluated in terms of Time to Impact (TTI) and true track retention, which also depict the advantage of the proposed strategy.

Identification of non-minimum-phase systems with finite impulse response (FIR) is addressed in the bispectrum domain. A phase retrieval algorithm, based on the log-bispectrum, is extended to log-magnitude reconstruction. Both linear-equation-based estimators are then combined to form an integrated, nonparametric system identification method. Weighted forms of these estimators are developed, which are asymptotically minimum-variance in the class of weighted least-squares estimators. Asymptotic variance expressions are derived for both the weighted and the unweighted forms. Theory and simulations illustrate that the approaches can identify non-minimum-phase MA (moving-average) models using output data which may be corrupted by additive Gaussian noise of unknown covariance. >

It is known, that unlike the Kalman filter (KF) finite impulse response (FIR) filters allow to avoid the divergence and unsatisfactory object tracking connected with temporary perturbations and abrupt object changes. The main challenge is to provide the appropriate choice of a sliding window size for them. In this paper, the new finite impulse response (FIR) filtering algorithm with the adaptive horizon size selection is proposed. The algorithm uses the receding horizon optimal (RHOFIR) filter which receives estimates, an abrupt change detector and an adaptive recurrent mechanism for choosing the window size. Monotonicity and asymptotic properties of the estimation error covariance matrix and the RHOFIR filter gain are established. These results form a solid foundation for justifying the principal possibility to tune the filter gain using them and the developed adaptation mechanism. The proposed algorithm (the ARHOFIR filter) allows reducing the impact of disturbances by varying adaptively the sliding window size. The possibility of this follows from the fact that the window size affects the filter characteristics in different ways. The ARHOFIR filter chooses a large horizon size in the absence of abrupt disturbances and a little during the time intervals of their action. Due to this, it has better transient characteristics compared to the KF and RHOFIR filter at intervals where there is temporary uncertainty and may provide the same accuracy of estimates as the KF in their absence. By simulation, it is shown that the ARHOFIR filter is more robust than the KF and RHOFIR filter for the temporarily uncertain systems.

MIMO system identification is a fundamental concern in a variety of applications. Various iterative and recursive MIMO system identification algorithms exist in the literature. The iterative algorithms suffer from high computational cost due to large matrix computations and recursive algorithms suffer from slow convergence speed. This paper proposes a fast recursive exact least squares algorithm for MIMO system identification with fast convergence speed and low computational cost. The recursions of the algorithm give rise to a lattice structure. The lattice structure is less sensitive to round-off errors, coefficients variations and can also be used for model order reduction. Although in this work we estimate an FIR (finite impulse response) model of the MIMO system, the framework can also be used for IIR (infinite impulse response) models, and for estimating linear periodically time varying (LPTV) and multivariable systems. The theory proposed is validated using simulation results.

The weighted least square (WLS) design of two-dimensional (2-D) linear-phase finite impulse response (FIR) filters with quadrantally symmetric or anti-symmetric magnitude responses is studied in this paper. Firstly, the necessary and sufficient condition for minimizing the WLS error is obtained in the form of matrix equation. Based on the matrix equation, a novel algorithm is derived for the WLS design of 2-D filters with two-valued weighting functions. Further, convergence of the algorithm is established and the computational complexity is analyzed. Because the new algorithm deals with the filter parameters in their natural 2-D form and the transition band is not sampled, the amount of computation required is reduced significantly, especially for high order cases. Finally, examples are presented to illustrate the performance of the proposed algorithm.