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Moving Target Indicator
Published in Bassem R. Mahafza, Introduction to Radar Analysis, 2017
Delay line cancelers with feedback loops are known as recursive filters. The advantage of a recursive filter is that through a feedback loop, we will be able to shape the frequency response of the filter. As an example, consider the single canceler shown in Figure 10.7. From the figure we can write () y(t)=x(t)−(1−K)w(t) () v(t)=y(t)+w(t) () w(t)=v(t−T).
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Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
where ai and bi are some proper real constants. When all the bi = 0, it is called a nonrecursive equation. recursive filter a digital filter that is recursively implemented. That is, the present output sample is a linear combination of the present and past input samples as well as the previously determined outputs. Traditionally, the term recursive filter is closely related to infinite impulse filter. In a nonrecursive filter the present output sample is only a linear combination of the present and past input samples. recursive function See recursive procedure.
A limit Kalman filter and smoother for systems with unknown inputs
Published in International Journal of Control, 2023
Grigorios Gakis, Malcolm C. Smith
An early stochastic treatment of unknown input and state estimation for discrete-time systems is Glover (1969). An approach is outlined, and recursive filter equations are provided, for an input with no assumed prior, or by taking the limit in the Kalman filter as where Q is the input covariance (the zero informational limit), assuming no direct feedthrough of the input to the measurement, and assuming left invertibility of CB. Subsequent work explored different formulations of optimality, e.g. Kitanidis (1987) who posed the problem as a constrained optimisation with a free gain matrix parameter. The work continued with Darouach et al. (1995) that reformulated the problem as a state estimation of a singular stochastic system which is solved by employing a generalised least squares approach. Later, Darouach and Zasadzinski (1997) show the optimality of the filter in Kitanidis (1987) among the set of recursive filters and produce stability results, while Kerwin and Prince (2000) verify optimality among the set of all linear filters. In Gillijns and De Moor (2007a) the scope of the filter in Kitanidis (1987) is expanded by simultaneously estimating both the state and unknown input. Bitmead et al. (2019) return to the zero informational limit formulation of Glover (1969) to provide a full derivation and to show that the resulting filter recursions coincide with those given in Kitanidis (1987) and Gillijns and De Moor (2007a).
A novel design of low-cost hearing aid devices using an efficient lifting filter bank with a modified variable filter
Published in Expert Review of Medical Devices, 2022
N Subbulakshmi, R Manimegalai, G Rajakumar, T Ananth Kumar, Umadevi Kosuri
Answers to all the above questions lead to different types of filter bank techniques. Another essential part of the digital hearing aid device is the peripheral auditory system. The input signal is passed through the filter bank of the hearing aid and peripheral auditory system before reaching the brainstem. Based on the literature findings, it is observed that the proposed novel lifting-based filter bank (NLFB) design has some of the issues such as power consumption, area occupation, and more delay. In order to address these issues, the proposed NLFB method plans to contribute the following: The proposed design has reasonable power consumption and less area occupation because of the modified variable recursive structure comparing to interpolated filter bank.Lifting algorithm decides the number of sublevels of the algorithm that determines the hardware design complexity.Advantages of both modified recursive filter and lifting algorithm delivers high speed in the signal processing system of the hearing aid device.Noise reduction is also an important factor in enhancing the speech signal quality over the noisy environment in the hearing aid devices. Hence, the proposed system is suitable for those kinds of problems.
On the equivalence between the unbiased minimum-variance estimation and the infinity augmented Kalman filter
Published in International Journal of Control, 2020
Bo Ding, Tianping Zhang, Huajing Fang
If no prior information about the input is available, the unknown input and state can be estimated by the MVU algorithm (Gillijns & De Moor, 2007). In the following, we will give the main result about the MVU algorithm. Consider the recursive filter of the form where is the state estimation, is the unknown input estimation, and are the intermediate values. and are the gain matrix, the optimal of which are shown as the following two lemmas, respectively.