A three-state Kalman tracker using position and rate measurements

Ramachandra, K. V.; Mohan, B.R.; Geetha, B. R.

doi:10.1109/7.249127

Cited by 14 publications

(7 citation statements)

References 10 publications

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“…Here, we derive the necessary and sufficient condition for the stability of an α-β filter that considers the Doppler shift expressed by Eqs. (15) to (18). The conditions related to stability obtained in this section hold regardless of the process noise.…”

Section: The Stability Conditions Of An α-β Filter That Considers Thementioning

confidence: 82%

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Stability condition and steady‐state solution of various α–β filters for linear FM pulse compression radars

Amishima

Ito

Kosuge

2004

Electron Comm Jpn Pt III

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Pulse compression is often used in radar to increase the detection range while suppressing the peak transmission power and to prevent a drop in the range resolution. However, a drawback of this technique is the target range is observed offset by an amount proportional to the range rate of the target. On the other hand, various α–β filters have been derived based on the differences in motion models. These filters define the process noise in a discrete system in terms of the velocity, the acceleration, or the n‐th derivative of the acceleration, or discretized after defining the process noise in a continuous system in terms of the acceleration. For the process noise in a discrete system defined in terms of the acceleration, we propose an α–β filter that tracks while internally correcting the bias observation error described above. In this paper, we show a necessary and sufficient stability condition of various stable α–β filters that track while internally correcting the bias observation error. We show that the stable gain region does not depend on the Doppler shift time constant and is invariant. Then we formulate the relationship between α and β and the error covariance matrix. In addition, for α–β filters where the process noise in a discrete system is defined in terms of the velocity or the acceleration, or where the process noise in a continuous system is defined in terms of the acceleration and then discretized, we showed that, in practice, the α–β filter with the process noise defined in terms of the velocity in discrete time, has superior performance, when the performance is measured in terms of error covariance matrix given a fixed maneuver index. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(6): 13–22, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10134

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Section: The Stability Conditions Of An α-β Filter That Considers Thementioning

confidence: 82%

“…Usually, the performance index of an α-β filter is the steady-state error covariance matrix [6,10,17,18]. The error covariance matrix indicates the variance of the Kalman filter tracking errors.…”

Section: Theorem 31mentioning

confidence: 99%

Stability condition and steady‐state solution of various α–β filters for linear FM pulse compression radars

Amishima

Ito

Kosuge

2004

Electron Comm Jpn Pt III

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“…Therefore, the design of appropriate process noise is conducted empirically and/or by Monte Carlo simulations (see Section 6 of [6]). Consequently, it is simpler to design an appropriate α-β-γ filter than to construct a Kalman filter or EKF [7,23,[26][27][28].…”

Section: Steady-state Error For a Target With Constant Jerk (Trackingmentioning

confidence: 99%

“…Thus, the relationship between tracking accuracy and measurement noise is very important for the implementation of α-β-γ filters using both position and velocity measurements. Although position-velocity-measured (PVM) tracking filters have been investigated [23][24][25][26][27][28], the number of such studies is quite small compared with those on general tracking filters that measure only position. Additionally, most studies on PVM tracking filters use Kalman or particle filters.…”

mentioning

confidence: 99%

Performance analysis of α- β- γtracking filters using position and velocity measurements

Saho

Masugi

2015

EURASIP J. Adv. Signal Process.

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This paper examines the performance of two position-velocity-measured (PVM) α-β-γ tracking filters. The first estimates the target acceleration using the measured velocity, and the second, which is proposed for the first time in this paper, estimates acceleration using the measured position. To quantify the performance of these PVM α-β-γ filters, we analytically derive steady-state errors that assume that the target is moving with constant acceleration or jerk. With these performance indices, the optimal gains of the PVM α-β-γ filters are determined using a minimum-variance filter criterion. The performance of each filter under these optimal gains is then analyzed and compared. Numerical analyses clarify the performance of the PVM α-β-γ filters and verify that their accuracy is better than that of the general position-only-measured α-β-γ filter, even when the variance in velocity measurement noise is comparatively large. We identify the conditions under which the proposed PVM α-β-γ filter outperforms the general α-β-γ filter for different ratios of noise variance in the velocity and position measurements. Finally, numerical simulations verify the effectiveness of the PVM α-β-γ filters for a realistic maneuvering target.

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“…The filter estimates the optimum range, range-rate, range-acceleration and rangejerk. The position coordinate of the vehicle is assumed to be measured by a track-while-scan radar sensor at uniform sampling intervals of time T seconds through random noise [5][6][7]..…”

Section: Introductionmentioning

confidence: 99%

Four State Filter with Position Measurements and also with Position and Doppler Measurements

Geetha¹,

Rahman²

2013

IJCA

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A one-dimensional, four state Kalman tracking filter is described for two cases: In case 1, the filter is described for position measurements only and in case 2, the filter is described for both position and Doppler measurements. The filter estimates the range, the range-rate, the rangeacceleration and the range-jerk of a moving target such as an aircraft moving with constant jerk perturbed by a plant noise of zero mean and constant variance which accounts for maneuvers and/or other random factors. In case 1, the range coordinate of the vehicle is assumed to be measured by a track-while-scan radar sensor and incase 2, the rangerate (Doppler) measurements are obtained by a trackwhile-scan radar sensor which employs pulsed Doppler processing such as a moving target detector providing unambiguous Doppler data [1,2]. The measurements are obtained at uniform sampling intervals of time T seconds and all measurements are noisy. The filter structures have been defined and the steady state results are given for both cases.

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A three-state Kalman tracker using position and rate measurements

Cited by 14 publications

References 10 publications

Stability condition and steady‐state solution of various α–β filters for linear FM pulse compression radars

Stability condition and steady‐state solution of various α–β filters for linear FM pulse compression radars

Performance analysis of α- β- γtracking filters using position and velocity measurements

Four State Filter with Position Measurements and also with Position and Doppler Measurements

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