Gauss–Newton filtering incorporating Levenberg–Marquardt methods for tracking

Nadjiasngar, Roaldje; Inggs, Michael

doi:10.1016/j.dsp.2012.12.005

Cited by 15 publications

(5 citation statements)

References 12 publications

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“…(1). In fact, similar deterministic Markov models have been applied in noise reduction methods (Kostelich and Schreiber, 1993), MHE (Michalska and Mayne, 1995), and the GN filter (Nadjiasngar and Inggs, 2013). Interestingly, Judd's shadowing filter yields more reliable and even more accurate results than the Bayesian filters when nonlinearity is significant while the noise is largely observational (Judd and Stemler, 2009), or when the objects do not display any significant random motion at the length and the time scales of interest (Judd, 2015).…”

Section: Circular Statisticsmentioning

confidence: 99%

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Liu

et al. 2017

Frontiers Inf Technol Electronic Eng

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Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov-Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed 'Gaussian conjugacy' in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity.

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Section: Circular Statisticsmentioning

confidence: 99%

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Liu

et al. 2017

Frontiers Inf Technol Electronic Eng

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“…the Kalman filter, against the Cramer-Rao lower bound (CRLB), the CRLB needs to incorporate time-history information as the tracking filter does. We validate this theory with measured data in the form of a field experiment where a commercial airliner was tracked using a recursive Gauss Newton filter (RGNF) [9]. Doppler-only tracking theory: Assuming that a target is moving in a two-dimensional (2D) Cartesian coordinate system, the position X p = [x n y n ] and velocity V n = [ẋ nẏn ] of the target at time t n are represented by the state vector as X n = [x nẋn y nẏn ] T , where [ • ] T is the transpose and the bold italic face notation is used to represent a vector.…”

mentioning

confidence: 80%

“…the Kalman filter, against the Cramer‐Rao lower bound (CRLB), the CRLB needs to incorporate time‐history information as the tracking filter does. We validate this theory with measured data in the form of a field experiment where a commercial airliner was tracked using a recursive Gauss Newton filter (RGNF) [9].…”

Section: Introductionmentioning

confidence: 99%

Target tracking using Doppler‐only measurements in FM broadcast band commensal radar

Maasdorp

Inggs²,

Nadjiasngar³

2015

Electron. lett.

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Radar research using transmitters of opportunity (commensal radar (CR)) has experienced a resurgence in popularity. Most published results to date used a multiple transmitter, single receiver site configuration with combinations of bearing, range and Doppler for target localisation. Doppler-only tracking has received the least attention. This reported work demonstrates with field measurements, using a single frequency modulation broadcast radio transmitter and multiple, spatially distributed, low-cost CR receivers, that Doppler-only tracking is achievable with target position accuracies of 150 m, despite a course range resolution.

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“…presented a series of non-sequential/optimizationbased estimation and forecasting works, particularly in the area of chaotic systems, e.g., [21]- [25], which remove the use of the state transition noise. Actually, similar deterministic Markov models have been applied in noise reduction methods [58], moving horizon estimator [59] and Gauss-Newton filter [19], [20]. Interestingly, Judd's shadowing filter yields more reliable and even more accurate performance than the Bayesian filters -however, a fairer comparison should be made between shadowing filters with Bayesian smoothers, using the same amount of observation data -in the case when the nonlinearity is significant, but the noise is largely observational [11], or when the objects do not typically display any significant random motions at the length and the time scales of interest [24].…”

Section: A Discrete-time Trajectory Estimationmentioning

confidence: 99%

Joint Smoothing and Tracking Based on Continuous-Time Target Trajectory Function Fitting

Chen

Sun

et al. 2019

IEEE Trans. Automat. Sci. Eng.

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We present a continuous time state estimation framework that unifies traditionally individual tasks of smoothing, tracking, and forecasting (STF), for a class of targets subject to smooth motion processes, e.g., the target moves with nearly constant acceleration or affected by insignificant noises. Fundamentally different from the conventional Markov transition formulation, the state process is modeled by a continuous trajectory function of time (FoT) and the STF problem is formulated as an online data fitting problem with the goal of finding the trajectory FoT that best fits the observations in a sliding timewindow. Then, the state of the target, whether the past (namely, smoothing), the current (filtering) or the near-future (forecasting), can be inferred from the FoT. Our framework releases stringent statistical modeling of the target motion in real time, and is applicable to a broad range of real world targets of significance such as passenger aircraft and ships which move on scheduled, (segmented) smooth paths but little statistical knowledge is given about their real time movement and even about the sensors. In addition, the proposed STF framework inherits the advantages of data fitting for accommodating arbitrary sensor revisit time, target maneuvering and missed detection. The proposed method is compared with state of the art estimators in scenarios of either maneuvering or non-maneuvering target.

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Gauss–Newton filtering incorporating Levenberg–Marquardt methods for tracking

Cited by 15 publications

References 12 publications

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Target tracking using Doppler‐only measurements in FM broadcast band commensal radar

Joint Smoothing and Tracking Based on Continuous-Time Target Trajectory Function Fitting

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