Adaptive target tracking with serial Kalman filters

Tracking is regarded as one of the most fundamental tasks in computer vision. It is used in many computer vision applications in fields such as surveillance, robotic navigation and 3D reconstruction to name but a few. Despite decades of research, the goal of fully automatic tracking of arbitrary types of objects in real world conditions is still an open problem. In this paper, we take a step toward the goal of general real-world tracking, and demonstrate a unified generative model for Bayesian multifeature, adaptive target tracking, or AMFT for short (Adaptive Multiple Feature Tracker). We derive a unified generative model for multi-sensory adaptive tracking which cleanly integrates tracking and the modeling of appearance change across multiple features in the same framework. The unified multi-feature observation model ensures that if one feature is not confident, e.g., color after an object crosses into a region of shadow, it is automatically down-weighted in its contribution to the appearance model update. In this way, without pre-training of specific object models, we achieve an extensible tracker for general object types, robust to real-world problems of clutter, appearance/lighting change and target model drift. The standard modeling assumptions made by a non-adaptive generative model are illustrated by the probabilistic graphical model in Figure 1(a). The unknown target state (e.g., location, size, velocity) xt is assumed to change with time t according to some process parameterized by A. At every time t, we make some noisy observations zt of the target xt (e.g., raw image or color histograms). The target is then tracked online by computing the posterior, p(xt |z1:t) over the true target location recursively. In the case of the Kalman filter (KF), all the distributions involved are Gaussian. In the case of the particle filter (PF), all the distributions involved are represented non-parametrically by a set of samples [1]. The true target model, e.g., the appearance or color histogram to search for, is assumed to be part of the parameters H, i.e., it is known and fixed by an operator or initialized by some external process. In many cases however, the true appearance of the target H may change significantly in time, e.g., the appearance changes when a subject moves between shade and sunlight. This is the case for outdoor surveillance applications and is the motivation for this research. Adaptive trackers [2, 3, 4, 6] have been proposed to update the target appearance online in various heuristic ways. We can formalise this more general modeling assumption generatively, by the generalized dynamic Bayesian network illustrated in Figure 1(b). In contrast to Figure 1(a), the true target model which was previously included in the fixed parameters H, is now included as the the initial condition y0 of a dynamic latent variable yt , formalizing the modeling assumption that the target appearance can change over time. In addition to the target state xt , the target appearance yt will therefore be incrementally and recursively updated as part of the process of inferring the latent variables in this model p(xt ,yt |z1:t). The latent space is of course now greatly expanded, and poses a more challenging inference problem than that of Figure 1(a). In Section 2 of the paper, we detail the specific parametric form of the model and an efficient inference algorithm. We evaluate our method (AMFT) against three contemporary trackers: A standard single feature particle filter (PF), mean-shift (MS) [5] and incremental visual tracking (IVT) [4]. The PF and MS trackers are non-adaptive color-based trackers, while IVT aims for pose and illumination change robustness by performing online adaptation in a subspace appearance model. Note that the AMFT, PF and IVT trackers track object scale, but MS does not. We evaluated these methods on a series of challenging video clips exhibiting a wide variety of data and object types for tracking, including far-field indoor and outdoor pedestrians with and without carried objects, vehicle tracking, and near-field indoor face trackH 1 x2 x3

The problem of tracking a manoeuvring target with sequentially correlated measurement noise is considered in the paper. Using Singer's method to model the manoeuvring target, the correlated measurement noise can be decorrelated by reformulating the measurement equation such that the conventional Kalman filter can be directly applied in this tracking problem. An analytical error analysis for this processing is derived. If some of the parameters are unknown, the conventional innovation correlation method can usually be employed to estimate these parameters adaptively. This method assumes that the measurement noise is white. If the measurement noise is sequentially correlated, this technique is not valid and the parameters can not be estimated with sufficient accuracy to obtain the desired tracking performance. By considering the effect of noise correlation, a modified computationally efficient method known as a multiple-level estimator is presented to improve the performance in estimating the unknown parameters in the presence of correlated measurement noise. >

The Kalman filter has been extensively applied into the integrated strapdown inertial navigation system (SINS) and global positioning system (GPS). As the estimation of Kalman filter requires the correct measurement noise statistics, the uncertainty of GPS noise can degrade the accuracy of Kalman filter. In order to achieve the accurate navigation results with measurement noise uncertainty, an innovation covariance method-based adaptive Kalman filter is proposed. According to the innovation covariance method, a scale matrix is utilized to reduce the deviation of innovation covariance between its calculated value and the actual value. Next the filter gain is modified with this scale matrix. Moreover, a weighted innovation covariance estimator is proposed to obtain more accurate estimation of innovation covariance. The proposed adaptive Kalman filter is validated in the SINS/GPS system, and the estimation accuracy and navigation results of the SINS/GPS system with measurement noise uncertainty are greatly improved.

For linear dynamic systems with white process and measurement noise, the Kalman filter is known to be the minimum variance linear state estimator. In the case that the random quantities are Gaussian, then the Kalman filter is the minimim variance state estimator. However, in the application of Kalman filters known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the optimal filter. Previous work by the authors demonstrated an analytic method of incorporating deterministic state equality constraints in the Kalman filter. This paper extends that work to develop the properties of Kalman filters in the presence of statistical state constraints. That is, given a linear system such that the expected values of the state variables satisfy some linear equality, we can constrain the Kalman filter estimates to satisfy those constraints. This results in a family of constrained filters with each member parameterized by a weighting matrix. This paper derives several interesting properties of the constrained Kalman filters.

Trajectory tracking control of ROVs considering external disturbances and measurement noises using ESKF-based MPC

For multi-target tracking, the IMM (interactive multiple model) algorithm has been proposed. The IMM is expected to reduce tracking errors for both nonmaneuvering and maneuvering targets. However, the IMM requires a heavy computational burden, because it utilizes multiple Kalman filters in parallel. On the other hand, the Kalman filter with a turning acceleration estimator, which can adapt a maneuvering target, has been proposed. The Kalman filter with a turning acceleration estimator is a single two-stage type filter and has a problem of setting threshold for the maneuver detector. In this paper, we propose the hybrid filter with a constant-velocity (CV) filter and a turning acceleration estimation filter. The proposed filter does not require a maneuver detector, because it integrates the outputs of two filters using the likelihood of each filter. And its computational requirement is smaller than the IMM, since it consists of only two Kalman based filters. The proposed method can prevent deteriorating tracking accuracy by reducing the risk of maneuver misdetection when a target maneuvers. We evaluate the performance of the proposed filter by computer simulation, and show the effectiveness of the proposed filter, comparing with the conventional Kalman filter and the two-stage Kalman filter.

A required assumption of a Kalman filter, the most-widely-used state estimator in avionic systems, is the Gaussian and whiteness of process and measurement noise. If the assumption fails, the performance of the Kalman filter degrades, and its estimation results are no longer optimal. In fact, many avionic applications produce colored noise, and the parameters of colored noise models are typically unknown beforehand without additional information about the noise statistics. In addition, the functions of each underlying model-nonlinear dynamic and measurement models - are sometimes improper or partially unknown. To estimate the states of systems with unknown correlations of each instance of noise and uncertain modeling errors of parametric models, we propose a novel approach that incorporates the kernel embedding of distributions into the extended Kalman filter. In our approach, kernel embedding maps process and measurement residuals, defined by differences between outputs of approximate system models and collected training data, into a reproducing kernel Hilbert space to generate nonparametric models in the functional space. Results from Monte Carlo simulations demonstrate that the proposed method, compared to existing methods (e.g., extended Kalman filter and Gaussian process-based filter), improves the accuracy of state estimation under colored noise conditions.

This paper proposes a new phase tracking algorithm for the 802.11a system. Since this system illuminates the basic structure of 802.11a system, and introduces the OFDM frame generation principle based the transmitter, phase error estimation and channel estimation. On the basis of this, this paper presents a phase tracking scheme based on adaptive Kalman filter, and then simulates the process based on 802.11a system. The result indicates that the BER has been improved because of this adaptive phase tracking scheme.

Constrained two-stage Kalman filter for real-time state estimation of systems with time-varying measurement noise covariance

Robust unscented Kalman filter with adaptation of process and measurement noise covariances

The widely used traditional Kalman filter-type power system dynamic state estimator is unable to address the unknown and non-Gaussian system process and measurement noise as well as dynamical model uncertainties. To this end, this paper proposes a decentralized H-infinity unscented Kalman filter that leverages the strength of the H-infinity criteria developed in robust control for handling system uncertainties with the advantage of the UKF for addressing strong model nonlinearities. Specifically, the statistical linerization approach is used to derive a linear-like batch-mode regression model similar to the linear Kalman filter. This allows us to resort to the linear H-infinity Kalman filter framework for the development of the proposed H-infinity UKF in the Krein space. An analytical form is also derived to tune the parameter of the H-infinity criterion. Two decoupled models are presented to enable the decentralized implementation of the H-infinity UKF using the local PMU measurements. Extensive simulation results carried out on the IEEE 39-bus system show that the proposed H-infinity UKF is able to bound the influences of various types of measurement and model uncertainties while obtaining accurate state estimates.

New analytical solutions of steady-state Kalman gains are presented for a discrete-time tracking filter with correlation in both the measurement noise and the target maneuver. The measurement noise model is a first-order discrete Markov process characterized by a correlation coefficient /spl rho/. The target motion is examined for an exponentially correlated acceleration maneuver type in which the vehicle oscillation such as wind-induced-bending is also considered. The present solution method is based on factorizing the observed spectral density matrix /spl Psi/(z) in frequency domain. The algorithm proposed here gives the Kalman gain matrix directly. For a case when the steady-state error covariance matrix is desired, such gains can be incorporated with the algebraic Riccati equation.

SummaryThis paper presents a novel state estimation approach for linear dynamic systems when measurements are corrupted by outliers. Since outliers can degrade the performance of state estimation, outlier accommodation is critical. The standard approach combines outlier detection utilizing Neyman‐Pearson (NP) type tests with a Kalman filter (KF). This approach ignores all residuals greater than a designer‐specified threshold. When measurements with outliers are used (ie, missed detections), both the state estimate and the error covariance matrix become corrupted. This corrupted state and covariance estimate are then the basis for all subsequent outlier decisions. When valid measurements are rejected (ie, false alarms), potentially using the corrupted state estimate and error covariance, measurement information is lost. Either using invalid information or discarding too much valid information can result in divergence of the KF. An alternative approach is moving‐horizon (MH) state estimation, which maintains all recent measurement data within a moving window with a time horizon of length L. In MH approaches, the number of measurements available for state estimation is affected by both the number of measurements per time step and the number of time steps L over which measurements are retained. Risk‐averse performance‐specified (RAPS) state estimation works within an optimization setting to choose a set of measurements that achieves a performance specification with minimum risk of outlier inclusion. This paper derives and formulates the MH‐RAPS solution for outlier accommodation. The paper also presents implementation results. The MH‐RAPS application uses Global Navigation Satellite Systems measurements to estimate the state of a moving platform using a position, velocity, and acceleration model. In this application, MH‐RAPS performance is compared with MH‐NP state estimation.

This paper investigates the application of multisensor data fusion (MSDF) technique to enhance the state estimation of a nonlinear plant. The proposed method is based on Kalman filters approach to improve the state estimation obtained by the novel adaptive unscented Kalman filter (AUKF). The common trend for the KF implementation assumes pre-specified fixed distribution matrices for both process and measurement noises. Here, however, the variance matrices for both process and measurement noise signals are assumed unknown a priori and thus incrementally estimated and updated using a sliding time window paradigm within which an estimation of the noise variance is calculated and adaptively updated each time the window is shifted forward. The proposed methodology is tested on a simulated continuous stirred tank reactor (CSTR) problem to estimate 4 states of this nonlinear plant. The simulation results demonstrate the superiority of the suggested method in state estimation compared with a previously reported approach.

We present a distributed observer for nonlinear systems, which can be used to estimate the state of a central plant with unknown parameters using a network of sensors that measure noisy linear combinations of the state. Our state estimator is based on the unscented Kalman filter and the dual Kalman filter method, which runs two Kalman filters in parallel for both state and parameter estimation. This allows us to improve estimates of the central plants parameters in order to improve state estimates, and vice versa. Furthermore, using results from stochastic stability analysis, we prove that under certain conditions the expected value of the proposed algorithm's estimation error is bounded. This result also shows us that as t goes to infinity, the error bound scales as a function of the largest eigenvalue of the sensor noise covariance matrix. Lastly, we demonstrate the ability of our state estimator to accurately track the state of nonlinear systems through simulations.