Chun Yang

Nonlinear constrained tracking of targets on roads

Ground targets are constrained to move on the Earths surface and are most likely to travel along a road network. For targets on road, their interaction with the environment and with each other particularly at intersections is more structured, thus useful to tracking algorithms. Indeed, the knowledge of terrain database and road maps can be used as constraints and incorporated into the tracking algorithms. In this paper, we set forth a nonlinear formulation of tracking multiple interacting targets along road networks and apply nonlinear filtering techniques (namely, the extended Kalman filter, the unscented Kalman filter, the particle filter, and a hybrid Kalman particle filter) to the problem for such scenarios as air-to-ground surveillance. Simulation results are present to illustrate the performance of the nonlinear filters with the nonlinear formulation as compared to conventional ones.

Performance Measures of Covariance and Information Matrices in Resource Management for Target State Estimation

In target tracking, sensor resource management (SRM) assigns to each target a best combination of sensors, which requires performance analysis of track filter updates. Two popular implementations of track filters are the Kalman filter (or covariance filter) and the information filter. SRM with Kalman filters attempts to minimize the estimation error covariance matrix-based scalar performance measures, whereas SRM with information filters aims to maximize the information matrix-based counterpart. In this paper, we investigate issues related to scalar performance measures and, in particular, compare the use of trace, determinant, and eigenvalues of the covariance matrix or information matrix as scalar performance measures. The study demonstrates which matrix measures are appropriate for resource management applications. Furthermore, the study shows when the matrix measures lead to equivalent goals. While this analysis is agnostic to the type of measurement, the paper demonstrates how to accommodate bearing and range measurements. Overall, the analysis provides insight about how sensor measurements best reduce uncertainty so that we can properly exploit performance measures to satisfy requirements of practical tracking and SRM applications.

Kalman Filtering with Nonlinear State Constraints

In [Simon and Chia, 2002], an analytic method was developed to incorporate linear state equality constraints into the Kalman filter. When the state constraint is nonlinear, linearization was employed to obtain an approximately linear constraint around the current state estimate. This linearized constrained Kalman filter is subject to approximation errors and may suffer from a lack of convergence. In this paper, we present a method that allows exact use of second-order nonlinear state constraints. It is based on a computational algorithm that iteratively finds the Lagrangian multiplier for the nonlinear constraints. The method therefore provides better approximation when higher order nonlinearities are encountered. Computer simulation results are presented to illustrate the algorithm

Mobile positioning via fusion of mixed signals of opportunity

In this article, we investigated several SOOPs for mobile positioning without GPS and compared their signal characteristics for navigation and tracking. Critical issues in positioning with SOOP were discussed, which include the lack of independent SOOP (poor GDOP), SOOP clock errors, 2-D vs. 3-D solutions, multipath and NLOS signals, and signal integrity, among others. We described the development of mobile test-beds with hardware and software features and presented field test results. The signals of opportunity that we have successfully acquired and tracked with our test-beds and then used to derive navigation solutions include GPS, DTV, GSM, and IS95/CDMA2000 (1xRTT) signals. Based on the comparative assessments and test results, this article advocates the use of mixed (hybrid/fused) signals of opportunity, which has the potential to alleviate several technical difficulties faced by positioning with SOOP. Our ongoing effort is to expand our software radios to include other communication and broadcast signals and modulation schemes and to perform cooperative position localization.

Optimal Placement of Heterogeneous Sensors for Targets with Gaussian Priors

An optimal strategy for geometric sensor placement to enhance target tracking performance is developed. Recently, a considerable amount of work has been published on optimal conditions for single-update placement of homogeneous sensors (same type and same measurement quality) in which the targets are either assumed perfectly known or the target location uncertainty is averaged out via the expected value of the determinant of the Fisher information matrix (FIM). We derive conditions for optimal placement of heterogeneous sensors based on maximization of the information matrix to be updated by the heterogeneous sensors from an arbitrary Gaussian prior characterizing the uncertainty about the initial target location. The heterogeneous sensors can be of the same or different types (ranging sensors, bearing-only sensors, or both). The sensors can also make, over several time steps, multiple independent measurements of different qualities. Placement strategies are derived and their performance is illustrated via simulation examples.

Mutual-aided target tracking and identification

Mutual-aided target tracking and target identification schemes are described by exploiting the couplings between the target tracking and target identification systems, which are typically implemented in a separate manner. A hybrid state space approach is formulated to deal with continuous-valued kinematics, discrete-valued target type, and discrete-valued target pose (inherently continuous but quantized). We identify and analyze ten possible mutual aiding mechanisms with different complexity in different levels. The coupled tracker design is illustrated within the context of JointSTARS using GMTI and HRRR measurements as well as digital terrain and elevation data (DTED) and road map among others. The resulting coupled tracking and identification system is expected to outperform the separately designed systems particularly during target maneuvers, for recovering from temporary data dropout, and in a dense target environment.

Post-correlation semi-coherent integration for high-dynamic and weak GPS signal acquisition

Acquisition and ultimate tracking of a weak GPS signal faces several technical challenges, notably, possible data bit sign reversal every 20 ms and tolerable frequency error inversely proportional to the integration interval. Brute force search over all possible combinations of the unknown values is computationally prohibitive. Assisted GPS relying on external infrastructure for timing, data bit, and frequency error information is costly. Coherent techniques such as the block accumulating coherent integration over extended interval (BACIX) have recently been proposed to increase coherent integration. Although efficient, such coherent methods may still be too expensive except for high-end receivers and may not maintain the SNR performance when there are large frequency changes over the extended integration interval. In this paper, we set forth a novel method that utilizes the semi-coherent scheme for post-correlation integration. It is named as block accumulating semi-coherent integration of correlations (BASIC) and can be viewed as an extension of the BACIX algorithm. Although less sensitive than coherent integration, semi-coherent integration based on inter-block conjugate products is computationally more efficient. In addition, it can handle large frequency changes. The BASIC algorithm is first formulated in the paper. Computer simulation results are then presented to illustrate the operation and performance of the BASIC algorithm for joint estimation of the initial frequency, chirping rate (rate of change in frequency), bit sync, and bit sign pattern.

Nonlinear tracking evaluation using absolute and relative metrics

Tracking performance is a function of data quality, tracker type, and target maneuverability. Many contemporary tracking methods are useful for various operating conditions. To determine nonlinear tracking performance independent of the scenario, we wish to explore metrics that highlight the tracker capability. With the emerging relative track metrics, as opposed to root-mean-square error (RMS) calculations, we explore the Averaged Normalized Estimation Error Squared (ANESS) and Non Credibility Index (NCI) to determine tracker quality independent of the data. This paper demonstrates the usefulness of relative metrics to determine a model mismatch, or more specifically a bias in the model, using the probabilistic data association filter, the unscented Kalman filter, and the particle filter.

Cooperative position location with signals of opportunity

When the reception of GPS signals becomes unreliable, an alternative is to explore signals of opportunity (SOOP) for positioning. Broadcast digital radio transmissions (e.g., digital TV signals) contain field and segment sync codes, which can be used for ranging even though it was not originally designed for so. Another example is the wireless local area network (WLAN) signals. However, there are two major difficulties. Although the location of SOOP sources is known, the number of independent SOOP sources and their geometric distribution may not be favorable for precise positioning. Besides, the clocks of SOOP transmitters are not synchronized, each subject to a different bias and drift. To respond to the 2009 NAECON Grand Challenge, we set forth a cooperative position location approach. The proposed concept makes use of differential ranges between cooperative devices to a common SOOP source, the relative ranges between the cooperative devices, and displacement measurements by the cooperative devices. The cooperation among networked location devices not only allows them to choose the most appropriate positioning mechanism but also provides them with additional measurements to reduce the number of SOOP otherwise required. In addition to data exchange, the radio link between two cooperative devices also allows for estimation of their clock offset. This leads to a joint position location solution via fixed-point smoothing. In this paper, we present the proposed system concept, its subsystems, and their operations and also analyze preliminary simulation results.

A simple maneuver indicator from target’s range-doppler image

Tracking maneuvering targets presents a great challenge to airborne surveillance radar signal processing and sensor systems management systems. Smears caused by an uncompensated maneuver (either translational or rotational) affect target identification (ID) with distorted target images. An unexpected maneuver introduces large position estimation errors to a tracker and in the worst case loss of track. On the other hand, a sensor manager relies upon an expected performance of a tracker to schedule its resources so as to maintain target ID/tracker performance. To aid a sensor management cost function, we present a simple target maneuver indicator (TMI) specifically for the operational condition of target maneuverability. It relates the slope of a targets range-Doppler image to the underlying turn rate, if the target undergoes a maneuver. As an intermediate product of the range profile formation process, this approach provides an easy and quick indication of target maneuverability and, under favorable conditions, an estimate of such a maneuver (e.g., the turn rate), which can be incorporated into the tracking algorithm of the tracker.