Paul R. Kalata

The Tracking Index: A Generalized Parameter for α-β and α-β-γ Target Trackers

A generalized, optimal filtering solution is presented for the target tracking problem. Applying optimal filtering theory to the target tracking problem, the tracking index, a generalized parameter proportional to the ratio of the position uncertainty due to the target maneuverability to that due to the sensor measurement, is found to have a fundamental role not only in the optimal steady-state solution of the stochastic regulation tracking problem, but also in the track initiation process. Depending on the order of the tracking model, the tracking index solution yields a closed form, consistent set of generalized tracking gains, relationships, and performances. Using the tracking index parameter, an initializing and tracking procedure in recursive form, realizes the accuracy of the Kalman filter with an algorithm as simple as the well-known α-β filter or α-β-γ filter depending on the tracking order.

Sensor fusion for mobile robot navigation

We review techniques for sensor fusion in robot navigation, emphasizing algorithms for self-location. These find use when the sensor suite of a mobile robot comprises several different sensors, some complementary and some redundant. Integrating the sensor readings, the robot seeks to accomplish tasks such as constructing a map of its environment, locating itself in that map, and recognizing objects that should be avoided or sought. The review describes integration techniques in two categories: low-level fusion is used for direct integration of sensory data, resulting in parameter and state estimates; high-level fusion is used for indirect integration of sensory data in hierarchical architectures, through command arbitration and integration of control signals suggested by different modules. The review provides an arsenal of tools for addressing this (rather ill-posed) problem in machine intelligence, including Kalman filtering, rule-based techniques, behavior based algorithms, and approaches that borrow from information theory, Dempster-Shafer reasoning, fuzzy logic and neural networks.

/spl alpha/-/spl beta/ target tracking with track rate variations

Considers the theoretical and practical implementation of the /spl alpha/-/spl beta/ tracking process under the influence of track rate variations and/or track period perturbations. These considerations are necessary when the /spl alpha/-/spl beta/ tracker is used in the Benchmark 96 target tracking problem, a challenge to the tracking community to generate tracking solutions to for a set of maneuvering targets under the influence of false alarms, mis-detections and electronic countermeasures which upset the constant track measurement rate. The tracking solution must be able to handle track period perturbations. This paper describes the process to select and adjust the /spl alpha/-/spl beta/ parameters during track initiation and track perturbations due to mis- or false detections.

An Information-theoretic Interpretation of Stability and Observability

Many dynamical models which have been analyzed in the context of system theory, can also be viewed as communication channels with memory. In this interpretation, the systems input is a transmitted message and the observation, or output, is the received message. Information-theoretic measures like entropy, mutual information and capacity can therefore be employed, and key concepts in system thery, such as observability, controllability and stability, can be expressed in information-theoretic terms. In this paper we study certain linear Markovian models from this viewpoint Observability of a Markovian linear discrete-in system is shown to be related to entropies of the initial state and the output observation. Stability is found to pertain to the capacity of the channel which represents the system. The derived relations expose the role of information flow in dynamical system behavior and suggest applications for other liner and nonlinear models.

Explicit formulas for two state Kalman, H/sub 2/ and H/sub /spl infin// target tracking filters

The continuous time, two state, target tracking problem is considered from the Kalman, H/sub 2/, and H/sub /spl infin// filter viewpoint. While previous treatments were numerical in nature, analytic transient responses and infinite horizon solutions with analytic performance expressions are presented here. Tracking indices, involving the maneuver and measurement uncertainties, are shown to have a role for both the steady state and transient responses. In addition, the H/sub /spl infin// tracker has a sensor index involving the performance bound and measurement uncertainty, which, along with the tracking index, plays a significant role in the H/sub /spl infin// tracker expressions. Analytical expressions for the probability of target escape, the probability that the target position will be outside the radar beamwidth (BW), are developed not only to compare the performance of various trackers, but also as a design tool to meet tracking specifications. Examples illustrate the performance of the target trackers as a function of the error gain upper bound.

Range gate pull off (RGPO): detection, observability and /spl alpha/-/spl beta/ target tracking

This paper considers the range gate pull off (RGPO) tracking problem, an electronic counter measure (ECM) which is included in the Benchmark 96 Target Tracking Problem. In RGPO, the target senses the radar pulse and repeats it with a control delay. The amplified, repeated/delayed pulse results in a false range measurement with signal-to-noise (S/N) ratio larger than the real target range measurement confusing the radar/target detection and tracking process. A false range measurement, r/sup ft//sub k/, appears along with the true range measurement, r/sub k/, and depending on the controlled delay motion causes range tracking bias, velocity and/or acceleration pull-off {r/sub po/, v/sub po/, a/sub po/} and eventually lost target track. Fundamental characteristics of the RGPO are considered from a target tracking viewpoint: the nature of the RGPO, the detection of true and false range measurements, the tracking observability, and the RGPO range /spl alpha/-/spl beta/ tracking. It is shown that it is impossible to track the true target using the false range measurement. Ironically, it is also shown that the RGPO false measurements intended to defeat target tracking contains information which can be used to improve the true target track. A practical RGPO /spl alpha/-/spl beta/ matrix tracking process is presented which tracks both true and false targets with improved performance.

Observability conditions for biased linear time invariant systems

This paper addresses the existence of bias estimators in linear time invariant (LTI) systems. One approach to bias estimation is state augmentation, in which a new state corresponding to each unknown bias term is appended to the state vector. The Kalman filter is then applied to the augmented system and the biases are identified as part of the filtering process. A simplified observability rank test for the existence of bias estimators for a LTI system with unknown, constant state and measurement biases has been recently derived. A reduced row observability test matrix is used to show a necessary and sufficient condition for complete bias observability. This paper investigates the use of additional measurements in the system and their ability to alter the bias observability conditions of the system. Examples are presented.

On Kalman, H/sub /spl infin// and H/sub 2/ target tracking: probability of target escape

This paper considers the Kalman, H/sub /spl infin// and H/sub 2/ continuous time, steady state, target tracking problem. The target escape criteria is examined, in particular the probability that the position estimate will sufficiently degrade causing the target to be outside the radar beam width. Analytical expressions for the probability of target escape are developed not only to compare the performance of the various filters, but also as a design tool to meet tracking specifications. It is shown that the Kalman and H/sub 2/ trackers have a lower probability of escape than the H/sub /spl infin// tracker when the target manoeuvrability is Gaussian and within the tracker design setting. Conversely, the H/sub /spl infin// process generally has a lower probability of escape than the Kalman and H/sub 2/ trackers when the target manoeuvrability is a pulse acceleration.

Optimal and sub-optimal fusion of α-β target tracks

This paper considers the optimal and sub-optimal fusion of position measurements to track a maneuvering target. The sub-optimal technique allows α-β filters to operate on measurements separately, yielding distinct target tracks. These tracks are then fused into one via a linear combiner. Derived in closed-form is the inter-relational performance between the α-β filters and the MSE optimal coefficients of the linear combiner. The optimal technique uses a Kalman filter to derived an α-β Matrix Fusion Tracker in closed-form. The α-β Matrix Fusion Tracker is a set of optimal α-β fusion tracking parameters based solely on measurement errors, measurement update time and target maneuverability. It is shown that the α-β Matrix Fusion Tracker is equivalent to a steady-state Kalman filter with stationary noise processes. Furthermore, it is shown that the measurement fusion process can be reduced to a single optimal α-β filter operating on the combined measurement from two measurement inputs. This technique results in the derivation of the α-β Fusion Tracker. Numerical examples are presented to show the relative performance between optimal and sub-optimal fusion techniques and also to verify all derived results.

Discrete time H/sub /spl infin// control/estimation applied to the target tracking problem using a variation of parameters approach

Provides a complete derivation of the discrete time H/sub /spl infin// controller and filter using a variation of parameters approach. We show that the H/sub /spl infin// filter has a similar structure to the Kalman filter. These results are consistent with existing derivations under alternative techniques. Conditions, derived from the variational technique, which provide for filter existence are presented. As an example, the Kalman, H/sub 2/, and H/sub /spl infin// filters are applied to the steady state target tracking problem where their performance is examined.