Felix Govaers

An Exact Solution to Track-to-Track-Fusion at Arbitrary Communication Rates

Track-to-track fusion (T2TF) aims at combining locally preprocessed information of individual trackers at a fusion center. Particularly, such schemes are obligatory in many applications of distributed sensors because of limited communication resources. If T2TF yields equivalent results compared with a Kalman filter (KF) processing all measurements from every sensor, it might be called optimal T2TF. It is well known that this can be achieved for deterministically moving targets, or if the local sensor tracks produced at all individual scan times are available in the fusion center. However, if such a full-rate communication is not available, achieving optimal performance is a great challenge due to cross-correlations between the local tracks. In this paper, we show that track decorrelation and therefore optimal T2TF can be achieved if sensor properties such as the measurement error covariance and measurement function are known at the each tracking system. To this end, local tracks have to be modified and local optimality has to be given up. As a result, we provide a distributed Kalman-type processing scheme for maneuvering targets, which yields optimal T2TF results at arbitrarily chosen instants of time by communicating and combining the local sensor tracks. Applications can be found in tracking scenarios with dynamically changing bandwidth constraints.

Coupled sonar inertial navigation system for pedestrian tracking

This paper presents a novel method for indoor pedestrian tracking using inertial sensing and sonar sensors. The zero velocity updating technique, which is used to enhance the performances of inertial sensing, cannot observe heading, resulting in a horizontal position drift. Sonar sensors are used as complementary technique to correct heading. The main idea is to extract a partial map of surrounding walls. Sonar returns are processed via the Hough transformation to extract wall segments (line features). The first detected segments will initiate a wall landmark. The pedestrian relative distance to next detected segments that are associated to a stored wall landmark, is considered to be his relative distance to that wall. An extended Kalman filter based solution to Bearing-Range simultaneous localization and mapping is used. The state vector is a concatenation of pedestrian position and positions of first points of each stored wall landmark, to which the virtual Bearing-range measurements are pointing. Both inertial and coupled sonar inertial tracks are visually compared to the true trajectory.

Evaluation of network effects on the Kalman filter and accumulated state density filter

Command and control applications are important especially in tactical scenarios. For such scenarios wireless multi-hop networks may be deployed as they can be used even when there is no infrastructure left. Due to the specific characteristics of these networks the problem of Out-of-Sequence (OoS) measurements for tracking applications arises. In this paper, we present an exhaustive, realistic evaluation of OoS measurements induced by network protocol effects. To this end, we compare a standard Kalman filter to an accumulated state density filter. The results show that in wireless multi-hop networks a filter that can deal with OoS measurements is needed.

Out-of-sequence processing of cluttered sensor data using multiple evolution models

In target tracking applications, the full information on the kinematic target states accumulated over a certain time window up to the present time is contained in the joint probability density function of these state vectors, given the time series of all sensor data. In the structure of this Accumulated State Density (ASD) has been revealed. Furthermore, ASDs enable us to process Out-of-Sequence (OoS) measurements in a neat and straightforward way. This paper presents an algorithm for the processing of OoS measurements in situations with more relaxed assumptions. On the one hand, sensors often return ambiguous measurement data. Then, measurement association methodologies as the Multi-Hypothesis Tracker (MHT) are required. On the other hand, the evolution model in use might not be unique. The well-known approach to this challenge is the Interacting Multiple Model (IMM) filter. In this paper, an IMM/MHT extension to the ASD paradigm is discussed, tested by simulation, and evaluated.

Generalized solution to smoothing and out-of-sequence processing

The increasing trend towards multi-sensor systems is driving a requirement for distributed tracking algorithms. In such systems, communication links often suffer from varying delays, which leads to timely disordered data at the fusion center. The challenge of online processing delayed data is generally known as the Out-of-Sequence (OoS) problem. An exact solution to this problem is given by the Accumulated State Density (ASD) filter. However, the Rauch-Tung-Striebel retrodiction1 is inherently integrated to the ASD approach. This implies that a certain number of states has to be updated at each filtering step. In this paper, we present the generalized solution to the OoS problem. In particular, we derive the exact update formula for single states, which refer to older and newer instants of time than a given measurement. As a consequence, OoS data can be processed without applying retrodiction. This also includes a novel smoothing scheme, which uses the exact cross-covariances of a measurement and a past state without any recursion. A numerical evaluation shows that this smoothing scheme is about 25% faster than the Rauch-Tung-Striebel equations while still being exact.

An exact solution to track-to-track fusion using accumulated state densities

Originally the Accumulated State Density (ASD) has been proposed to provide an exact solution to the out-of-sequence measurement problem. To this end, the posterior of the joint density of all states accumulated over time was derived for a single sensor scenario. An exact solution for T2TF has been published as the Distributed Kalman Filter (DKF). However, the DKF is exact only if global knowledge in terms of the measurement models for all sensors are available at a local processor. This paper demonstrates that an exact solution for T2TF can also be achieved as a convex combination of local ASDs generated at each node in a distributed sensor system. This method crucially differs from the DKF, in that an exact solution is achieved without each processing platform being required to have knowledge of the global information. Therefore, this theoretical development has significant potential for achieving exact T2TF in practical problems. The resulting algorithm is called the Distributed Accumulated State Density (DASD) filter.

Device-free indoor localization using a distributed network of autonomous UWB sensor nodes

In this paper we describe a method for localization of multiple persons using a distributed network of autonomous ultra-wideband sensor nodes. The persons do not carry any devices or tags to aid their detection, but are instead detected by using the time variations they impose on the measured channel impulse response between a transmitter and a receiver. The described method uses background subtraction and constant false alarm rate algorithms for person detection. Range tracking is incorporated for removal of clutter and false observations. The range information of the persons with respect to each sensor is fused using a maximum likelihood function. Here, we analyze the influences of range tracking on location estimation. In addition, two location estimation approaches are compared. The first approach fuses the available range information of the persons with respect to all sensors of the network. In the second approach locations are estimated by each sensor node and are later fused with the location estimates from the other sensors. The system implementation and selected methods for device-free person range estimation and sensor data fusion are verified in a realistic measurement scenario with two moving persons and through-wall operation of all sensors. The method can be used for near real-time localization and tracking of multiple moving persons.

Information form distributed Kalman filtering (IDKF) with explicit inputs

With the ubiquity of information distributed in networks, performing recursive Bayesian estimation using distributed calculations is becoming more and more important. There are a wide variety of algorithms catering to different applications and requiring different degrees of knowledge about the other nodes involved. One recently developed algorithm is the distributed Kalman filter (DKF), which assumes that all knowledge about the measurements, except the measurements themselves, are known to all nodes. If this condition is met, the DKF allows deriving the optimal estimate if all information is combined in one node at an arbitrary time step. In this paper, we present an information form of the distributed Kalman filter (IDKF) that allows the use of explicit system inputs at the individual nodes while still yielding the same results as a centralized Kalman filter.

Target existence probability in the distributed Kalman filter

In this paper, the target existence probability for a single target in clutter is derived. More specifically, the paper considers target existence in the distributed Kalman filter. First, a conceptual solution is derived explicitly for a two-sensor case, and second a moment-matching approximation is performed, which enables computational tractability. The results can be generalized to arbitrary numbers of sensors.

Track-before-detect in distributed sensor applications

In this article, we propose a new extension to a Dynamic Programming Algorithm (DPA) approach for Track-before-Detect challenges. This extension enables the DPA to process time-delayed sensor data directly. Such delay might appear because of delays in communication networks. The extended DPA is identical to the recursive standard DPA in case of all sensor data appear in the timely correct order. Furthermore, an intense evaluation of the Accumulated State Density (ASD) filter is given on simulation data. Last but not least, we apply a combination of DPA and ASD on data of a real radar system and present the resulting tracks. Our experience concerning this combination is a seamless cooperation between the track initialization by DPA and a track maintenance by ASD filter.