The integration of multiple sensors for the purpose of forming an integrated air picture has been intensely investigated in recent years. Assuming no sensor biases and minimal communication latencies, the optimal picture can be formed when all the sensor information is communicated to each network node. The state vectors for a given target at each node should be very similar. However, this does not occur in the presence of sensor bias which has an adverse effect on tracking performance. A method to account for the location, measurement, and attitude biases of the sensors must be employed to improve the accuracy of the target state estimates. This paper presents an absolute sensor alignment method to estimate the sensor bias in a multi-target environment. The output of the alignment process is used to compensate the sensor measurements employed in the tracking process. A comparison is made between the composite tracks generated using compensated and uncompensated measurements from multiple sensors.
The purpose of absolute sensor alignment is to determine the measurement and attitude biases of a sensor in an absolute reference frame. It has been well-documented that the performance of composite tracking with multiple sensors can severely degrade if the sensor measurements are not corrected for the bias. There are well-established metrics to assess the performance of tracking techniques and quantify the effects of other functions on the tracking process. However, there is a lack of metrics to assess sensor alignment techniques apart from other functions. The purpose of this paper is to present metrics for absolute sensor alignment techniques that assess performance apart from other functions. An absolute sensor alignment technique is presented and simulation results are employed to illustrate the alignment metrics.
KEYWORDS: Sensors, Data communications, Monte Carlo methods, Data processing, Data fusion, Matrices, Error analysis, Computing systems, Target recognition, Sensor fusion
Sensor data fusion has long been recognized as a means to improve target tracking. Common practice assumes that the sensors used an synchronous, i.e., they have identical data rate, measurements are taken at the same time, and have no communication delays between sensors platform and central processing center. Such assumptions are invalid in practice. This paper deals with removing such assumptions when considering the multi-sensor target tracking case. In particular, it assumes that the sensors used can have different data rates and communication delays between local and central platforms. A new target tracker using asynchronous sensors is proposed and derived in this paper. The performance of the filter is compared to the optical sequential filter using simulated targets.
The integration of multiple sensors for the purpose of forming a single integrated air picture has been intensely investigated in recent years. Assuming no sensor biases and minimal communication latencies, the ideal picture can be formed when all the sensor information is communicated to each network node. The state vector for each target at every node should be identical under this ideal condition. However, this is not the situation when sensor bias is considered since it has an adverse effect on the tracking performance by increasing the estimation error. A method to account for the location, measurement, and attitude biases of the sensors must be employed to provide more accurate state estimates of the target. This paper will present a method for estimating sensor measurement bias in a multi- target environment. The output of the bias estimation process will be employed to compensate the sensor measurements for the tracking of highly maneuvering aircraft. Utilizing the common tracks of multiple sensors, a comparison between compensated and uncompensated techniques will be provided through simulation.
KEYWORDS: Error analysis, Detection and tracking algorithms, Filtering (signal processing), Sensors, Switching, Process modeling, Performance modeling, Time metrology, Monte Carlo methods, Kinematics
A numeric solution for the fusion of multiple tracks produced form an arbitrary number of asynchronous measurements has been recently developed. This track fusion solution is a weighted sum of the values associated with the previous fused estimate and the multiple individual estimates. This optimal asynchronous track fusion algorithm (OATFA) has properties that are identical to the Kalman filter. However, the deficiencies of the Kalman filter when tracking maneuvering targets are also exhibited by the OATFA but can be overcome with the use of the Interacting Multiple Model (IMM) algorithm. Consequently, it should be possible to replace the Kalman filter commonly employed in a conventional IM algorithm with the OATFA to from the IMM- OATFA. The IMM-OATFA will be developed and simulation result will be used to compare this performance with a conventional IMM tracker.
KEYWORDS: Sensors, Error analysis, Filtering (signal processing), Data processing, Radar, Algorithm development, Monte Carlo methods, Time metrology, Detection and tracking algorithms, Data fusion
An analytic solution for the fusion of track estimates produced from two asynchronous measurements has been recently developed. The fusion process can occur at any time in the interval between the arrival of the second measurement of a fusion interval and the first measurement of the next fusion interval. The solution was stipulated to be a weighted sum of the previous fused estimate and the two individual estimates. The matrix weights are the unknowns for which a solution was formulated. This fusion process has properties that are identical to the Kalman filter. Even though this technique is a breakthrough, it is restricted to the fusion of only two estimates. The objective of this paper is to provide a numeric solution to this track fusion problem with an arbitrary number of asynchronous measurements. Simulation results will be employed to compare the performance of the Kalman filter and the track fusion algorithm in a multisensor environment.
KEYWORDS: Sensors, Filtering (signal processing), Error analysis, Detection and tracking algorithms, Data processing, Data fusion, Composites, Monte Carlo methods, Sensor performance, Switching
the integration of multiple sensors for the purpose of forming a Single Integrated Air Picture (SIAP) is currently being intensely investigated. There are only a few existing techniques that enable SIAP development. Assuming there are no sensor biases and communication latencies, the ideal picture can be formed when all the sensor information is available at each network node. The target state vectors for each picture are identical when they are generated using the same time-ordered data and algorithms. However, this is impractical in a tactical environment and several techniques, such as conventional filtering, optimal track and hybrid fusion, and tracklets, have been proposed to form the SIAP with a reduced amount of data. A combination of techniques will be needed since no single one has the ability to adequately form the picture. The estimation techniques can also be employed to perform sensor alignment. Alignment is the foundation by which the SIAP can be constructed. This paper presents track fusion and tracklet techniques for the purpose of performing target tracking and sensor alignment. Simulation results will be used to illustrate the performance of the estimation techniques.
KEYWORDS: Sensors, Composites, Error analysis, Detection and tracking algorithms, Filtering (signal processing), Radar, Spherical lenses, Data modeling, Monte Carlo methods, Information fusion
The integration of multiple sensors for target tracking is complex but has the potential to provide very accurate state estimates. For most applications, each sensor provides its information to a central location where the integration is performed and the resulting composite track can be very accurate when compared to the individual sensor tracks. This composite track has the potential to provide enhanced system decisions and targeting information not otherwise available. However, sensor bias can severely degrade composite tracking performance when it is not properly considered. This paper presents algorithms and simulation result for the composite tracking of maneuvering targets through the use of multisensor-multisite integration in the presence of sensor residual bias.
The integration of multiple sensors for target tracking has been intensely investigated in recent years. The techniques for integrating multiple sensors are complex but have the potential to provide very accurate state estimates. For most systems, each sensor provides its information to a central location where the integration is performed. This approach is typically employed for a single platform and the resulting composite track can be very accurate when compared to the individual sensor tracks. Additional platforms can also contribute their information to improve this composite track. This composite track has the potential for enhanced system decisions and to provide targeting information not otherwise available. This paper presents algorithms for the composite tracking of maneuvering targets through the use of effective multisensor-multiplatform integration and simulation results illustrating the benefits of the proposed approach.
The measurements for two targets will be merged when the targets are closely-spaced with respect to the resolution of the radar. Improved monopulse processing techniques for an electronically scanned array (ESA) can be used to compute a measurement for each target and used to update the state estimates. However, a substantial amount of radar resources is required to perform this operation. The integration of the ESA with additional sensors has the potential to enhance the tracking and reduce the resource allocation requirements of the ESA when targets are unresolved. A complementary sensor would provide measurements for both targets and can be employed to form a composite track for the ESA. The tracks will not be merged and the ESA can better utilize its resources. This paper presents algorithms for the tracking of maneuvering targets and multisensor integration for effective ESA resource management when tracking of maneuvering targets and multisensor integration for effective ESA resource management when tracking unresolved targets. The sensor suite includes an ESA and an IR Search and Track sensor. The effect of sensor integration on tracking performance and ESA resource allocation will be presented for single and multiple sensor configurations.
KEYWORDS: Antennas, Radar, Error analysis, Erbium, Solids, Sensors, Algorithm development, Detection and tracking algorithms, Statistical analysis, Signal to noise ratio
When two targets are closely-spaced with respect to the resolution of a radar, the measurements of the two targets will be merged when the target echoes are not resolved in angle, range, or radial velocity (i.e., Doppler processing). Monopulse processing is considered for direction-of-arrival (DOA) estimation of two unresolved Rayleigh targets with known relative radar cross section (RCS). The probability distribution of the complex monopulse ratio is developed for two unresolved Rayleigh targets. The Fisher information matrix and Cramer Rao bounds are developed for the DOA estimation of two unresolved Rayleigh targets using a standard monopulse radar. When the two Rayleigh targets are separated by more than one-half of the radar beamwidth, DOA estimation is accomplished for each target by treating the other target as interference. When the two targets are separated by less than one- half of a beamwidth, the antenna boresight is pointed between the two targets, and the mean of the in-phase (i.e., the real part) monopulse ratio and the variance of the in-phase and quadrature monopulse ratios are utilized to estimate the DOAs of the two targets. Simulation results that illustrate performance of the DOA estimators are given along with a simple tracking example.
The integration of multiple sensors for target tracking and resource management has been intensely investigated and several effective techniques have been developed. These conventional techniques employ decision-directed logic and are very complex but have the potential to improve performance. For most systems, each sensor provides its information to a central location where the integration occurs. The central track is employed for system decisions and it is typically not used by the individual sensors. This low level of integration provides a manageable tracking environment but restricts the potential for system improvement. An electronically scanned array (ESA) is highly controllable and has the ability to greatly enhance tracking performance. Resource allocation for an ESA is critical since it must support multiple functions, and several modern techniques have been developed to enhance its performance as a stand-alone sensor by effectively managing its time-energy budget. The integration of an ESA with other sensors can further enhance the tracking and reduce the resource allocation requirements of the ESA. This paper presents a technique for ESA resource management through the use of multisensor integration. The proposed technique avoids the decision-directed logic associated with conventional techniques by employing the interacting multiple model (IMM) algorithm. Simulation results are provided to demonstrate the effectiveness of this modern integration technique.
A stand-off jammer broadcasting wideband nose causes many problems for a tracking algorithm and is one of the Electronic Counter Measure (ECM) techniques employed in the benchmark problem, Benchmark problems for tracking maneuvering targets have been very helpful in the comparison of proposed algorithms because the problems address some 'real world' tracking issues such ECM, false alarms, and target maneuvers. An accurate estimate of the jammer position and power can be accomplished with passive tracking or through the use of the non-target detections during main- lobe jamming. Recent work in the area of monopulse processing provides a method for debiasing the target measurements in the presence of a jammer and employs dwell averaging through the use of multiple frequencies. Proper beam-pointing is also required to maintain an accurate target track. This paper presents a method for tracking maneuvering targets in the presence of jamming as defined by the benchmark problem. Simulation results that illustrate the performance of the measurement debiasing technique and beam-pointing control are also presented.
KEYWORDS: Detection and tracking algorithms, Error analysis, Switching, Performance modeling, Personal digital assistants, Electronic filtering, Algorithm development, Filtering (signal processing), Molybdenum, Monte Carlo methods
Target tracking in clutter is difficult because there can be several contact-to-track associations for a given track update. The nearest neighbor approach is traditionally used but probabilistic methods, such as probabilistic data association (PDA), have since proved more capable. Tracks are also lost during maneuvers and the interacting multiple model (IMM) algorithm has been demonstrated to be effective at tracking maneuvering targets by responding to different target modes. By combining the IMM and PDA, the resulting algorithm responds to target maneuvers and is effective in clutter. The interacting multiple bias model (IMBM) algorithm is also an effective technique when tracking maneuvering targets but considers the target acceleration a system bias. The bias is estimated in an IMM algorithm framework and then used to compensate a constant velocity filter estimate. The integrated PDA filter will be incorporated into the IMBM algorithm and applied to tracking maneuvering targets in clutter. A performance comparison of IMM and IMBM techniques for tracking maneuvering targets in clutter will also be presented.
This paper presents a solution to a second benchmark problem for tracking highly maneuvering targets in the presence of False Alarms (FA) and Electronic Counter Measures (ECM) and involves beam pointing control of a phased array radar. The proposed solution utilizes an Interacting Multiple Model (IMM) algorithm in conjunction with the Integrated Probabilistic Data Association Filter (IPDAF) when there are measurements of uncertain origin. The output of the IMM algorithm is used to compute the time for the next measurement in order to maintain a given level of tracking performance which was established to prevent track loss. A testbed simulation program that includes the effects of target amplitude fluctuations, beamshape, missed detections, target maneuvers, FA, ECM, and track loss was used to evaluate performance. For this benchmark problem, the `best' tracking algorithm is the one that requires a minimum amount of radar energy while satisfying a 5% lost track constraint.
Track maintenance refers to the process of fusing sensor contacts to existing tracks in order to estimate the target state. Target tracking in cluttered environments is difficult because there can be several contact-to-track associations for a given track. The Nearest Neighbor (NN) approach, which uses the contact nearest the predicted measurement, is an early maintenance algorithm for clutter but its performance greatly suffers because alternative hypotheses are not considered. Probabilistic methods, such as the Probabilistic Data Association (PDA) and Integrated PDA (IPDA), are superior because all hypotheses are considered. The PDA inherently assumes that the track exists where as the IPDA does not. A single PDA or IPDA filter has difficulty with maneuvering targets and will therefore be incorporated into the Interacting Multiple Model (IMM) algorithm. For illustrative purposes, simulation studies will be used to compare the performance of the algorithms.
Since phased array radars have the ability to perform adaptive sampling, proper radar control can improve many aspects associated with the tracking of multiple maneuvering targets. Techniques have been developed to significantly reduce the sampling of a maneuvering target in which the savings in the radar time-energy budget can be reallocated to accomplish other functions. However, controlling the revisit time becomes more difficult when the target is maneuvering in the presence of false alarms. The technique proposed in this paper used the Interacting Multiple Model (IMM) algorithm and Integrated Probabilistic Data Association Filter (IPDAF), combined to form the IMM-IPDAF, to track maneuvering targets and control the radar revisit time in the presence of false alarms.
Since phased array radars have the ability to perform adaptive sampling of the target trajectory by radar beam positioning, proper control of the radar has the potential for significantly improving many aspects associated with the tracking of multiple maneuvering targets. When supported by additional sensors, the sampling of the phased array radar can be reduced significantly. However, controlling the revisit times of the phase array radar becomes more difficult. The technique proposed in this paper uses the Interacting Multiple Model algorithm to track maneuvering targets and control the radar revisit time and pointing when the radar is supported by a Precision Electronic Support Measures (PESM) sensor. Algorithms for tracking with multiple sensors, computing the radar revisit time, and pointing the radar are presented in this paper. Performance comparisons are given with the radar using adaptive data rates and the PESM providing measurements at regular intervals and intermittently.
An algorithm for the automatic formation of tracks is developed for maneuvering targets in cluttered environments. This track formation algorithm consists of Integrated Probabilistic Data Association Filters (IPDAFs) in an Interacting Multiple model (IMM) configuration, and it is referred to as the IMM-IPDAF algorithm. The IMM portion of the IMM-IPDAF will consist of several filters based on different dynamical models to handle target maneuvers. Each of the filters will be an IPDAF to deal with the problem of track existence in the presence of clutter. Although the primary purpose of this paper is to deal with the track formation problem, the IMM-IPDAF can also be used for the maintenance of existing tracks and the termination of tracks for targets when they disappear. For illustrative purposes, simulations will be used to compare the performance of the IMM-IPDAF algorithm to other track formation algorithms.
One of the more difficult problems in target tracking involves the use of a phased array radar to track an aircraft performing high speed maneuvers. Most tracking algorithms use single motion model track filters whose performance can degrade significantly when the target maneuvers. Multiple model algorithms can be used to improve the tracking accuracy and avoid the decision-directed techniques of single model track filters for maneuvering response. The interacting multiple model (IMM) algorithm uses multiple models that interact through state mixing to track a target maneuvering through an arbitrary trajectory. When tracking highly maneuvering targets with a phased array radar (i.e., agile beam), the issue of radar beam pointing is critical because poor pointing can lead to missed detections and eventually declaring lost tracks. The IMM algorithm provides a better method for beam pointing when compared to single model filters. This paper compares single and multiple model track filters with track loss as a measure of effectiveness. The effects of target maneuvers, data rate, track filter configuration, and radar beam pointing on the percentage of tracks lost are discussed. A phased array radar simulation that includes a fluctuating target, probability of detection, radar beamshape effects, and monopulse processing was used to assess the track loss performance of each algorithm.
This paper presents a solution to a benchmark problem for tracking maneuvering targets. The benchmark problem involves beam pointing control of a phased array (i.e., an agile beam) radar against highly maneuvering targets. The proposed solution utilizes an interacting multiple model (IMM) algorithm that includes a constant velocity model, a constant thrust model, and a constant speed turn model. The output error covariance of the IMM algorithm is used to compute the time for the next measurement so that a given level of tracking performance is maintained. Using this on-line measure of tracking performance automatically takes into account target range, target maneuvers, missed detections, and strength of the returns. A testbed simulation program that includes the effects of target amplitude fluctuations, beamshape, missed detections, finite resolution, target maneuvers, and track loss is used to evaluate the performance of the proposed algorithm. The `best' tracking algorithm as defined by the benchmark problem is the one that requires a minimum number or radar dwells while satisfying a constraint of 4% on the maximum number of lost tracks. The proposed technique lost less than 2% of the tracks and provided average sample periods of 3.6 s for the commercial aircraft trajectory and 1.9 s for targets maneuvering with as much as 7 g's.
One of the more difficult targets to track is an aircraft performing high speed maneuvers. The Interacting Multiple Model (IMM) algorithm uses multiple models that interact through state mixing to track a target maneuvering through an arbitrary trajectory. The IMM algorithm provides significantly better tracking results when compared to a single model track filter. To improve tracking performance, multiple sensors can be used to provide more information about the target. Using the measurements from several sensors with a single motion model track filter can provide improved track performance when compared to a single sensor system. Since single sensor track filters use decision-directed approaches for maneuver response, using multiple sensors with a single model track filter would be difficult to implement because periodic measurement updates cannot be expected and the sensors may be dissimilar with different accuracies. Thus a very complex tracking algorithm would be required. While the tracking performance of a single model may improve with additional sensors, it can be erratic for maneuvering targets. Using multiple sensors with the IMM algorithm can improve the IMM algorithm performance without the erratic performance exhibited by single model trackers. Target tracking with multisensor systems is described along with the IMM algorithm. Comparisons of track performance with IMM algorithm and single motion model track filters are presented for several sensor systems.
Several multiple model techniques have been applied to the tracking of maneuvering targets. The two techniques which provide the best tracking performance for maneuvering targets are the Second Order General Pseudo-Bayesian (GPB2) and Interacting Multiple Model (IMM) algorithms. In both algorithms, the dynamics of the system is represented by multiple models which are hypothesized to be correct and model switching probabilities governed by a first order Markov process. The authors have developed an extension of the IMM algorithm, the second order Interacting Multiple Model (IMM) algorithm, which provides improved tracking performance when compared to that of the IMM and GPB2 algorithms for applications with large measurement errors and low data rates. In the IMM2 algorithm, the state estimate is computed under each possible model hypothesis for the two most recent sample periods with each hypothesis using a different combination of the previous model- conditional estimates. Thus, the IMM2 algorithm requires r2 filters for r models. The development of the IMM2 algorithm is given along with a summary of multiple model estimation for tracking maneuvering targets and simulation results for the IMM, GPB2, and IMM2 algorithms.
Since phased array radars have the ability to perform adaptive sampling by the radar beam, proper control of the radar has the potential for significantly improving many aspects associated with the tracking of multiple maneuvering targets. The technique proposed in this paper uses the Interacting Multiple Model (IMM) algorithm to track maneuvering targets and control the sampling time and energy levels. Since the output of the IMM algorithm better represents the accuracy of the state estimates during a maneuver than a single model filter, the IMM algorithm is used to compute and on-line measure of tracking performance to determine the scheduling time of the next track update sample period in order to maintain a given level of performance. The sample time is computed as the one positive root of a polynomial equation of the sample period. The model probabilities of the IMM algorithm are also used to schedule the energy level of a radar dwell. As a result, the update times for the filter are a function of track filter performance and the target trajectory. Algorithms for computing the sample time and energy level using the output of the IMM algorithm are developed in this paper. Performance comparisons are given for the IMM algorithm using constant data rates, scheduled energy levels, and adaptive data rates.
The interacting multiple method (IMM) algorithm is an effective technique for tracking maneuvering targets. The IMM algorithm uses multiple models that interact through state mixing to track a target maneuvering through an arbitrary trajectory. The state estimates are mixed according to their model probabilities and the model switching probabilities that are governed by an underlying Markov chain. In the IMM algorithm, the probability pij of switching from model i to model j is often assumed to be uniform between each measurement update. However, for multiple sensors operating asynchronously or a sensor with a probability of detection less than one, the data will be aperiodic. To overcome this limitation, the model switching probabilities are modeled as time-dependent. IMM algorithms with constant and time-dependent model switching probabilities are evaluated for the cases of a two sensor tracking system and a sensor with a probability of detection of detection less than one.
KEYWORDS: Detection and tracking algorithms, Lithium, Kinematics, Data modeling, Signal processing, Data processing, Switching, Error analysis, Motion models, Coastal modeling
The interacting multiple model (IMM) algorithm uses multiple models that interact through state mixing to track a target maneuvering through an arbitrary trajectory. However, when a target maneuvers through a coordinated turn, the acceleration vector of the target changes magnitude and direction, and the maneuvering target models commonly used in the IMM (e.g., constant acceleration) can exhibit considerable model error. To address this problem an IMM algorithm that includes a constant velocity model, a constant speed model with the kinematic constraint for constant speed targets, and the exponentially increasing acceleration (EIA) model for maneuver response is proposed. The constant speed model utilizes a turning rate in the state transition matrix to achieve constant speed prediction. The turning rate is calculated from the velocity and acceleration estimates of the constant speed model. The kinematic constraint for constant speed targets is utilized as a pseudomeasurement in the filtering process with the constant speed model. Simulation results that demonstrate the benefits of the EIA model and the kinematic constraint to the IMM algorithm are given. The tracking performance of the proposed IMM algorithm is compared with that of an IMM algorithm utilizing constant velocity and constant turn rate models.
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