Real-Time Wind Estimation and Tracking with Transponder Downlinked Airspeed and Heading Data

The use of magnetic heading and true air speed measurements made on board civil airplanes to assist in radar tracking is described. The data are telemetered via the air-ground data link of the mode S radar system. A new filter, similar to the first-order Kalman filter, is developed using velocity measurements to bias its prediction equations. This filter follows satisfactorily maneuvers, and estimates, in real time, the wind in the vicinity of the airplane. Finally a scheme is described to remove false data due to data-link corruption.     

A three-state Kalman tracker using position and rate measurements

A three-state Kalman tracker is described for tracking a moving target, such as an aircraft, making use of the position and rate measurements obtained by a track-white-scan radar sensor which employs pulsed Doppler processing, such as the moving target detector providing unambiguous Doppler data. The steady-state filter parameters have been analytically obtained under the assumption of white noise maneuver capability. The numerical computations of these parameters are in excellent agreement with those obtained from the recursive Kalman filter matrix equations. The solution for the case when only the range measurements are available is obtained as a special case of this model. Graphs of normalized covariances and gains are presented to illustrate how the solution depends on different parameters     

A Probabilistic Strongest Neighbor Filter Algorithm for m Validated Measurements

A new form of the probabilistically strongest neighbor filter (PSNF) algorithm taking into account the number of validated measurements is proposed. The probabilistic nature of the strongest neighbor (SN) measurement in a cluttered environment is shown to be varied with respect to the number of validated measurements. Incorporating the number of validated measurements into design of the PSNF produces a consistent and cost effective data association method. Simulation studies show that the new filter is less sensitive to the unknown spatial clutter density and is more reliable for practical target tracking in nonhomogeneous clutter than the existing PSNF. It has similar performances to the probabilistic data association filter amplitude information (PDAF-AI) with much less computational complexities.     

基于改进容积卡尔曼滤波的惯性/光流组合自主测速方法

针对容积卡尔曼滤波算法在惯性/光流组合测速数据融合时出现由于各系统输出数据频率不一致导致融合精度有限的问题,提出了一种基于多速率残差校正的改进容积卡尔曼滤波算法.通过当前时刻误差估算组合导航系统残差,再使用估算后的残差对速度估计值进行补偿,最终实现惯性/光流组合系统速度测量值的数据融合.实验结果表明,通过提出的改进容积...     

IMM estimator with out-of-sequence measurements

In multisensor tracking systems that operate in a centralized information processing architecture, measurements from the same target obtained by different sensors can arrive at the processing center out of sequence. In order to avoid either a delay in the output or the need for reordering and reprocessing an entire sequence of measurements, such measurements have to be processed as out-of-sequence measurements (OOSMs). Recent work developed procedures for incorporating OOSMs into a Kalman filter (KF). Since the state of the art tracker for real (maneuvering) targets is the interacting multiple model (IMM) estimator, the algorithm for incorporating OOSMs into an IMM estimator is presented here. Both data association and estimation are considered. Simulation results are presented for two realistic problems using measurements from two airborne GMTI sensors. It is shown that the proposed algorithm for incorporating OOSMs into an IMM estimator yields practically the same performance as the reordering and in-sequence reprocessing of the measurements. Also, it is shown how the range rate from a GMTI sensor can be used as a linear velocity measurement in the tracking filter.     

Coordinate Conversion and Tracking for Very Long Range Radars

The problem of tracking with very long range radars is studied in this paper. First, the measurement conversion from a radar's r-u-v coordinate system to the Cartesian coordinate system is discussed. Although the nonlinearity of this coordinate transformation appears insignificant based on the evaluation of the bias of the converted measurements, it is shown that this nonlinearity can cause significant covariance inconsistency in the conventionally converted measurements (CM1). Since data association depends critically on filter consistency, this issue is very important. Following this, it is shown that a suitably corrected conversion (CM2) eliminates the inconsistency. Then, initialized with the converted measurements (using CM2), four Cartesian filters are evaluated. It is shown that, among these filters, the converted measurement Kalman filter with second order Taylor expansion (CM2KF) is the only one that is consistent for very long range tracking scenarios. Another two approaches, the range-direction-cosine extended Kalman filter (ruvEKF) and the unscented Kalman filter (UKF) are also evaluated and shown to suffer from consistency problems. However, the CM2KF has the disadvantage of reduced accuracy in the range direction. To fix this problem, a consistency-based modification for the standard extended Kalman filter (E1KF) is proposed. This leads to a new filtering approach, designated as measurement covariance adaptive extended Kalman filter (MCAEKF). For very long range tracking scenarios, the MCAEKF is shown to produce consistent filtering results and be able to avoid the loss of accuracy in the range direction. It is also shown that the MCAEKF meets the posterior Carmer-Rao lower bound for the scenarios considered.     

PDAF with multiple clutter regions and target models

This paper presents the theory of a new multiple model probabilistic data association filter (PDAF). The analysis is generalized for the case of multiple nonuniform clutter regions within the measurement data that updates each model of the filter. To reduce the possibility of clutter measurements forming established tracks, the solution includes a model for a visible target. That is, a target that gives sensor measurements that satisfy one of the target models. Other features included in the algorithm are the selection of a fixed number of nearest measurements and the addition of signal amplitude to the target state vector. The nonuniform clutter model developed here is applicable to tracking signal amplitude. Performance of this algorithm is illustrated using experimentally recorded over-the-horizon radar (OTHR) data.     

Multiple model nonlinear filtering for low signal ground target applications

The design and implementation of a multiple model nonlinear filter (MMNLF) for ground target tracking using ground moving target indicator (GMTI) radar measurements is described. Like the well-known interacting multiple model Kalman filter (IMMKF), the MMNLF is based on the theory of hybrid stochastic systems. However, since it models the probability distribution for the target in a region, rather than just the distribution's first and second moments, a nonlinear filter is able to capture more fine-grained detail of the target motion and requires fewer models than typical IMMKF implementations. This is illustrated here with a two-model MMNLF in which one motion model incorporates terrain constraints while the second is a nearly constant velocity (CV) model. Another feature of the MMNLF is that it enables incorporation of prethresholded measurements. To implement the filter, the target state conditional probability density is discretized on a set of moving grids and recursively updated with sensor measurements via Bayes' formula. The conditional density is time updated between sensor measurements using alternating direction implicit (ADI) finite difference methods, generalized for this hybrid application. In simulation testing against low signal-to-interference-plus-noise ratio (SINR) targets, the MMNLF is able to maintain track in situations where single model filters based on either of the component models or filters that use thresholded data fail. Potential applications of this work include detection and tracking of foliage-obscured moving targets.     

Analytical Steady State Solution for a Kalman Tracking Filter

Analytical expressions are given for the steady state solution to a Kalman tracking filter used in a track-while-scan radar system. The radar sensor measures range and range rate, and both these measurements are utilized in the filter. The solution for range measurements only is obtained as a special case. Graphs are also given which show how the solution depends on different parameters.     

Estimating Optimal Tracking Filter Performance for Manned Maneuvering Targets

The majority of tactical weapons systems require that manned maneuverable vehicles, such as aircraft, ships, and submarines, be tracked accurately. An optimal Kalman filter has been derived for this purpose using a target model that is simple to implement and that represents closely the motions of maneuvering targets. Using this filter, parametric tracking accuracy data have been generated as a function of target maneuver characteristics, sensor observation noise, and data rate and that permits rapid a priori estimates of tracking performance to be made when maneuvering targets are to be tracked by sensors providing any combination of range, bearing, and elevation measurements.     

Batch Recursive Data Compression Schemes for INS Error Estimation

Application of new data compression schemes to aided inertial navigation systems is presented. The need for data compression is motivated by the fact that the external aiding system generates frequent but inaccurate position measurements, which have to be processed by a processor whose computation capability is limited. Two new data compression techniques are presented and their efficiency is demonstrated through covariance simulation runs as well as computational complexity analysis. These schemes are characterized by their ability to process batches of measurements recursively and efficiently. It is demonstrated that the resulting estimation accuracy is comparable to that produced by a Kalman filter which processes optimally the same amount of data, while the required computational effort is reduced.     

Tracking of crossing targets with imaging sensors

The authors present an algorithm for the tracking of crossing targets using the centroid measurement and the centroid offset measurement of the distributed image formed by the targets. The measurements are obtained by a forward-looking infrared (FLIR) imaging sensor. The joint probabilistic data association merged-measurement coupled filter (JPDAMCF) is used for state estimation which performs filtering in a coupled manner for the targets with common measurements. Two filters are examined: one assuming the displacement noise white and the other one modeling it correctly as autocorrelated. The latter is shown to yield substantially better performance. The proposed algorithm demonstrates the usefulness of the JPDAMCF for tracking crossing targets in combination with the models for the centroid and offset measurements. Even though the centroid offset measurement requires more computations and a more complex model for estimation, it yields significantly better results if the filter accounts for its colored measurement noise     

A Tracking Filter in Spherical Coordinates Enhanced by De-noising of Converted Doppler Measurements

Tracking problem in spherical coordinates with range rate (Doppler) measurements, which would have errors correlated to the range measurement errors, is investigated in this paper. The converted Doppler measurements, constructed by the product of the Doppler measurements and range measurements, are used to replace the original Doppler measurements. A de-noising method based on an unbiased Kalman filter (KF) is proposed to reduce the converted Doppler measurement errors before updating the target states for the constant velocity (CV) model. The states from the de-noising filter are then combined with the Cartesian states from the converted measurement Kalman filter (CMKF) to produce final state estimates. The nonlinearity of the de-noising filter states are handled by expanding them around the Cartesian states from the CMKF in a Taylor series up to the second order term. In the mean time, the correlation between the two filters caused by the common range measurements is handled by a minimum mean squared error (MMSE) estimation-based method. These result in a new tracking filter, CMDN-EKF2. Monte Carlo simulations demonstrate that the proposed tracking filter can provide efficient and robust performance with a modest computational cost.     

Removal of Out-of-Sequence Measurements from Tracks

In multisensor tracking systems that operate in a centralized or distributed information processing architecture, measurements from the same target obtained by different sensors can arrive at the processing center out of sequence due to system latencies. In order to avoid either a delay in the output or the need for reordering and reprocessing entire sequences of measurements, such latent measurements have to be processed by the tracking filter as out-of-sequence measurements (OOSM). Recent work developed a "one-step" procedure for incorporating OOSM with multiple-time-step latency into the tracking filter, which, while suboptimal, was shown to yield results very close to those obtained by reordering and reprocessing an entire sequence of measurements. The counterpart of this problem is the need to remove (revocate) measurements that have already been used to update a track state. This can happen in real-world systems when such measurements are reassigned to another track. Similarly to the problem of update with an OOSM, it is desired to carry out the removal of an earlier measurement without recomputing the track estimate (and the data association) using possibly a long sequence of subsequent measurements one at a time. A one-step algorithm is presented for this problem of removing a multistep OOSM.     

Multi-EAP:Extended EAP for multi-estimate extraction for SMC-PHD filter

The ability to extract state-estimates for each target of a multi-target posterior, referred to as multi-estimate extraction (MEE), is an essential requirement for a multi-target filter, whose key performance assessments are based on accuracy, computational efficiency and reliability. The probability hypothesis density (PHD) filter, implemented by the sequential Monte Carlo approach, affords a computationally efficient solution to general multi-target filtering for a time-varying num-ber of targets, but leaves no clue for optimal MEE. In this paper, new data association techniques are proposed to distinguish real measurements of targets from clutter, as well as to associate par-ticles with measurements. The MEE problem is then formulated as a family of parallel single-estimate extraction problems, facilitating the use of the classic expected a posteriori (EAP) estima-tor, namely the multi-EAP (MEAP) estimator. The resulting MEAP estimator is free of iterative clustering computation, computes quickly and yields accurate and reliable estimates. Typical sim-ulation scenarios are employed to demonstrate the superiority of the MEAP estimator over existing methods in terms of faster processing speed and better estimation accuracy.     

A relative navigation system for formation flight

A relative navigation system based on both the Inertial Navigation System (INS) and the Global Positioning System (GPS) is developed to support situational awareness during formation flight. The architecture of the system requires an INS/GPS integration across two aircraft via a data link. A fault-tolerant federated filter is used to estimate the relative INS errors based on relative GPS measurements and a range measurement obtained from the data link. The filter is constructed based on a reduced-order model of the relative INS error process. A method for analyzing the filter performance is presented. A case involving two helicopters in formation flight is studied under three different night trajectories to account for the effect of vehicle motion on the INS state transition matrix. The results of the covariance analysis are compared with actual night results over an instrumented test range.     

Suboptimal filter design with pseudomeasurements for targettracking

A suboptimal Kalman filter design method is presented for the problem of tracking a maneuvering target. The design method is essentially based on linear target dynamics and linear-like structured measurements called pseudomeasurements. The pseudomeasurements are obtained by manipulating the original nonlinear measurements algebraically. The resulting filter has computational advantages over other filters with similar performance. Also, a variant of the Berg model is proposed as a target acceleration model under the assumption of a coordinated turn maneuver. The proposed model is consistent with the underlying assumption. Monte Carlo computer simulation results are included to demonstrate the effectiveness of the proposed suboptimal filter associated with the target acceleration model     

Digital tracking filters with high order correlated measurement noise

The existing algorithms for the design of digital filters with colored measurement noise involve a restriction on the dimension of the measurement error model. Kalman filter equations and state space partition are used to formulate an optimal tracking filter without such restrictions. The input to the new filter are two consecutive measurements, and it is initialized by using the first available measurements and the error model correlation matrix. Several examples illustrate the filter formulation and initialization.     

Adaptive Maximum Likelihood Receiver for Direct-Ranging Applications

Recent interest in direct-ranging navigation methods has prompted new research into practical receiver structures which provide improved signal processing. Maximum likelihood receivers are compared with conventional phase-locked receivers by theoretical and simulation methods as phase estimators based on signal measurements only. Signal-to-noise ratio (SNR) enhancement is examined and filter recommendations made. An adaptive maximum likelihood receiver is then developed which uses both signal measurements and a priori data to improve phase estimation accuracy. Simulation results indicate a 33.3 dB processing gain yielding a ranging error standard deviation of ±15 feet for zero dB received SNR. Nonadaptive and adaptive receivers are fabricated, flight tested, and experimental results reported.     

Reduced state estimator for systems with parametric inputs

A reduced state estimator is derived for systems with bounded parameters as inputs. Optimal filter gains are derived for minimizing the total covariance of the estimation error due to measurement noise and parameter uncertainty. It is shown that these filter gains for a two-state system with a Gaussian parameter satisfy the Kalata relation in steady state. Equations are also derived for optimally filtering measurements in arbitrary time order. This reduced state estimator offers novelties over a traditional Kalman filter in its application to the class of problems considered. The total error covariance, which is minimized, makes no use of plant noise. Furthermore, the filter is easier to optimize in high dimensional and multiple sensor applications as well as in processing out-of-sequence measurements.