Self-Tuning Multisensor Weighted Measurement Fusion Kalman Filter

For the multisensor systems with unknown noise variances, based on the solution of the matrix equations for the correlation function, the on-line estimators of the noise variance matrices are obtained, whose consistency is proved using the ergodicity of sampled correlation function. Further, two self-tuning weighted measurement fusion Kalman filters are presented for the multisensor systems with identical and different measurement matrices, respectively. Based on the stability of the dynamic error system, a new convergence analysis tool is presented for a self-tuning fuser, which is called the dynamic error system analysis (DESA) method. A new concept of convergence in a realization is presented, which is weaker than the convergence with probability one. It is rigorously proved that the proposed self-tuning Kalman fusers converge to the steady-state optimal Kalman fusers in a realization or with probability one, so that they have asymptotic global optimality. A simulation example for a target tracking system with 3 sensors shows their effectiveness.     

Properties of Staggered PRF Radar Spectral Components

Expressions for moving target indicator (MTI) improvement factor limitation due to pulse repetition frequency (PRF) staggering and loss of target detectability for various values of Doppler frequency in the passband are presented. It is also shown that the product of variance of stagger periods and clutter variance is an important parameter determining the performance of a staggered PRF MTI radar.     

Track-to-track fusion with dissimilar sensors

An analysis is described of a kinematic state vector fusion algorithm when tracks are obtained from dissimilar sensors. For the sake of simplicity, it is assumed that two dissimilar sensors are equipped with nonidentical two-dimensional optimal linear Kalman filters. It is shown that the performance of such a track-to-track fusion algorithm can be improved if the cross-correlation matrix between candidate tracks is positive. This cross-correlation is introduced by noise associated with target maneuver that is common to the tracking filters in both sensors and is often neglected. An expression for the steady state cross-correlation matrix in closed form is derived and conditions for positivity of the cross-correlation matrix are obtained. The effect of positivity on performance of kinematic track-to-track fusion is also discussed     

On optimal track-to-track fusion

Track-to-track fusion is an important part in multisensor fusion. Much research has been done in this area. Chong et al. (1979, 1986, 1990) among others, presented an optimal fusion formula under an arbitrary communication pattern. This formula is optimal when the underlying systems are deterministic, i.e., the process noise is zero, or when full-rate communication (two sensors exchange information each time they receive new measurements) is employed. However, in practice, the process noise is not negligible due to target maneuvering and sensors typically communicate infrequently to save communication bandwidth. In such situations, the measurements from two sensors are not conditionally (given the previous target state) independent due to the common process noise from the underlying system, and the fusion formula becomes an approximate one. This dependence phenomena was also observed by Bar-Shalom (1981) where a formula was derived to compute the cross-covariance of two track estimates obtained by different sensors. Based on this results a fusion formula was subsequently derived (1986) to combine the local estimates which took into account the dependency between the two estimates. Unfortunately, the Bayesian derivation made an assumption that is not met. This work points out the implicit approximation made and shows that the result turns out to be optimal only in the ML (maximum likelihood) sense. A performance evaluation technique is then proposed to study the performance of various track-to-track fusion techniques. The results provide performance bounds of different techniques under various operating conditions which can be used in designing a fusion system.     

Probability hypothesis density filter with adaptive parameter estimation for tracking multiple maneuvering targets

The probability hypothesis density (PHD) filter has been recognized as a promising tech-nique for tracking an unknown number of targets. The performance of the PHD filter, however, is sensitive to the available knowledge on model parameters such as the measurement noise variance and those associated with the changes in the maneuvering target trajectories. If these parameters are unknown in advance, the tracking performance may degrade greatly. To address this aspect, this paper proposes to incorporate the adaptive parameter estimation (APE) method in the PHD filter so that the model parameters, which may be static and/or time-varying, can be estimated jointly with target states. The resulting APE-PHD algorithm is implemented using the particle filter (PF), which leads to the PF-APE-PHD filter. Simulations show that the newly proposed algorithm can correctly identify the unknown measurement noise variances, and it is capable of tracking mul-tiple maneuvering targets with abrupt changing parameters in a more robust manner, compared to the multi-model approaches.     

The Effect of the Common Process Noise on the Two-Sensor Fused-Track Covariance

This note deals with the effect of the common process noise on the fusion (combination) of the state estimates of a target based on measurements obtained by two different sensors. This problem arises in a multisensor environment where each sensor has its information processing (tracking) subsystem. In the case of an ?-? tracking filter the effect of the process noise is that, over a wide range of its variance, the uncertainty area corresponding to the fused estimates is about 70 percent of the single-sensor uncertainty area as opposed to 50 percent obtained if the dependence is ignored.     

Canonical transform for tracking with kinematic models

A canonical transform is presented that converts a coupled or uncoupled kinematic model for target tracking into a decoupled dimensionless canonical form. The coupling is due to non-zero off-diagonal terms in the covariance matrices of the process noise and/or the measurement noise, which can be used to model the coupling of motion and/or measurement between coordinates. The decoupled dimensionless canonical form is obtained by simultaneously diagonalizing the noise covariance matrices, followed by a spatial-temporal normalization procedure. This canonical form is independent of the physical specifications of an actual system. Each subsystem corresponding to a canonical coordinate is characterized by its process noise standard deviation, called the maneuver index as a generalization of the tracking index for target tracking, which characterizes completely the performance of a steady-state Kalman filter. A number of applications of this canonical form are discussed. The usefulness of the canonical transform is illustrated via an example of performance analysis of maneuvering target tracking in an air traffic control (ATC) system.     

Maneuvering target tracking using IMM method at high measurementfrequency

The problem of tracking a maneuvering target with a high measurement frequency is considered. The measurement noise is significantly correlated when the measurement frequency is high. A simple decorrelation process is proposed to enhance the interacting multiple model (IMM) algorithm to track a maneuvering target with correlated measurement noise. It is found that the decorrelation process may improve system performance significantly, especially in velocity and acceleration estimations     

An improved quaternion Gauss–Newton algorithm for attitude determination using magnetometer and accelerometer

For the vector attitude determination, the traditional optimal algorithms which are based on quaternion estimator(QUEST) measurement noise model are complicated for just two observations. In our application, the magnetometer and accelerometer are not two comparable kinds of sensors and both are not small field-of-view sensors as well. So in this paper a new unit measurement model is derived. According to the Wahba problem, the optimal weights for each measurement are obtained by the error variance researches. Then an improved quaternion Gauss–Newton method is presented and adopted to acquire attitude. Eventually, simulation results and experimental validation employed to test the proposed method demonstrate the usefulness of the improved algorithm.     

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.     

Use of measurements from an imaging sensor for precision targettracking

The extraction of measurements for precision tracking of the centroid of a target from a forward-looking infrared imaging sensor is presented. The size of the image of the target is assumed to be small, i.e. around 10 pixels. The statistical characterization of the centroid of the target is obtained. Similarly, the statistical properties of the image correlation of two frames, which measures the target offset, are derived. Explicit expressions that map the video noise statistics into measurement noise statistics are obtained. The offset measurement noise is shown to be autocorrelated. State variable models for tracking the target centroid with these measurements are then presented. Simulation results and quantitative conclusions about achievable subpixel tracking accuracy are given. It is shown that the filter that models the autocorrelated measurement noise provides the best performance     

应用卡尔曼滤波的机载雷达跟踪系统

本文论述将滤波理论应用于机载雷达中对单个目标进行距离、速度、方位角和高低角跟踪的多环反馈系统。首先根据目标和天线的相对运动建立控制四坐标跟踪环所需的状态矢量微分方程,然后推导相应的非线性滤波算法。最后给出计算机的模拟结果。计算机模拟的结果清晰地说明采用最佳滤波的系统性能比通常的有很大改善,并且这种瞄准轴坐标系的最佳系统对目标的随机机动是不灵敏的。 本文所讨论的方法和得出的结论可以延用到地面雷达、舰载雷达以及其他有源和无源的跟踪系统。     

A nonlinear IMM algorithm for maneuvering target tracking

In target tracking, the measurement noise is usually assumed to be Gaussian. However, the Gaussian modeling of the noise may not be true. Noise can be non-Gaussian. The non-Gaussian noise arising in a radar system is known as glint noise. The distribution of glint noise is long tailed and will seriously affect the tracking performance. We develop a new algorithm that can effectively track a maneuvering target in the glint environment The algorithm incorporates the nonlinear Masreliez filter into the interactive multiple model (IMM) method. Simulations demonstrate the superiority of the new algorithm     

Discrete-time min-max tracking

The problem of optimal state estimation of linear discrete-time systems with measured outputs that are corrupted by additive white noise is addressed. Such estimation is often encountered in problems of target tracking where the target dynamics is driven by finite energy signals, whereas the measurement noise is approximated by white noise. The relevant cost function for such tracking problems is the expected value of the standard H/sub /spl infin// performance index, with respect to the measurement noise statistics. The estimator, serving as a tracking filter, tries to minimize the mean-square estimation error, and the exogenous disturbance, which may represent the target maneuvers, tries to maximize this error while being penalized for its energy. The solution, which is obtained by completing the cost function to squares, is shown to satisfy also the matrix version of the maximum principle. The solution is derived in terms of two coupled Riccati difference equations from which the filter gains are derived. In the case where an infinite penalty is imposed on the energy of the exogenous disturbance, the celebrated discrete-time Kalman filter is recovered. A local iterations scheme which is based on linear matrix inequalities is proposed to solve these equations. An illustrative example is given where the velocity of a maneuvering target has to be estimated utilizing noisy measurements of the target position.     

一种基于冗余测量的自适应卡尔曼滤波算法

针对目前自适应滤波算法的不足,在测量系统量测噪声方差未知的情况下,设计了一种基于冗余测量的自适应卡尔曼滤波(RMAKF)算法。通过对系统冗余测量值的一阶、二阶差分序列进行有效的统计分析,可以准确估计系统量测噪声统计特性,进而在滤波过程中自适应调节噪声方差阵R,提高滤波精度。以全球定位系统/惯性导航系统(GPS/INS)松组合导航系统为对象进行了仿真实验,结果表明该算法在测量系统噪声特性未知或发生改变时,可对其进行准确估计,在采用低精度惯性器件情况下,滤波结果较其他主要自适应卡尔曼滤波算法有较明显的改进。     

Performance evaluation of track fusion with information matrixfilter

In a multisensor environment, each sensor detects multiple targets and creates corresponding tracks. Fusion of tracks from these, possibly dissimilar, sensors yields more accurate kinematic and attribute information regarding the target. Two methodologies have been employed for such purpose, which are: measurement fusion and state vector fusion. It is well known that the measurement fusion approach is optimal but computationally inefficient and the state vector fusion algorithms are more efficient but suboptimal, in general. This is so because the state vector estimates to be fused obtained from two sensors, are not conditionally independent in general due to the common process noise from the target being tracked. It is to be noted that there are three approaches to state vector fusion, which are: weighted covariance, information matrix, and pseudomeasurement. This research is restricted solely to performance evaluation of the information matrix form of state vector fusion. Closed-form analytical solution of steady state fused covariance has been derived as a measure of performance using this approach. Note that the results are derived under the assumptions that the two sensors are synchronized and no misassociation or merged measurement is considered in the study. Results are compared with those using Monte Carlo simulation, which was used in the past to predict fusion system performance by various authors. These results provide additional insight into the mechanism of track fusion and greatly simplify evaluation of fusion performance. In addition, availability of such a solution facilitates the trade-off studies for designing fusion systems under various operating conditions     

Efficient target tracking using dynamic programming

A dynamic programming (DP) algorithm has been developed for the detection and tracking of subpixel-sized, low signal-to-noise ratio (SNR) targets observed by side-or forward-looking imaging sensors. A distinguishing feature of this approach is that target detection and tracking are combined into a single optimization procedure that takes into account statistical models of target motion, background noise, and clutter. Current work has led to a number of technical innovations that improve the performance and efficiency of the DP tracking algorithm, including the development of a new track scoring function, and an extension to the basic DP algorithm that reduces computation requirements by over an order of magnitude. A prototype infrared (IR) target tracking system incorporating these enhancements has been implemented for a step-starting IR camera application. Sensitivity improvements of several decibels over conventional sequential detection and tracking algorithms were realized     

Architectures and algorithms for track association and fusion

Target tracking using multiple sensors can provide better performance than using a single sensor. One approach to multiple target tracking with multiple sensors is to first perform single sensor tracking and then fuse the tracks from the different sensors. Two processing architectures for track fusion are presented: sensor to sensor track fusion, and sensor to system track fusion. Technical issues related to the statistical correlation between track estimation errors are discussed. Approaches for associating the tracks and combining the track state estimates of associated tracks that account for this correlation are described and compared by both theoretical analysis and Monte Carlo simulations     

基于OTHR与纯角度传感器群数据关联的模式辨识与定位精度提升

 天波超视距雷达(OTHR)目标跟踪面临着"三低"(低检测概率、低数据率和低测量精度)和"多径"(多条传播路径)的挑战,因此传播模式的准确辨识与目标定位精度提升是改善跟踪能力的关键。首先利用纯角度传感器群获得目标地理位置的初步估计,然后采用极大似然估计建立了OTHR的传播模式和杂波模式的辨识规则,进而利用最小方差估计准则实现OTHR和纯角度传感器群的量测融合。仿真结果表明,此算法的模式辨识正确率很高,能明显提升方位角的测量精度,但是不能明显提升径向距的精度。     

Update with out-of-sequence measurements in tracking: exact solution

In target tracking systems measurements are typically collected in "scans" or "frames" and then they are transmitted to a processing center. In multisensor tracking systems that operate in a centralized manner, there are usually different time delays in transmitting the scans or frames from the various sensors to the center. This can lead to situations where measurements from the same target arrive out of sequence. Such "out-of-sequence" measurement (OOSM) arrivals can occur even in the absence of scan/frame communication time delays. The resulting "negative-time measurement update" problem, which is quite common in real multisensor systems, was solved previously only approximately in the literature. The exact state update equation for such a problem is presented. The optimal and two suboptimal algorithms are compared on a number of realistic examples, including a GMTI (ground moving target indicator) radar case.