A PDF multisensor multitarget tracker

A previously presented probability density function (pdf) multitarget tracker is extended to a more complex and difficult problem. The input data is bearing measurements from multiple sensors over time, which includes clutter (false alarms) and true measurements (from detected targets) with errors. Targets may be missed. The output is the real-time determination of the number of targets present and their geographic x,y location. The implementation is the recursive numerical computation of the discrete pdf of each target and is derived from the conceptual joint pdf of all targets     

GPS navigation with increased immunity to modeling errors

A robust extended Kalman filter (EKF) is presented for GPS navigation with outlying errors in the GPS measurements due to failed satellites or unmodeled errors. In this approach, the innovation step of the conventional EKF is modified using the robust statistics concept to obtain a more accurate state estimate in the presence of outlying errors. Performance of the proposed robust EKF in comparison with the conventional EKF, and adaptive EKF is demonstrated through simulation results.     

A fusion and learning algorithm for landing aircraft tracking:compensating for exhaust plume disturbance

An algorithm is presented for tracking a landing aircraft using fusion of two different passive sensors, a laser range finder (LRF) and a forward-looking infrared (FLIR) camera. The main feature of this algorithm is its ability to identify and compensate for an exhaust plume disturbance. The algorithm is based on the extended Kalman filter (EKF) and the filtering confidence function (FCF) which introduces a learning approach to the tracking problem. The results of a simulation using the learning tracking algorithm and the EKF alone are presented and compared     

Streamlining measurement iteration for EKF target tracking

The estimation problem is defined, and a review of how the linear estimation approach of Kalman filtering is extrapolated to form an extended Kalman filter (EKF), applicable for state estimation in nonlinear systems is presented. A mechanization of an EKF variation known as an iterated EKF, offering improved tracking performance, is treated. A streamlined version of an iterated EKF that has a lesser computational burden (fewer operations per cycle or time step) than prior formulations is offered. A nonlinear filtering application example, to be used as a testbed for this new approach, is described, and the detailed modeling considerations as needed for exoatmospheric random-variable radar target tracking are discussed. The performance of the streamlined mechanization is illustrated in this radar target tracking example, and comparisons are made with the performance of an EKF without measurement iteration     

A PDF multitarget tracker

A probability density function (pdf) based approach to the multitarget tracking problem is presented. The input data are obtained by measurements over time from a front-end detector. The desired output is the number of targets present and the parameters of each target. The same approach has previously been used for time delay detection and tracking problems and is adapted to this problem This approach is an alternative to the traditional approach of “association” and “tracking” on the measurements     

The Effect of Jamming on Monopulse Accuracy

An expression is applied for the probability density function (pdf) of the monopulse ratio when skin echoes from a passive target are contaminated by interference from a jammer. The analysis is valid for arbitrary signal-to-jam ratio and arbitrary locations of the target and jammer in the beam. For an on-axis skin target and a stand-off jammer at an off-axis location, the "pulling" effect of the jammer and the accuracy of the angle estimate are compared with the approximations currently employed in radar performance analysis. The pdf of the monopulse ratio for large and for small signal-to-jam ratios is presented, showing that the pdf is bimodal at small signal-to-jam ratio.     

Adaptive Two-Stage Extended Kalman Filter for a Fault-Tolerant INS-GPS Loosely Coupled System

The well-known conventional Kalman filter requires an accurate system model and exact stochastic information. But in a number of situations, the system model has an unknown bias, which may degrade the performance of the Kalman filter or may cause the filter to diverge. The effect of the unknown bias may be more pronounced on the extended Kalman filter (EKF), which is a nonlinear filter. The two-stage extended Kalman filter (TEKF) with respect to this problem has been receiving considerable attention for a long time. Recently, the optimal two-stage Kalman filter (TKF) for linear stochastic systems with a constant bias or a random bias has been proposed by several researchers. A TEKF can also be similarly derived as the optimal TKF. In the case of a random bias, the TEKF assumes that the information of a random bi?s is known. But the information of a random bias is unknown or partially known in general. To solve this problem, this paper proposes an adaptive two-stage extended Kalman filter (ATEKF) using an adaptive fading EKF. To verify the performance of the proposed ATEKF, the ATEKF is applied to the INS-GPS (inertial navigation system-Global Positioning System) loosely coupled system with an unknown fault bias. The proposed ATEKF tracked/estimated the unknown bias effectively although the information about the random bias was unknown.     

Recursive estimation of radar biases using electronic charts

This work describes the application of the extended Kalman filter (EKF) to the estimation of range and bearing biases in marine radars by performing a map-matching between the data from hydrographic charts and the radar images. By defining at least two corresponding points from the radar image and the electronic charts, the technique provides a rapid and accurate calibration in range and bearing, giving also estimates for the speed, heading, latitude, and longitude of the ship. The method is tested with simulated data to check convergence and later with real data obtained from a navigation console installed on a patrol boat The technique does not require GPS nor speed information from the ship log unit, however it is shown that their inclusion can improve the estimation.     

An Upper Bound on Detection Probability for Fluctuating Signals

In the theory of signal detectability, the signal-to-noise ratio (SNR), defined as the quotient of the average received signal energy and the spectral density of the white Gaussian noise, is a fundamental parameter. For a signal which is exactly known, or known except for a random phase, this ratio uniquely defines the detection performance which can be achieved with a matched filter receiver. However, when the signal amplitude is a random parameter, the detection performance is changed and must be determined from the probability density function (pdf) of the amplitude. Relative to the case of a constant signal amplitude, such signal amplitude fluctuation usually degrades performance when a high probability of detection (Pd) is required, but improves performance at low values of Pd; the corresponding change in the required SNR is the so-called signal fluctuation loss Lf. Thus, since Lf in some cases represents an improvement in performance for low values of Pd, a question of at least theoretical interest is: how large might this improvement be, when the class of all signal amplitude pdf's is considered. The solution, presented here, results in a lower bound on the signal fluctuation loss Lf as a function of Pd, or equivalently an upper bound on Pd as a function of SNR. The corresponding most favorable pdf was determined using the Lagrange multiplier technique and results of a numerical maximization are included to provide insight into the general properties of the solution.     

EMD-EKF方法研究

应用扩展卡尔曼滤波(EKF)时需要估计量测噪声的统计特性。文中针对观测噪声统计特性描述不准确导致的EKF性能下降的问题,利用经验模态分解方法(Empirical Mode Decomposition,EMD)可以分离信号和噪声的特性,提出了一种在未知量测噪声条件下的EKF方法。该方法可以跟踪观测噪声的变化,即实现了对量测噪声的估计,从而解决了在未知量测噪声的情况下的EKF问题。仿真结果表明可运用于无源定位中。     

On-line Vehicle Motion Estimation from Visual Terrain Information Part II: Ground Velocity and Position Estimation

An algorithm, combining velocity/height estimates, obtained from an airborne body fixed image shift estimator with auxiliary on-board measurements and sparsely stored terrain profile information constitutes an entirely passive autonomous navigation system suitable for moderate-g flight missions. Two versions are addressed. The "naive estimator," in which altitude estimates are multiplied by velocity/height estimaters, yields ground velocity. Position, obtained by integration, diverges with time. The "extended Kalman filter" (EKF) version, in which velocity and position are defined as state space components, locks on the stored terrain profile and does not diverge with time. It degenerates into the "naive estimator" if the terrain is completely flat. Numerical examples indicate excellent performance potential of the EKF estimator.     

Multiple Gaussian Targets: The Track-on-Jam Problem

When a radar with amplitude comparison monopulse arithmetic encounters signals from multiple Gaussian sources it will "point" to the centroid of the incident radiation. The probability density function (pdf) of the monopulse ratio when N independent samples of difference and sum signals are processed in a maximum likelihood receiver is derived. For finite jam-to-noise ratio the estimate has a bias which is independent of N. The variance in the estimate does however depend upon N. Central moments of order less than or equal 2N - 2 exist and are given by a simple formula. Plots of the pdf and its bias and variance for various jam-to-noise ratios, locations of the centroid with respect to the boresight direction, and number of samples processed are presented in the accompanying figures.     

UKF方法及其在方位跟踪问题中的应用

采用UKF(Unscented Kalman Filter)方法处理了平面内地面站对目标的方位跟踪的估计问题。目标的位置和速度由选定的高斯分布采样点来近似，在每个更新过程中，采样点随着状态方程传播并随着非线性测量方程变换，由此不但得到目标位置和速度的均值及较高的计算精度，而且避免了对非线性方程的线性化过程。仿真结果表明，UKF方法比传统的扩展卡尔曼滤波(EKF)算法有更高的估计精度，并能有效地克服非线性严重时，方位跟踪问题中很容易出现的滤波发散问题。     

Noise subspace techniques in non-gaussian noise using cumulants

We consider noise subspace methods for narrowband direction-of-arrival or harmonic retrieval in colored linear non-gaussian noise of unknown covariance and unknown distribution. The non-gaussian noise covariance is estimated via higher order cumulants and combined with correlation information to solve a generalized eigenvalue problem. The estimated eigenvectors are used in a variety of noise subspace methods such as multiple signal classification (MUSIC), MVDR and eigenvector. The noise covariance estimates are obtained in the presence of the harmonic signals, obviating the need for noise-only training records. The covariance estimates may be obtained nonparametrically via cumulant projections, or parametrically using autoregressive moving average (ARMA) models. An information theoretic criterion using higher order cumulants is presented which may be used to simultaneously estimate the ARMA model order and parameters. Third- and fourth-order cumulants are employed for asymmetric and symmetric probability density function (pdf) cases, respectively. Simulation results show considerable improvement over conventional methods with no prewhitening. The effects of prewhitening are particularly evident in the dominant eigenvalues, as revealed by singular value decomposition (SVD) analysis     

基于无迹卡尔曼滤波法的串联型电池系统 荷电状态估计研究

以锂离子电池为载体的电源系统为航天器稳定可靠运行提供了一种有效的方式.多个电池单体经串联可扩大电池系统容量,即串联型电池系统.为准确估计串联型锂离子电池系统的荷电状态(State of Charge,SOC),针对扩展卡尔曼滤波(Extended Kalman Filter,EKF)计算复杂、精度不高等问题,结合串联型电池系统空间状态方程,提出基于无迹卡尔曼滤波法(Unscented Kalman Filter,UKF)的串联型电池系统荷电状态估计算法.在恒流和脉冲两种工况下,通过对比分析UKF与EKF算法的仿真结果与实验数据的匹配情况,证明了提出算法的准确性和高鲁棒性.     

Quadratic extended Kalman filter approach for GPS/INS integration

GPS/INS integration system has been widely applied for navigation due to their complementary characteristics. And the tightly coupled integration approach has the advantage over the loosely coupled approach by using the raw GPS measurements, but hence introduces the nonlinearity into the measurement equation of the Kalman filter. So the typical method for navigation using measurements of range or pseudorange is by linearizing the measurements in an extended Kalman filter (EKF). However, the modeling errors of the EKF will cause the bias and divergence problems especially under the situation that the low quality inertial devices are included. To solve this problem, a quadratic EKF approach by adding the second-order derivative information to retain some nonlinearities is proposed in this paper. Simulation results indicate that the nonlinear terms included in the filtering process have the great influence on the performance of integration, especially in the case that the low quality INS is used in the integrated system. Furthermore, a two-stage cascaded estimation method is used, which circumvents the difficulty of solving nonlinear equations and greatly decreases the computational complexity of the proposed approach, so the quadratic EKF approach proposed in this paper is of great value in practice.     

Tracking in Clutter using IMM-IPDA?Based Algorithms

We describe three single-scan probabilistic data association (PDA) based algorithms for tracking manoeuvering targets in clutter. These algorithms are derived by integrating the interacting multiple model (IMM) estimation algorithm with the PDA approximation. Each IMM model a posteriori state estimate probability density function (pdf) is approximated by a single Gaussian pdf. Each algorithm recursively updates the probability of target existence, in the manner of integrated PDA (IPDA). The probability of target existence is a track quality measure, which can be used for false track discrimination. The first algorithm presented, IMM-IPDA, is a single target tracking algorithm. Two multitarget tracking algorithms are also presented. The IMM-JIPDA algorithm calculates a posteriori probabilities of all measurement to track allocations, in the manner of the joint IPDA (JIPDA). The number of measurement to track allocations grows exponentially with the number of shared measurements and the number of tracks which share the measurements. Therefore, IMM-JIPDA can only be used in situations with a small number of crossing targets and low clutter measurement density. The linear multitarget IMM-IPDA (IMM-LMIPDA) is also a multitarget tracking algorithm, which achieves the multitarget capabilities by integrating linear multitarget (LM) method with IMM-IPDA. When updating one track using the LM method, the other tracks modulate the clutter measurement density and are subsequently ignored. In this fashion, LM achieves multitarget capabilities using the number of operations which are linear in the: number of measurements and the number of tracks, and can be used in complex scenarios, with dense clutter and a large number of targets.     

M-ary CPSK Detection with Noisy Reference and Interferences

A general expression of the error probability on an M-ary coherent phase-shift-keyed (MCPSK) signal purturbed by a noisy reference carrier, multiple interferences, and additive Gaussian noise is presented taking into account the frequencey divider in the carrier recovery circuit. First, a new expression for the probability density function (pdf) of the phase of a composite wave of signal, multiple interferences, and additive Gaussian noise is derived. Then this result and a pdf of the phase error modified from the Tikhonov distribution are used to obtain the erro probability of an MCPSK detector. In addition, the comparison between the error probabilities with and without the frequency divider is given, and it is found that the estimation is more pessimistic when the frequency divider is included.     

估计理论在飞行数据相容性检验中的应用

飞行数据相容性检验在飞行试验数据分析中是很重要的。由于飞行试验测量数据中存在着各种过程噪声(如大气紊流)和测量噪声(如尺度因子偏差、常值系统偏差等),这些误差将会导致飞行数据各通道之间不相容。利用估计理论进行飞行状态估计,同时估计出未知的尺度因子,系统偏差,即进行飞行轨迹重构被认为是飞行数据相容性(一致性)检验的强有力的工具。本文利用推广卡尔曼滤波和信息平方根滤波及平滑进行高速飞机飞行数据的相容性检验,提出了飞机纵向运动和全面运动的新模型,通过仿真和实际计算得出满意的结果。     

Tracking an incoming ballistic missile using an extended interval Kalman filter

The important tracking problem by radar of an incoming ballistic missile system, which contains uncertainty in modeling and noise in both dynamics and measurements, is studied. The classical extended Kalman filter (EKF) is no longer applicable to such an uncertain system, and so a new extended interval Kalman filter (EIKF) is developed for tracking the missile system. Computer simulation is presented to show the effectiveness of the EIKF algorithm for this uncertain and nonlinear ballistic missile tracking problem.