Converted Measurement Kalman Filter Research Articles

Bistatic Radar Tracking With Significantly Improved Bistatic Range Accuracy

Tracking with bistatic radar measurements is a challenging problem due to the nonlinear relationship between the radar measurements and the Cartesian coordinates, especially for long distances. This nonlinearity leads, for 3-D bistatic radar, to a nonellipsoidal measurement uncertainty region in Cartesian coordinates, similar to a thin contact lens, that causes consistency problems for a tracking filter. The recently developed conversion of the bistatic radar measurements into Cartesian coordinates enables to maintain consistency by using a converted measurement Kalman filter. However, such a filter suffers from a poor bistatic range accuracy, limiting the multitarget tracking performance in a dense environment of targets or clutter. A solution is suggested by using a filter in the measurement coordinate system and converting its results into Cartesian coordinates. Consistent Cartesian estimation is obtained together with significantly improved filtered bistatic range accuracy. The latter is important in data association, resulting in a measurement-to-track association gates that are over an order of magnitude smaller compared to the Cartesian filters. It is shown that if the data association is performed in sensor coordinates, the (Cartesian) volume of the contact lens association region is over 20 times smaller than if it is performed in Cartesian coordinates because the ellipsoid in the latter case is extremely conservative.

Research on Extended Target-Tracking Algorithms of Sea Surface Navigation Radar

To solve the problem of false tracks generated by breakdowns and clutter in point-target tracking in polar coordinates, a fusion tracking algorithm based on a converted measurement Kalman filter and random matrix expansion is proposed. The converted measurement Kalman filter (CMKF) transforms the polar coordinate data of the target at the current time into Cartesian coordinates without bias. Based on linear measurements and states, the position of the extended target and the group target was predicted and updated by using a random matrix, and its track was drawn by combining the nearest neighbors to realize the tracking of the size, shape and azimuth of the extended target. Compared with point-target tracking, the accuracy of extended multi-target tracking was increased by 45.8% based on data measured using NAVICO navigation radar aboard ships at sea. The experimental results showed that the improved method in this paper could effectively reduce the interference of clutter on target tracking and provide more information about the target motion features.

Expediting recovery of autonomous underwater vehicles in dynamic mission environments: A system‐of‐systems challenge for underwater warfare

AbstractAs autonomous underwater vehicle (AUV) adoption increases, operators demand advanced behaviors from commercial off‐the‐shelf systems. However, new behaviors can often only be deployed operationally once assured. This paper overviews research into expediting recovery to an operator's vessel through a custom homing behavior, demonstrating technology advancement in conjunction with test and evaluation activities. Advanced docking infrastructure and frameworks are still under development, yet current AUV operations require rapid and reliable recovery when mission factors change. Homing is achieved with a directional acoustic transponder providing range and bearing data to the AUV from the operator's vessel. A converted measurement Kalman filter processes range and bearing data that generates dynamic waypoints for the AUV through MOOS‐IvP as a backseat driver; a universal approach and filtering that is unique from prior AUV research. Results from simulations and field trials were analysed through a modular and experimental Test & Evaluation framework that was adopted specifically to help verify and validate the new AUV behavior, including systematic variations in recovery boat manoeuvres. The process includes documented use for the first time in AUV research of combinatorial screening (high throughput testing) and an average standardized residual metric to focus development early, encourage constructive iteration and build operational and engineering trust. Consistent homing was demonstrated with localization within 0.3 m and homing within 1.8 m of a moving digital acoustic transponder.

Decorrelated Debiased Converted Measurement Kalman Filter for Phased Array Radar Tracking System

In this article, the target tracking of phased array radars with measurements specified in the direction cosine coordinate system is considered. The converted measurement Kalman filter is a widely adopted technique since it allows tracking in the coordinate system in which the dynamics of targets are described. The converted measurement Kalman filter has two types of inherent bias: conversion and estimation biases. The compensation of conversion bias has been examined by earlier studies using the debiasing technique in the presence of estimation bias. This article, therefore, introduces decorrelated debiased converted measurement Kalman filter (DDCMKF) in the direction cosine coordinate system to relieve the estimation bias. The decorrelation between the Kalman gain and measurement residual by applying conditioning on predicted position estimates is first introduced. The range-rate measurement is subsequently incorporated as a pseudo-measurement form after the derivation of decorrelated converted position. Finally, a sequential DDCMKF in direction cosine coordinates is developed using the derived converted position and range-rate measurement models. Adopting sequential filtering for incorporating the range-rate measurement reduces computation complexity and alleviates its strong nonlinearity. Numerical simulations are conducted to evaluate the performance of DDCMKF against other types of tracking filters in the direction cosine coordinate system. Simulation results show that the proposed DDCMKF achieves preferable error performance while maintaining consistency, especially in short-range tracking with relatively large direction cosine errors.

An EM algorithm for target tracking with an unknown correlation coefficient of measurement noise

In practical applications, the range rate used in a target tracking algorithm will further increase the strong nonlinearity between the measurement and the state, and the unknown correlation coefficient of measurement noise between the range and the range rate will cause suboptimal gain of the filter, which will seriously affect the performance of the filter. In this paper, an expectation maximization (EM)-based sequential modified unbiased converted measurement Kalman filter is proposed for target tracking with an unknown correlation coefficient of measurement noise between the range and the range rate. Firstly, a pseudo measurement is constructed by multiplying the range and the range rate to reduce the strong nonlinearity. The mean and covariance of converted errors are subsequently derived using modified unbiased converted measurement (MUCM) to weaken the error caused by the linearization of the measurement equation, which will effectively improve the dynamic accuracy of target tracking. Then, the converted errors of the position and the pseudo measurement are decorrelated by Cholesky factorization to facilitate the subsequent identification of the correlation coefficient, and the posterior probability distribution of the state is obtained using sequential filtering within the Bayesian framework. Finally, the EM is introduced in the updating procedure of the pseudo measurement to estimate both the target state and the correlation coefficient. The target tracking scenario with an unknown correlation coefficient is built to demonstrate the validity and feasibility of the proposed algorithm. Simultaneously, the results of the normalized error squared validate the consistency of the MUCM.

Decorrelated unbiased converted measurement for bistatic radar tracking

Bistatic radar target tracking is challenging due to the fact that the measurements are nonlinear functions of the Cartesian state. The converted measurement Kalman filter (CMKF) converts the raw measurement into Cartesian coordinates prior to tracking and is superior to the extended Kalman filter for certain problems. The challenges of CMKF are debiasing the converted measurement and approximating the converted measurement error covariance. Due to no closed form of biases, we utilize the second-order Taylor series expansion of the conventional measurement conversion to find the conversion bias in bistatic radar and propose the unbiased converted measurement (UCM). In order to decorrelate the converted measurement error covariance from the measurement noise, we evaluate the covariance using the prediction in Bayesian recursive filtering, designated as the decorrelated unbiased converted measurement (DUCM). Monte Carlo simulations show that the DUCM is unbiased and consistent, and the DUCM filter exhibits an improved performance compared with the conventional CMKF and the UCM filter in bistatic radar tracking.

A Local Environment Model Based on Multi-Sensor Perception for Intelligent Vehicles

Accurate perception of the driving environment is a key technology for intelligent vehicles. Given some critical problems such as low robustness, low detection precision, difficulty in actual deployment, we propose a local environment model (LEM) based on multi-sensor fusion technology through Lidar, millimeter-wave (MMW) radar, camera, and ultrasonic radar. The local environment model mainly consists of the drivable area and the dynamic target list. The drivable area is extracted by the ground gradient threshold algorithm. Based on it, we propose an effective trim algorithm to make the drivable area model more practical. Furthermore, low-cost ultrasonic radars are deployed to compensate for the blind area of Lidar. The dynamic target list is established by local tracking and global tracking in the forward area. Kalman filter and converted measurement Kalman filter (CMKF) are adopted in the local tracking of Lidar, camera, and MMW radar. In the global tracking, the global nearest neighbor (GNN) algorithm is used for data association and the optimal distributed estimation fusion (ODEF) algorithm is used for sensor fusion. To improve the robustness of tracking, we use an assignment method to better exploit sensor performance. Finally, the vehicle experiment is carried out in the campus environment. Experimental results indicate that the proposed algorithm can avoid the false detection of the drivable area and realize real-time multi-target dynamic tracking. Therefore, the robustness and accuracy of the local environment model is verified.

Sequential unbiased converted measurement non‐linear filter with range rate in ECEF coordinates

Air-to-air target tracking is a challenging task for practical military and civilian applications. In this study, an unbiased converted measurement Kalman filter in Earth-centred Earth-fixed (ECEF) coordinates (E-UCMKF) is proposed for air-to-air target tracking, which takes account for noisy measurements from the airborne radar and the inertial navigation system/global navigation satellite system. The unbiased measurement conversion approach from spherical coordinates to ECEF coordinates is presented, and the Kalman filter is implemented for target state estimation with the unbiased converted measurements and the corresponding measurement error covariances. Besides, when range-rate measurements are available to the processor, a sequential unbiased converted measurement non-linear filter in ECEF coordinates with range-rate measurements (E-SUCMNFwR) is developed, which constructs a pseudo measurement to decorrelate the range-rate measurement noise from the unbiased converted measurement noise, and estimates the state sequentially by the E-UCMKF and a modified cubature Kalman filter. Target tracking scenarios with different sensor accuracies are presented to demonstrate the validity of the proposed algorithms. Simulation results validate the consistency of the proposed unbiased measurement conversion. The results also show that the proposed E-UCMKF and E-SUCMNFwR outperform the conventional algorithms in terms of the position and velocity root-mean-square error, demonstrating their effectiveness and practicality.

An improved algorithm for target trajectory prediction in the active protection system based on converted measurement Kalman filter

Fast and accurate prediction of the trajectory is the prerequisite for the successful interception of the incoming target by the active protection system (APS) of armoured vehicles. The traditional least-squares algorithm is susceptible to large errors in the initial stage of the tracking process, and the prediction of interception points converges slowly. This paper proposes an interception point prediction algorithm that combines the Kalman filter and least-squares estimation. By dynamically determining the convergence of the least-squares prediction, a converted measurement Kalman filter is used in the initial tracking stage to obtain higher prediction accuracy of the interception point. Simulations are performed in the scenario of the interception process of the APS. The results prove that the algorithm can effectively accelerate the convergence of the interception point prediction process.

Improved converted measurement Kalman filter for satellite‐borne multi‐target tracking

This study introduces a special converted measurement Kalman filter (CMKF) algorithm which apply to satellite for tracking target. Typical CMKF applies to radar which measures targets in spherical coordinate system. The new algorithm can be used by satellite which measures target's latitude and longitude. Improved CMKF algorithm tracks target in simple situation but is not able to deal with multi-target and information missing situation. Multiple hypothesis tracking (MHT) can track multi-target accurately and has the ability to initial track and end track at all times. For satellite, MHT use improved CMKF to calculate cost matrix and update the state estimate and estimate covariance. In the simulation, tracking process is simulated by MATLAB. Single target measured by satellite can be tracked accurately by CMKF algorithm. MHT can track multi-target accurately and distinguish the information missing rightly.

Maneuvering Acceleration Estimation Algorithm Using Doppler Radar Measurement

An algorithm to estimate the tangential and normal accelerations directly using the Doppler radar measurement in an online closed loop form is proposed. Specific works are as follows: first, the tangential acceleration and normal acceleration are taken as the state variables to establish a linear state transition equation; secondly, the decorrelation unbiased conversion measurement Kalman filter (DUCMKF) algorithm is proposed to deal with the strongly nonlinear measurement equation; thirdly, the geometric relationship between the range rate and the velocity direction angle is used to obtain two estimators of the velocity direction angle; finally, the interactive multiple model (IMM) algorithm is used to fuse the estimators of the velocity direction angle and then the adaptive IMM of current statistical model based DUCMKF (AIMM-CS-DUCMKF) is proposed. The simulation experiment results show that the accuracy and stability of DUCMKF are better than the sequential extended Kalman filter algorithm, the sequential unscented Kalman filter algorithm, and converted measurement Kalman filter algorithms; on the other hand they show that the AIMM-CS-DUCMKF can obtain the high accuracy of the tangential and normal accelerations estimation algorithm.

A sequential converted measurement Kalman filter in the ECEF coordinate system for airborne Doppler radar

For an airborne Doppler radar, the carrying platform is moving and has time-varying attitudes. The filtering algorithms applicable to local coordinate system are not suitable anymore. In this paper, we propose a sequential converted measurement Kalman filter (SCMKF) with Doppler, which is based on the earth-centered earth-fixed (ECEF) coordinate system. First, to effectively utilize Doppler measurement with probable correlation with slant range, the correlated Doppler and range are decorrelated by the Cholesky factorization. The range component remains unchanged while the Doppler component is changed. Second, by a series of coordinate transformations with unchanged range component and other observations, the converted position measurement is obtained. Meanwhile, the corresponding error covariance is derived by using Taylor series expansion. With the resulting converted measurement and covariance, the target state is filtered by the converted measurement Kalman filter (CMKF), which is extended to the ECEF system. Finally, the filtered state is updated sequentially with the changed Doppler. Compared with the posterior Cramer–Rao lower bound as well as the CMKF, the proposed SCMKF is shown to be an efficient solution, and is superior to the CMKF. Although the gain brought from low-accuracy Doppler is limited, the introduction of high-accuracy Doppler can improve tracking performance significantly.

A Sequential Converted Measurement Kalman Filter with Doppler Measurements in ECEF Coordinate System

When there is the correlation between Doppler and slant range, previous literatures have presented some sequential filter algorithms. However, they are only applied to simplified fixed radar’ s local coordinate system. As a result, a Sequential converted measurement Kalman filter (SCMKF) with Doppler measurements based on the Earth centered earth fixed (ECEF) coordinate system applicable to a moving airborne platform which has time varying attitude is proposed. Firstly, the correlated Doppler and range are decorrelated using the Cholesky factorization, then the converted position measurements are obtained by a series of coordinate transformation with unchanged range component and other observations, such as azimuth and elevation angles; the corresponding error covariances are derived which are used to the Converted measurement Kalman filter (CMKF). Finally the sequential filter is implemented for changed pseudo-Doppler measurements. The proposed method is validated through Monte Carlo test compared with the performance of CMKF with just converted position measurements and traditional SCMKF with Doppler which ignores the correlation between Doppler and range noises, and the conclusion is obtained that utilizing Doppler information correctly can improve tracking performance, nevertheless, the improvement gain of filter accuracy is limited, which can provide some references for engineering application.

Automatic Sea-Surface Obstacle Detection and Tracking in Forward-Looking Sonar Image Sequences

Automatic sea-surface object detection and tracking for safe autonomous underwater vehicle and submarine surfacing is a critical issue in relation to the accidents reported in the last decades. Here, we propose an efficient tool to detect and track sea-surface obstacles by processing forward-looking sonar images. The proposed method can detect either still or moving objects with and without wake. For each image sequence, a sequential procedure is proposed to detect various obstacle signatures. Then, target positions and velocities are estimated in Cartesian coordinates using the debiased converted measurement Kalman filter and the joint probabilistic data association filter. Detection and tracking stages exchange information in order to reduce the number of false alarms. Promising results are obtained using real data collected at sea with various objects and scenarios.

Unscented Kalman filter‐aided Gaussian sum filter

A non-linear filter is developed for continuous-time systems with observations/measurements carried out in discrete-time. The filter developed can approximate the a priori and a posteriori probability density function (pdf) with weighted Gaussian sums inside specific search regions. To make the approximations, first, Gaussians are placed with equal intervals inside the search regions and deterministic sample points are chosen within the search regions. The pdf values are then calculated at sample points using numerical solution of the Fokker–Planck equation for the a priori pdf and using Bayes’ rule for the a posteriori pdf. These values are used to find the weights of Gaussians using least-squares method. This process is similar to curve fitting with Gaussian radial basis functions. Inside the search regions, locations of the sample points and mean and covariance values of Gaussians are found by the help of a unscented Kalman filter (UKF). By adjusting the width of the search regions, all the parts, or the ones close to mean values of pdfs, can be approximated. The performance of the filter developed is analysed using a non-linear system with a single-state variable and two radar tracking applications. It is compared with particle filter, UKF and converted measurement Kalman filter for these cases.

Nonlinear-Filtering with Interacting Multiple-Model Algorithm for Coastal Radar Target Tracking System

This paper presents a performance evaluation of nonlinear filtering with Interacting Multiple Model (IMM) algorithm for implementation on Indonesian coastal radar target tracking system. On this radar, target motion is modeled using Cartesian coordinate but target position measurements are provided in polar coordinate (range and azimuth). For this implementation, we investigated two types of nonlinear filtering, Converted Measurement Kalman Filter (CMKF) and Unscented Kalman Filter (UKF). IMM algorithm is used to anticipate target motion uncertainty. Many simulations on radar target tracking are developed under assumption that noise characteristic is known. In this paper, the performance of IMM-CMKF and IMM-UKF is evaluated for condition that radar doesn’t know noise characteristic and there is mismatch on noise modeling. Results from simulation show that IMM-CMKF has better performance than IMM-UKF when tracking maneuvering trajectory. Results also show that IMM-CMKF is more robust than IMM-UKF when there is mismatch on noise modeling.

Pseudo steady state filters for target tracking with polar measurements

Target tracking under the linear and Gaussian assumption is a well known problem. In this case, the optimal state estimate is delivered by the standard Kalman filter. However, for real world systems, this assumption is not satisfied. A commonly encountered problem for the tracking community is: target tracking in a Cartesian frame of reference, with measurements delivered by radar in polar coordinates. In this paper we propose two novel static versions of the Debiased Converted Measurements Kalman Filter (DCMKF) and the Unscented Kalman Filter (UKF), that use the well known αβ filter. The proposed filters are: the Debiased Converted Measurement αβ Filter (DCMαβ) and the Unscented αβ filter (Uαβ). The RMSE calculated by means of Monte Carlo simulations is used to assess the performances of these new filters. The simulations results show that, the proposed filters are much simpler and thus 60% less computational time demanding and have acceptable RMSE compared to that of the classical ones. These filters are also suitable for parallel implementation, which makes them potential candidates for real time applications on embedded systems.

Tracking with nonlinear measurement model by coordinate rotation transformation

A new filtering method is proposed to accurately estimate target state via decreasing the nonlinearity between radar polar measurements (or spherical measurements in three-dimensional (3D) radar) and target position in Cartesian coordinate. The degree of linearity is quantified here by utilizing correlation coefficient and Taylor series expansion. With the proposed method, the original measurements are converted from polar or spherical coordinate to a carefully chosen Cartesian coordinate system that is obtained by coordinate rotation transformation to maximize the linearity degree of the conversion function from polar/spherical to Cartesian coordinate. Then the target state is filtered along each axis of the chosen Cartesian coordinate. This method is compared with extended Kalman filter (EKF), Converted Measurement Kalman filter (CMKF), unscented Kalman filter (UKF) as well as Decoupled Converted Measurement Kalman filter (DECMKF). This new method provides highly accurate position and velocity with consistent estimation.

Constant turn model for statically fused converted measurement Kalman filters

In this paper, the discrete temporal evolution equation of pseudo-states is derived for the constant turn (CT) motion with known turn rate. The pseudo-state vector consists of the converted Doppler (the product of target true range and range rate) and its first derivative. Based on the resulting linear state equation, the converted Doppler measurement Kalman filter (CDMKF) is formulated to extract information from the converted Doppler measurements. The pseudo-states from the CDMKF are fused statically with the outputs of the well known converted position measurement Kalman filter (CPMKF) by a static minimum mean squared error (MMSE) estimator designed for the proposed CT model, resulting in the statically fused converted measurement Kalman filter (SF-CMKF). The validity of the proposed CT model and its benefits to state estimation with Doppler as well as position measurements are demonstrated by assessing the performance of the CDMKF and SF-CMKF. Comparative results show the superior performance of the proposed technique especially in challenging scenarios with large position measurement errors.

Decorrelated unbiased converted measurement Kalman filter

Converted measurement tracking is a technique that filters in the coordinate system where the underlying process of interest is linear and Gaussian and requires the measurements to be nonlinearly transformed to fit. The goal of the transformation is to allow for tracking in the coordinate system that is most natural for describing system dynamics. There are two potential issues that arise when performing converted measurement tracking. The first is conversion bias that occurs when the measurement transformation introduces a bias in the expected value of the converted measurement. The second is estimation bias that occurs because the estimate of the converted measurement error covariance is correlated with the measurement noise, leading to a biased Kalman gain. First, previously proposed unbiased conversions are examined. Following this, the decorrelated unbiased converted measurement approach is presented. Results show that to overcome conversion bias and estimation bias, an unbiased measurement conversion should be employed that calculates the converted measurement error covariance using the predicted measurement. The conversion approaches are evaluated in tracking scenarios relevant to radar and sonar measurements.