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A 'current model' concept for maneuvering targets is proposed in this paper and a modified Rayleigh density is proposed to describe the 'current' probability density of target maneuvering acceleration. The physical relation between the state (acceleration) estimate and the mean value of the state noise in the special case discussed here is also pointed out. Based on these two points, an adaptive Kalman filter for the mean and variance of the maneuvering acceleration is given. Some computer simulation results in one- and three-dimensional cases are given. The simulation results show that the proposed adaptive algorithm can estimate well the states of highly maneuvering targets.

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... When an estimator based on a single model was not adequate, an interacting multiple model (IMM) approach was presented to provide the state-of-the-art solutions to many problems such as air traffic control tracking [12,13], in which a two-model IMM with the NCV and NCT models is used to perform maneuvers. The Singer model is a popular model for characterizing target maneuvers [14]. In [15], this model was modified to be the mean-adaptive acceleration model. ...

... As shown in (14), the base state is augmented by the parameter vector that needs to be estimated, and thus the evolution of the augmented state from sampling step to can be written as ...

... When the target maneuvers occur, the RMSEs of the proposed SM-based algorithm do not rise as sharply as those KF algorithms, suggesting that the proposed SM-based algorithm has relatively more robust performance than those KF algorithms during the target maneuvers. At a larger window length value (at choice of 14), the performance of the SM-based algorithm becomes remarkably better than the online fitting (see Fig. 9). Fig. 10 presents average RMSEs of position and velocity estimates of the online fitting and proposed SM algorithms, in the case of four window length values. ...

The state estimation of a maneuvering target, of which the trajectory shape is independent on dynamic characteristics, is studied. The conventional motion models in Cartesian coordinates imply that the trajectory of a target is completely determined by its dynamic characteristics. However, this is not true in the applications of road-target, sea-route-target or flight route-target tracking, where target trajectory shape is uncoupled with target velocity properties. In this paper, a new estimation algorithm based on separate modeling of target trajectory shape and dynamic characteristics is proposed. The trajectory of a target over a sliding window is described by a linear function of the arc length. To determine the unknown target trajectory, an augmented system is derived by denoting the unknown coefficients of the function as states in mileage coordinates. At every estimation cycle except the first one, the interaction (mixing) stage of the proposed algorithm starts from the latest estimated base state and a recalculated parameter vector, which is determined by the least squares (LS). Numerical experiments are conducted to assess the performance of the proposed algorithm. Simulation results show that the proposed algorithm can achieve better performance than the conventional coupled model-based algorithms in the presence of target maneuvers.

... However, it is difficult to track such a maneuvering target with some unknown time-varying motion model. The current statistical (CS) model [13] can be utilized to model the time-varying motion model. The CS model assumes that given the current acceleration, the probability density function of the acceleration at the next instant is a modified Rayleigh density function whose mean value is the current acceleration. ...

... The CS model [13] is widely utilized in tracking a maneuvering target. When a target is maneuvering with a certain acceleration, the CS model assumes that its acceleration at the next time instant is limited within a range around the current acceleration. ...

... whereā l is the mean of maneuvering acceleration at time instant l. a l is the zero mean colored acceleration noise. α is the reciprocal of the maneuver time constant, and w l is white noise with zero mean and variance σ 2 w = 2ασ 2 [13]. Whenẍ l > 0, the probability density function is given by ...

A spatial-temporal processing framework integrated of speech enhancement and speech tracking is proposed in this paper for distant speech perception. First, weak speech signals are enhanced by the deconvolved conventional beamforming (DCBF) with a microphone array. By virtue of the narrow beamwidth and low sidelobes of the DCBF, the competing sources can be effectively suppressed without introducing extra speech distortion. Second, with the accurate bearing provided by the DCBF, the Cubature Kalman filter can be utilized to track the speech source of interest. By introducing a scaling factor in the current statistical motion model, a new tracking algorithm is proposed which is suitable for both maneuvering and nonmaneuvering speech sources. The introduced scaling factor can be adaptively adjusted to improve the tracking performance of the proposed algorithm for different motion models. Numerical results show that the proposed algorithm can provide better tracking performance than the conventional one. In particular, the tracking root mean square error can be reduced by half for some cases.

... However, the Singer model does not utilize the past estimated acceleration information to estimate the new value [25]. And the "current" model utilizes the estimated acceleration in the last step as the new acceleration mean and assumes a conditional PDF with this new acceleration mean, which improves the accuracy of state estimation [28]. Hence, the "current" model has better acceleration estimation accuracy than the Singer model. ...

... In contrast, the Singer model is the motion model of the normal Kalman filter. The state equation of the "current" model, proposed by [28], is illustrated below. ...

... To employ the adaptive Kalman filter or the normal Kalman filter, the process noise covariance matrix Q needs to be computed by the probability density function (PDF) of target acceleration. The PDF of the target acceleration in the "current" model is a conditional PDF ( | ) k f a a , which is a conditional Rayleigh density [28], as shown in Fig. 3. However, the PDF of target acceleration in the Singer model is an unconditional PDF, which is a symmetric ternaryuniform mixture distribution, as shown in Fig. 4. The PDF of target acceleration in the "current" model is shown below. ...

Cooperative adaptive cruise control (CACC) communicates the relevant preceding vehicle state data to the follower (ego) vehicle to improve the vehicle following capabilities. In general, the CACC utilizes the preceding vehicle’s desired acceleration from wireless communication as a feedforward term in the controller of the ego vehicle, which dominantly determines the total control input. However, communication loss would degrade CACC to adaptive cruise control (ACC), where the lack of the feedforward term during communication loss would increase the inter-vehicular distance, or otherwise, may lead to collision during vehicle emergency braking. This paper proposes a control algorithm with an adaptive Kalman filter estimating the acceleration of a preceding vehicle, and the estimated acceleration is implemented as a feedforward signal in the ego-vehicle CACC controller in case of communication loss. The proposed control algorithm is evaluated by experiments using mobile robots which emulate driving. Additionally, simulations of real vehicles are also conducted. The results of simulations and robot experiments show that the performance of implementing the adaptive Kalman filter during communication loss is better than fallback to ACC and the normal Kalman filter based on the Singer model.

... A famous example is target tracking, the state equation of which is excited by an unknown and time-varying forcing function. Most of the current target tracking methods [7]- [11] develop approximate state models of the real system and encounter difficulties when tracking highly maneuvering targets. In some demanding cases, multi-model method is applauded because the filtering error using one single model is unacceptable [11]. ...

... Most of the current target tracking methods [7]- [11] develop approximate state models of the real system and encounter difficulties when tracking highly maneuvering targets. In some demanding cases, multi-model method is applauded because the filtering error using one single model is unacceptable [11]. ...

The conventional Kalman filter demands complete knowledge of the actual filter model, which is usually inaccessible in practical problems. When dealing with the filtering problem with uncertainty, any improper prediction of the uncertainty may degrade the filtering performance and even lead to divergence phenomenon. In this paper, the innovation feedback Kalman filter, which introduces the innovation feedback controller to the Kalman filter equations, is newly proposed on the basis of automatic control theory to address the filtering problem with uncertainty and is different from other filtering methods. By studying the estimate error equations, the estimate bias is extracted and its propagation mechanism is formulated. The estimate bias propagation equations reveal that eliminating the estimate bias essentially equivalents to an output regulation problem with uncertain exosystem. And a concise yet effective innovation feedback controller is subsequently given as an example. The proposed method is applied to one-dimension target tracking scenario and its high estimation accuracy performance and good stability are simulated through a comparative analysis with the ideal filtering results.

... The Singer model [35] model the acceleration is zero-mean first-order stationary Markov process. Further, the extension of Singer model with an adaptive mean, is called mean-adaptive acceleration (MAA) model [36], which have to a non-zero mean of the acceleration. Specifically the acceleration a(k) =ã(k) +ā(k), whereã(t) is the zero-mean Singer acceleration process and a(k) is the mean of the acceleration. ...

... 2) Mixing: the mean and the covariance matrix for the jth mode-matched filter are given bŷ 3) Mode matched filtering: for j=1,2...N, use the estimate (35), covariance (36) and observation z(k) as input to match m j (k). The Kalman filer with unscented transformation (27)-(32) are used to yield x j (k|k) and P j (k|k). ...

Tracking maneuvering vehicles in complex dynamic environment is a challenging problem for advanced driver assistance system and autonomous driving systems. Most conventional vehicle tracking algorithms can not model the vehicle dynamic exactly because of the uncertain moving behavior. However, due to the on-road capability, vehicles have to subject to various constraints imposed by traffic rules and roads. Taking advantage of those context information can refine and improve the performance of tracking as it provides additional prior information for vehicles’ dynamic behavior. To achieve this goal, this paper presents a novel context-enhanced tracking approach that exploits the context information to reduce the uncertainty of dynamic estimation. A new context-based sojourn-time dependent semi-Markov (STDM) model, called sojourn-time dependent semi-Markov variable structure interacting multiple model (STDMVSIMM), is proposed to describe the vehicle’s longitudinal acceleration process. In order to cope with the context information into STDM model, a context-based Bayesian network is presented to replace the fixed model transition probabilities with sojourn-time dependent transition probabilities. Compared with traditional interacting multiple model tracking with fixed transition probability, this adaptation switching strategy makes the vehicle motion sequence closer to the natural behavior and improve the tracking performance. Furthermore, a novel pseudo-measurement is constructed to formulate the road-map constraint in tracking process for reducing uncertain on mobility constraints. Simulation results shows that the proposed STDM-VSIMM can achieve better performance after considering the context.

... While the second kind of algorithms conduct with no manoeuvre detection. They usually have well-designed structures to tolerate the state changing of the target, including modified input estimation algorithm [2,7], Singer model [8], current statistical model [9], interacting multiple model (IMM) method [10], et al. ...

... However, the manoeuvre is usually a Markov process, which means its value at one time is related to those at its neighbours [12]. Based on this concern, correlated noise becomes a better choice to model the target manoeuvre [8,9]. ...

In the past few decades, many manoeuvring target-tracking methods have been proposed. However, most of these methods require some priori knowledge about the target, which is hard to obtain in many scenarios. Here, a priori-knowledge-free (PKF) manoeuvring target-tracking method is proposed by introducing a time-varying polynomial-function-based motion model. The model order and coefficients are real-time estimated to guarantee a steady performance in both manoeuvring and non-manoeuvring situations. Numerical results are provided to validate the effectiveness of the proposed method.

... The white noise acceleration model is based on the assumption of independent and constant acceleration (Bar-Shalom et al. 2004). The asymmetrically distributed normal acceleration model and mean-adaptive acceleration model were derived based on the assumption that the acceleration of motion is a time-correlated stochastic process (Kendrick 1981;Zhou and Kumar 1984). These acceleration models cannot maintain great performance in the case of turning, and a constant turn rate model introduced the turn rate (Bar-Shalom 1990). ...

Micro-electromechanical systems and inertial measurement units (MEMS-IMUs) show great advantages in terms of price and size. Nevertheless, due to limitations of technology, their observations are easily affected by the surrounding environment (temperature, vibration, and electronic noise). Most methods resist the effect of gross errors by adjusting covariance matrices in the integrated navigation of a global navigation satellite system (GNSS) and inertial navigation system (INS). We propose a motion model-assisted integrated navigation method on the basis of a constant yaw rate and velocity (CTRV) model, which serves as a constraint condition and detects gross errors by a Chi-squared test. The results of the CTRV are used to correct the carrier state from INS mechanization. A field test was carried out to verify the performance of the CTRV-assisted method. Compared with a robust Kalman filter, the method improves the horizontal accuracy of position and velocity by more than 87% and 68%, respectively, in a medium-precision loosely and tightly coupled system, and of the velocity and attitude by more than 52% and 20%, respectively, in a low-precision loosely and tightly coupled system. Therefore, the CTRV-assisted method can significantly enhance the performance of GNSS/MEMS-IMU integrated navigation systems.

... Since the acceleration information of the non-cooperative target is unknown, it is difficult to describe the motion of the maneuvering target based on the traditional orbital dynamics model. An effective method to model the accelerations of the target is based on the stochastic process, such as the well-known Singer model [25] and its improved models, including the current statistical (CS) model [26], the jerk model [27,28], and the current statistical jerk (CSJerk) model [29]. The Singer model assumes that the target maneuvering acceleration is a stable time-dependent zero-mean first-order Markov process, which uses time-dependent colored noise instead of white noise to model the maneuvering acceleration. ...

Performance of the traditional Kalman filter and its variants can seriously degrade when they are used to track a non-cooperative continuously thrusting spacecraft. To overcome this shortcoming, an adaptive tracking method for relative state estimation of a non-cooperative target is proposed based on the interacting multiple model (IMM) algorithm. First, built upon a current statistical jerk (CSJerk) model, a robust CSJerk filtering (RCSJF) algorithm is developed, which can address the issue of low estimation accuracy and instability of traditional approaches at the moments when the spacecraft starts and ends thrusting. Second, the developed RCSJF algorithm is further used to form the model set of the IMM by incorporating different maximum jerk values, based on which an adaptive tracking method is presented that can track a non-cooperative target with different maneuvering levels. Simulation results show that the proposed method can effectively track the target across all thrusts levels under the conditions considered, and the convergence performance of the proposed method is improved in comparison to the CSJerk-based extended Kalman filter, especially at the start and end time of the maneuver.

... In the acceleration model, the Singer model [28] assumes that manoeuvring acceleration is a first-order time-dependent stationary Markov process with zero mean. The current statistical model [29] assumes that manoeuvring acceleration obeys the Rayleigh distribution, which can reflect manoeuvring changes more realistically. The typical turn model is the constant turn (CT) model, which approximates the target movement in a uniform circular motion. ...

Abstract Deep learning technology provides novel solutions for increasingly complex target tracking requirements. For traditional target tracking models, the movement of the target need to be simulated by a predefined mathematical model. However, it is extremely difficult to obtain sufficient information in advance, which makes it challenging to track changeable and noisy trajectories in a timely and precise manner. A deep learning framework is constructed for automatic trajectory tracking based on learning the dynamic laws of motion, called DeepGTT. Specifically, a trajectory generator and a trajectory mapper were designed to standardise trajectory data and construct trajectory mapping, which enable the long short‐term memory–based tracking network to learn general dynamic laws. Then, to discuss the interpretability of the model, the mechanism of the deep learning framework is considered and a memory factor matrix is defined. Finally, extensive experiments are conducted on various weak manoeuvring and manoeuvring scenarios to evaluate the algorithm. Experimental results demonstrate that the DeepGTT algorithm remarkably improves accuracy and efficiency compared with most conventional algorithms and state‐of‐the‐art methods. In addition, interpretability experiments qualitatively prove that the tracking network can perceive dynamic laws when estimating the target state.

... σ 2 ax,q and σ 2 ay,q are the covari-181 ance of acceleration in x direction and y direction, respectively. 182 q cs is related to the process noise in the CS model [39], and 183 diag(.) returns a block diagonal matrix. ...

In this paper, an efficient power allocation (PA) strategy is developed for maneuvering target tracking (MTT) in the collocated MIMO radar. The mechanism of our strategy is to implement the optimal PA based on the prior target maneuvering information in the tracking cycle. The predicted conditional Cramer—Rao lower bound (PC-CRLB) is derived, normalized and thus adopted as the optimization criterion, since the PC-CRLB is based on the most recently realized measurement and provides a more accurate lower bound than the standard posterior CRLB (PCRLB). We fully demonstrate that the established optimization model is convex. By exploiting the monotonic decreasing property of the objective function, an efficient sequential relaxation-based solver is proposed for the solution, where the PA for one target is identified that whether should be fixed on the minimum level at each iteration. Simulation results show the better tracking performance compared with the uniform allocation, and improved efficiency, compared with convex optimization tools.

... By adjusting the frequency coefficient of maneuvering to achieve better tracking effect, it has been widely used for nonlinear system [2,3]. The "current" statistical model was proposed as a representative of adaptive tracking algorithm [4]. In this model, the acceleration noise is assumed to In the process of target tracking, if the system model deviates from their actual values by unknown random bias, the virtual noise is usually used to reduce confidence level of the filter to the system model, but it is difficult to determine how much virtual noise to be added. ...

One purpose of target tracking is to estimate the states of targets, and unscented Kalman filter is one of the effective algorithms for estimating in the nonlinear tracking problem. Considering the characteristics of complex maneuverability, it is easy to reduce the tracking accuracy and cause divergence due to the mismatch between the system model and the practical target motion model. Adaptive fading factor is an effective counter to this problem, having been instrumental in solving accuracy and divergence problems. Fading factor can adaptively adjust covariance matrix online to compensate model mismatch error. Moreover, fading factor not only improves the filtering accuracy, but also automatically adjusts the error covariance in response to the different situation. The simulation results show that the adaptive fading factor unscented Kalman filter has more advantages in target tracking and it can be better applied to nonlinear target tracking.

... In addition, the motion acceleration of limb movement exhibits dynamic characteristics, a kinematical model of which needs to be considered. Markov Model has been proposed to characterize the motion acceleration dynamics using, such as Singer model [28], Jerk model [29], current statistical model [30], and White-noise model with constant acceleration model (CA), constant velocity model (CV) and coordinated turn (CT) [31]. The choice of model is mainly based on algorithm robustness, calculation complexity and accuracy. ...

Motion velocity, acceleration, and energy expenditure estimations are important in quantitative assessments for physical recovery and exercise-based interventions for post-stroke patients with partial losses of neurological functions. This paper proposes a novel wearable motion estimation device using a micro flow sensor, which realizes motion velocity, acceleration detection, and energy expenditure estimation for human limb motion. A homemade micro thermal flow sensor is used to detect motion velocity. Jerk-Kalman based algorithm is proposed to extract motion acceleration from the flow sensor outputs. Motion velocity and acceleration are used to estimate energy expenditure of limb motion. Calibration experiments and application cases are conducted to validate the effectiveness of the methodology. The micro flow sensor based motion estimation method is free of accumulated error, robust for dynamic motion measurement, and provides a promising auxiliary approach for evaluating energy expenditures of human limbs in rehabilitation training.

... For a normally running vehicle with a smooth steering within a small time interval, three [22,27,28]. ...

To release the strong dependence of the conventional inertial navigation mechanization on the a priori low-cost inertial measurement unit (IMU) error model, this research applies an unconventional multi-sensor integration strategy to integrate multiple low-cost IMUs and a global positioning system (GPS) for mass-market automotive applications. The unconventional integration strategy utilizes a basic three-dimensional (3D) kinematic trajectory model as the system model to directly estimate navigational parameters, and it allows the measurements from all of the sensors independently participating in measurement updates. However, the less complex kinematic model cannot realize smooth transitions between different motion statuses for the road vehicle with acceleration maneuvers. In this manuscript, we establish a more practical 3D kinematic trajectory model based on a “current” statistical Singer acceleration model to realize smooth transitions for the maneuvering vehicle. In addition, taking advantage of the unconventional strategy, we individually model the systematic errors of each IMU and the measurements of all sensors, in contrast to most existing approaches that adopt the common-mode errors for different sensors of the same design. A real dataset involving a GPS and multiple IMUs is processed to validate the success of the proposed algorithm model under the unconventional integration strategy.

... In the simulation, we use the CS model [32] for RMTT. Its maximum acceleration is set to 50 m/s 2 , and the manoeuvring frequency constant is set to 1/60. ...

In order to reduce the uncertainty of radar manoeuvring target tracking (RMTT) in cluttered background, a joint detection and tracking algorithm based on cognitive radar is proposed. First, a prism structure resolution cell of time‐delay, Doppler and azimuth is designed. Then, an approximate expression of measurement error covariance including waveform and detection threshold parameters is given. Then, based on the idea of human brain perception‐action cycle, a joint waveform and detection threshold adaptive tracking algorithm based on minimum information entropy criterion is proposed. Finally, a cognitive structure adaptive particle filter (CSAPF) algorithm, based on parallel structure of extended Kalman filter (EKF) and particle filter, are used with Probabilistic Data Association (PDA) algorithm for RMTT. During the process, CSAPF‐PDA can always obtain the best tracking performance with the minimum number of particle samples, thus effectively taking into account the tracking accuracy and efficiency. The effectiveness of the proposed algorithm is verified by simulation experiments.

Radar is an important tool for aiding in bird strike mitigation as part of overall safety management systems at civilian and military airfields. However, the diverse movement trajectories and irregular echo power fluctuations cause existing multitarget tracking algorithms to face many challenges such as detection uncertainty and maneuver uncertainty. Therefore, this paper proposes a robust tracking method focusing on target fluctuation and maneuver characteristics. Firstly, a tracking information feedback mechanism based on the fluctuation model of bird targets is established, and the measurement set in the predicted gate is reconstructed to solve the problem of track breakages caused by the echo power fluctuation. Secondly, an adaptive parameter filter model is designed to enhance maneuver adaptability. Finally, simulation and experimental data verification show that the proposed method is more adaptive to bird target characteristics and can effectively improve the tracking performance without significantly increasing computation.

Aiming at intercepting large maneuvering targets precisely, the guidance law of advanced self-seeking missiles requires not only inertial line-of-sight (LOS) angular rate but also target maneuvering acceleration. Moreover, the semi-strapdown stabilization platform has lost the ability to measure the inertial LOS angular rate directly, which needs to be extracted by numerical calculation. The differential operation commonly used in traditional methods can magnify the measurement error of the sensor, resulting in insufficient calculation accuracy of the line-of-sight angular rate. By analyzing the mathematical relationship between the missile–target relative motion and the angle tracking system, a multi-process-fusion integrated filter model of relative motion and angle tracking is presented. To overcome the defect that the infrared seeker cannot directly measure the missile–target distance, following the snake-hot-eye visual mechanism, a visual bionic imaging guidance method of estimating the missile–target relative distance from the infrared images is proposed to improve the observability of the filter model. Finally, target-tracking simulations verify that the estimation accuracy of target acceleration is improved by four times.

In some target tracking scenarios, the target motion is usually subject to various constraints. For a road-constrained target, the corresponding trajectory shape is independent to its dynamic characteristics due to the one-dimensional space of road. To exploit the knowledge of independence, this paper proposes a state estimation algorithm based on the separate modeling of target trajectory shape and dynamic characteristics, in which two versions based on different polynomials are considered. The idea of a sliding window is introduced, where a unique third- or second-degree polynomial with the coefficients to be estimated is used to model the target trajectory of each window. The unknown polynomial coefficients are augmented into the base state in the one-dimensional mileage coordinates and are estimated along with the base state. At every sampling period except the initial time, the proposed estimation algorithm starts the interaction stage with the previous updated base state of each filter and the modified parameter vector. The latter is determined by a least squares (LS) technique. Simulation results show that the two versions of the proposed algorithm achieve better performance than conventional estimation algorithms with coupled modeling.

The state estimation of a maneuvering target based on separate modeling of target trajectory shape and dynamic characteristics is studied in the absence of prior information about the target trajectory. Traditionally, target dynamics are described by motion models in Cartesian coordinates, in which the target trajectory is determined by target dynamic characteristics. However, due to target motions subjected to external environmental limitations such as roads, terrains, buildings, trees, flight routes, and sea-routes, the trajectory shape of a target is independent of target dynamic characteristics. In addition, although one-dimensional representation can be used to decouple the target trajectory from dynamic characteristics, it is unsuitable for direct tracking without knowing prior information about the target trajectory. For these reasons, this paper proposes a new estimation algorithm that models the target trajectory and dynamic characteristics separately as well as handles the issue of no prior information. The target trajectory over a sliding window is described by B-spline curves, which are functions of the arc length. The unknown control points defining the B-spline curves are put in the modified multiple model estimator framework and are estimated together with the base state. After the first estimation cycle, the control points entering into interaction stage of the proposed estimation algorithm are reset by the least squares (LS). Simulation results show that the proposed estimation algorithm is capable of achieving better performance than conventional tracking algorithms.

Purpose
The purpose of this study is to establish an effective tracking algorithm for small unmanned aerial vehicles (UAVs) based on interacting multiple model (IMM) to take timely countermeasures against illegal flying UAVs.
Design/methodology/approach
In this paper, based on the constant velocity model (CV), the maneuvering adaptive current statistical model (CS) and the angular velocity adaptive three-dimensional (3D) fixed center constant speed rate constant steering rate model, a small UAV tracking algorithm based on adaptive interacting multiple model (AIMM-UKF) is proposed. In addition, an adaptive robust filter is added to each model of the algorithm. The linear Kalman filter algorithm is attached to the CV model and the CS model and the unscented Kalman filter algorithm (UKF) is attached to the CSCDR model to solve the nonlinearity of the 3D turning model.
Findings
Monte-Carlo simulation comparison with the other two IMM tracking algorithms shows that in the case of different movement modes and maneuvering strength of the UAV, the AIMM-UKF algorithm makes a good trade-off between the amount of calculation and filtering accuracy, which can maintain more accurate and stable tracking and has strong robustness. At the same time, after testing the actual observation data of the UAV, the results show that the AIMM-UKF algorithm state estimation trajectory can be regarded as an actual trajectory in practical engineering applications, which has good practical value.
Originality/value
This paper presents a new small UAV tracking algorithm based on IMM and the advantages and practicability of this algorithm compared with existing algorithms are proved through experiments.

In this paper, we proposed an adaptive non-zero mean damping oscillation model, aiming to solve the trajectory tracking problem of hypersonic glide vehicles (HGVs). To this end, an adaptive non-zero mean damping oscillation model (ANMDO) is established based on the maneuver patterns of HGVs, the proposed model consists of the mean and maneuvering components of HGV's accelerations. In particular, a sine autocorrelation random process is applied to model the mean component, while a first-order Markov process is introduced to compensate its maneuvering counterpart that is taken as the perturbation. Moreover, we proceed to introduce the Kalman filter to estimate the trajectory, while the dynamic errors of the proposed model are analytically developed. Simulation results verified that the proposed model can achieve a better tracking accuracy and reasonable convergence compared with the conventional sine correlation model and the Singer model.

Intelligent vehicle positioning is an enabling technology for decision-making, trajectory planning, and motion control, and is a key technology in intelligent transportation systems (ITSs). In order to obtain a low-cost and high-precision positioning strategy, an integrated positioning strategy for intelligent vehicles based on the global navigation satellite system (GNSS), dead reckoning (DR), ultra-wide band (UWB), and visual map matching (VMM) was proposed in this paper. First, the error sources of the three independent positioning methods of GNSS, DR, and UWB were analyzed, and independent positioning algorithms with improved accuracy were proposed. Then, the fusion positioning algorithm of GNSS/DR/UWB with an adaptive information distribution coefficient was established using a federated Kalman filter to improve the positioning accuracy and continuity. Afterward, to avoid reliance on the previous moment, the positioning result was further corrected by VMM. Finally, offline simulation and real vehicle tests were conducted under typical working conditions with the impact of real-world noise and the real-motion states of vehicles. The results showed that the GNSS/UWB/DR/VMM positioning algorithm could effectively improve the positioning accuracy and reliability of intelligent vehicles at a low cost.

The study investigates the trajectory estimation problem of a noncooperative gliding flight vehicle with complex and atypical maneuvers. An active switching multiple model (ASMM) method is proposed. This method employs a motion behavior model set (MBMS), a motion behavior recognition algorithm, and an active switching estimation and fusion algorithm. First, a recognizable MBMS, which can capture all the motion behaviors of a gliding flight vehicle, is established. Then, a motion behavior recognition algorithm based on recurrent neural networks (RNNs) is developed to obtain the current probability of each motion behavior. Then, an active switching estimation and fusion algorithm is proposed, in which the adopted models are actively chosen at each time instant according to a model selection strategy. Last, the proposed ASMM method is applied to a noncooperative gliding flight vehicle. The simulation results show that the proposed method has higher estimation precision and better dynamic performance.

The accuracy of three-dimensional (3D) passive target tracking under strap-down system is usually affected by the measurement accuracy of attitude angular rate and attitude angle. In order to save the problem, a novel 3D passive target tracking method based on instrumental variable Kalman filter (IVKF) aided by the attitude dynamic is proposed. At first, the maneuvering target motion model is established based on the “current” statistical model and the filtering equation of MEMS inertial measurement unit (IMU) is also set up. Then, linearize the nonlinear state equations and replace the nonlinear measurement equations with pseudolinear equations. The 3D pseudolinear Kalman filter (PLKF) algorithm is derived according to the linear Kalman filter (KF). To counter the severe bias problems with PLKF, bias compensation and recursive instrumental variable (IV) methods are considered. In order to enhance observability of the system, a 3D motion tracking sliding-mode guidance law is deduced. Finally, some mathematical simulations were made to verify the effectiveness of the proposed method. The simulation results show the effect of the measurement accuracy and complexity of the algorithm are reduced, which proves the validity of the method.

Multi-frame track-before-detect (MF-TBD) is a model-based batch processing method. Assuming a particular model for the evolution of target states (e.g. a constant velocity model) within a batch processing time, MF-TBD integrates the target energy by taking advantage of the space-time correlations between a number of consecutive frames. Its performance is known to be heavily dependent on the accuracy of the motion model, and to substantially degrade when target maneuvers occur and motions do not follow the presumed model. We make two contributions towards addressing this problem. Firstly, we analyze and summarize the direct strategies to incorporate the effect of target maneuvers into MF-TBD. Our analysis shows that although these strategies are straightforward to implement, they either suffer from considerable performance loss or are computationally expensive. Motivated by the analysis, we propose a general measurement-directed (MD) strategy to address target maneuvers. It carries out an on-line study of target dynamics from the observations, and is capable of achieving both low computational complexity and high adaptability to different target maneuvers. Secondly, as the proposed MD strategy is a general framework without any particular model assumptions, we further derive its detailed implementation equations for linear motion and measurement models. Simulation results for various tracking scenarios are presented to demonstrate the effectiveness of the proposed MD strategy.

Meliorating a priori stochastic model of Kalman filer (KF) is always challenging. To address this challenge, this paper simultaneously estimates and corrects the variance components for all of the process noise and measurement matrix (Q & R) by a posteriori variance-covariance components estimation (VCE) algorithm, which makes the most of the process noise residuals and measurement residuals and measurement redundancy contribution. Unsurprisingly, in the conventional error states-based integration mechanization, the stochastic model tuning is not easy for IMU because of the error measurements between the observables from inertial sensors and other aiding sensors. This research utilizes an unconventional multi-sensor integration strategy, in which a 3D kinematic trajectory model is deployed as the main part of system equation and the systematic errors of each IMU and the measurements of all sensors are individually modelled. Furthermore, the weights of measurements from each inertial sensor are defined on the basis of the posterior variances, so that we could properly distribute the function of each measurement in the fusion algorithm. A real dataset involving GPS and multiple IMUs is processed to validate the proposed posteriori VCE algorithm by applying the unconventional integration strategy.

To solve t he occlusion p roblem of multiple moving o bject s in video surveillance , a target t racking algorit hm based o n combinatio n of glo bal feat ure matching and local feat ure matching is p ropo sed. In t his algo rit hm , t he met hods based on histogram and block segmentation are adopted to exp ress gray feat ures of t he target. The occlusion is p re2judged befo re it happens. When t here is occlusion , t he gray feat ures based o n block segmentation are used to t rack target. After occlusion , t he target is re2located by histgram matching. The experiment result s show t he effectiveness and superio rity of t he p ropo sed app roach .

The different methods of adaptive filtering are divided into four categories: Bayesian, maximum likelihood (ML), correlation, and covariance matching. The relationship between the methods and the difficulties associated with each method are described. New algorithms for the direct estimation of the optimal gain of a Kalman filter are given.

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.

Maneuvering target motion is modeled by introducing a binary random variable in the target state equation. The optimal estimate is shown to be a weighted combination of two Kalman filter estimates with weights depending on the likelihood ratio for the detection of a maneuver. A tracking scheme is proposed for maneuvering target tracking and illustrated in an example.

In the design of a tracking filter for air traffic control (ATC) applications, a maneuvering aircraft can be modelled by a linear system with random noise accelerations. A Kalman filter tracker, designed on the basis of a variance chosen according to the distribution of the potential maneuver accelerations, will maintain track during maneuvers and provide some improvement in position accuracy. However, during those portions of the flight path where the aircraft is not maneuvering, the tracking accuracy will not be as good as if no acceleration noise had been allowed in the tracking filter. In this paper, statistical decision theory is used to derive an optimal test for detecting the aircraft maneuver; a more practical suboptimal test is then deduced from the optimal test. As long as no maneuver is declared, a simpler filter, based on a constant-velocity model, is used to track the aircraft. When a maneuver is detected, the tracker is reinitialized using stored data, up-dated to the present time, and then normal tracking is resumed as new data arrives. In essence, the tracker performs on the basis of a piecewise linear model in which the breakpoints are defined on-line using the maneuver detector. Simulation results show that there is a significant improvement in tracking capability using the decision-directed adaptive tracker.

A new approach to estimating motion of a highly maneuverable aircraft target in an air-to-air tracking scenario is presented. An interactive filter system is developed that provides an improved estimate of target motion states by conditioning kinematic filter estimates on target aspect angle data. Pattern recognition techniques used with an electrooptical tracker are presumed to provide this target aspect information. A target orientation filter processes the aspect angle measurements by statistically weighting measured aspect angles with the current best estimate of target kinematics. The aerodynamic lift equation is used to relate approximate angle of attack to target velocity and acceleration. A novel statistical model for aircraft target normal acceleration is also developed to represent better the unknown target accelerations. Simulation results of realistic three-dimensional scenarios are presented to evaluate the performance of the interactive filter system.

A new approach to the three-dimensional airborne maneuvering target tracking problem is presented. The method, which combines the correlated acceleration target model of Singer [3] with the adaptive semi-Markov maneuver model of Gholson and Moose [8], leads to a practical real-time tracking algorithm that can be easily implemented on a modern fire-control computer. Preliminary testing with actual radar measurements indicates both improved tracking accuracy and increased filter stability in response to rapid target accelerations in elevation, bearing, and range.

A general method of continually restructuring an optimum Bayes-Kalman tracking filter is proposed by conceptualizing a growing tree of filters to maintain optimality on a target exhibiting maneuver variables. This tree concept is then constrained from growth by quantizing the continuously sensed maneuver variables and restricting these to a small value from which an average maneuver is calculated. Kalman filters are calculated and carried in parallel for each quantized variable. This constrained tree of several parallel Kalman filters demands only modest om; puter time, yet provides very good performance. This concept is implemented for a Doppler tracking system and the performance is compared to an extended Kalman filter. Simulation results are presented which show dramatic tracking improvement when using the adaptive tracking filter.

Two approaches to a nonlinear state estimation problem are presented. The particular problem addressed is that of tracking a maneuvering target in three-dimensional space using spherical observations (radar data). Both approaches rely on semi-Markov modeling of target maneuvers and result in effective algorithms that prevent the loss of track that often occurs when a target makes a sudden, radical change in its trajectory. Both techniques are compared using real and simulated radar measurements with emphasis on performance and computational burden.