Interacting Multiple Model Algorithm Research Articles

An Adaptive IMM Algorithm for a PD Radar with Improved Maneuvering Target Tracking Performance

A pulse-Doppler (PD) radar has the advantage of strong anti-interference ability, and it is often used as a solution for maneuvering target tracking. In the application of target monitoring and tracking in PD radars, the interacting multiple model algorithm (IMM) has become the main and preferred choice due to its flexibility and high accuracy. However, the probability transfer matrix in classical IMM algorithms generally depends on constant prior knowledge, and if a PD radar is tracking a strong maneuvering target, it is inevitable to encounter some limitations, such as the possibility of target tracking trajectory deviation, and even a loss of the target. The Markov probability transfer matrix is proposed with an adaptive modification ability in real time to overcome the above problems in this paper. Additionally, for improving the speed of switching between the models, the fuzzy control system for secondary updating of model probability is adopted. By this means, the tracking accuracy of maneuvering targets is enhanced. Compared with the classical IMM algorithm, the corresponding simulation results for the PD radar indicate that the overall tracking accuracy of the proposed adaptive IMM algorithm is improved by 19.6%. In conclusion, the continuity and accuracy of the target trajectory can be effectively improved with the proposed adaptive IMM algorithm in PD radar cases.

Vehicle Sideslip Angle estimation under critical road conditions via nonlinear Kalman filter-based state-dependent Interacting Multiple Model approach

The knowledge of Vehicle Sideslip Angle (VSA) can play an essential role in active safety vehicle control systems. However, due to the high costs of sensing instruments, this information is difficult to be directly measured onboard of series production vehicles, restricting de facto its application in practice. It follows that there is a need for online VSA estimation methods only based on available measurements from low-cost sensors. From this perspective, this work proposes a strategy based on Interacting Multiple Model (IMM) filters, which does not require tyre–road friction coefficient knowledge. By integrating the available onboard sensor data, the IMM estimates relevant information in different driving conditions leveraging a 2-Degrees Of Freedom (DOF) single-track vehicle model embedding a Dugoff tyre representation. Two alternative IMM algorithms based on the Extended (EKF) and Unscented Kalman filter (UKF) are developed. Moreover, while usually the transition probabilities among models in classical IMMs are fixed and set on prior information and/or dedicated analysis, here these conservative hypotheses are relaxed introducing a state-dependent Markov transition matrix based on a novel model switching algorithm. The effectiveness of the new proposed methods is evaluated on extensive non-trivial simulation scenarios through a Monte Carlo analysis exploiting an accurate 15-DOF vehicle model via a purposely designed high-fidelity co-simulation platform embedding the dSPACE software Automotive Simulation Model (ASM). Results provide a meaningful comparative performance analysis between the IMMEKF and IMMUKF solutions, as well as with respect to traditional IMM based on constant probabilities transition matrix, blue in both the EKF and UKF configuration. Finally, the developed IMM-based estimation strategy is tested in two realistic driving scenarios to assess the VSA estimation accuracy in case of abrupt changes in road surface conditions.

Information fusion for online estimation of the behavior of traffic participants using belief function theory

Motion planning algorithms for automated vehicles need to assess the intended behavior of other Traffic Participants (TPs), in order to predict the likely future trajectory of TPs and plan the motion consequently. Information resulting from several sources, like sensors, must be gathered and combined into a reliable estimate of the intended behavior of TPs. Such estimates must be sufficiently steady and quantify the inherent uncertainty around the assessment. We present a novel information fusion algorithm to combine information from different sources into a coherent and reliable estimate. To explicitly account for the uncertainty of estimates, we leverage the Belief Function Theory and evaluate and handle possible disagreements between estimates individually provided by the sources. The algorithm is flexible and can also handle sources that do not discern between some of the considered behaviors and are only capable of assessing the probability of unions or clusters of different behaviors. We discuss the strengths of the approach through simulations in SUMO, comparing it to the Interactive Multiple Model algorithm.

An Improved Interacting Multiple Model Algorithm With Adaptive Transition Probability Matrix Based on the Situation

An Improved Interacting Multiple Model Algorithm With Adaptive Transition Probability Matrix Based on the Situation

Adaptive filtering and smoothing algorithm based on variable structure interactive multiple model

For maneuvering target tracking, a novel adaptive variable structure interactive multiple model filtering and smoothing (AVSIMMFS) algorithm is proposed in this paper. Firstly, an accurate model of the variable structure interactive multiple model algorithm is established. Secondly, by constructing a new model subset based on the original model subsets, the matching accuracy between the model subset and the actual maneuvering mode of the target is improved. Then, the AVSIMMFS algorithm is obtained by smoothing the filtered data of the new model subset. Because of the combination of forward filtering and backward smoothing, the target tracking accuracy is further improved. Finally, in order to verify the effectiveness of the algorithm, the simulation is carried out on two cases. The simulation results show that the tracking performance of AVSIMMFS algorithm is better than other methods and has lower calculation cost.

Robust Interactive Multimodel INS/DVL Intergrated Navigation System With Adaptive Model Set

A Robust Interactive Multiple Model (RIMM) algorithm with the adaptive model set is proposed to improve the performance of Inertial Navigation System (INS) and Doppler Velocity Logs (DVL) integrated navigation system under complex measurement environment with undesirable heavy-tailed non-Gaussian noise. Specifically, an improved Huber kernel function is applied to the robust error state Kalman filter (ESKF) for its benefit of better resisting larger measurement outliers. In addition, a flexible adaptive model set update strategy is proposed where the model set is determined by the current and historical measurement information stored in the sliding window. And for model set update, the main model is no longer fixed, it will be determined based on the probability weights corresponding to each model. This innovative RIMM algorithm is compared with error state Kalman filter, Interactive Multiple Model (IMM) and Hybrid Interactive Multiple Model (HIMM) through simulations, AUV lake trial and semi-physical simulations. Experimental results show that our proposed algorithm has outstanding accuracy and robustness under heavy-tailed non-Gaussian noise environment.

Cooperative Navigation for Heterogeneous Air-Ground Vehicles Based on Interoperation Strategy

This paper focuses on the cooperative navigation of heterogeneous air-ground vehicle formations in a Global Navigation Satellite System (GNSS) challenged environment and proposes a cooperative navigation method based on motion estimation and a regionally optimal path planning strategy. In air-ground vehicle formations, unmanned ground vehicles (UGVs) are equipped with low-precision inertial navigation measurement units and wireless range sensors, which interact with unmanned aerial vehicles (UAVs) equipped with high-precision navigation equipment for cooperative measurement information and use the UAVs as aerial benchmarks for cooperative navigation. Firstly, the Interacting Multiple Model (IMM) algorithm is used to predict the next moment’s motion position of the UGVs. Then regional real-time path optimization algorithms are introduced to design the motion position of the high-precision UAVs so as to improve the formation’s configuration and reduce the geometric dilution of precision (GDOP) of the configuration. Simulation results show that the Dynamic Optimal Configuration Cooperative Navigation (DOC-CN) algorithm can reduce the GDOP of heterogeneous air-ground vehicle formations and effectively improve the overall navigation accuracy of the whole formation. The method is suitable for the cooperative navigation environment of heterogeneous air-ground vehicle formations under GNSS-challenged conditions.

Maneuvering target tracking based on an adaptive variable structure interactive multiple model filtering and smoothing algorithm

For maneuvering target tracking, the interactive multiple model (IMM) algorithm and its variants have shown good performance, among which the variable structure IMM (VSIMM) algorithm is the most widely studied one. The approximation degree of the algorithm and the matching degree of the model subset will affect the performance of the VSIMM. In addition, considering that smoothing can provide better estimation of the target state, a new adaptive VSIMM filtering and smoothing (AVSIMMFS) algorithm is proposed in this paper. First, an accurate model of the VSIMM algorithm is established, in which the IMM is run in parallel with and independently from the different model subsets, and the state estimation of the model subset with the highest probability is selected as the final estimation result. Then, an adaptive VSIMM (AVSIMM) algorithm was designed based on the VSIMM algorithm. The adaptation is reflected in the construction of a new model subset from the original model subsets, which improves the matching degree between the model subset and the actual maneuvering model of the target. Finally, by smoothing the filtering data of the AVSIMM algorithm, the AVSIMMFS algorithm is obtained. Because of the combination of forward filtering and backward smoothing, the target tracking accuracy is further improved. Simulation results show that the tracking performance of the AVSIMMFS algorithm is better than that of other methods.

Interaction-Aware Personalized Trajectory Prediction for Traffic Participant Based on Interactive Multiple Model

Trajectory prediction for traffic participants is a critical task for autonomous vehicles. The long-term trajectory prediction is challenging due to limited data and the dynamic characteristics of traffic participants. This paper presents an innovative interactive multiple model algorithm considering inter-vehicle interaction and driving behavior for the traffic participant's short-term and long-term trajectory prediction. The field experiment is conducted to acquire the human driver data, which is then preprocessed and analyzed with statistical methods. The clustering result of the critical gap is used to include the interactions between them, on which the gap satisfaction probability function is designed and aimed at describing the satisfaction probability of the current lane. The driving behavior is another promising candidate to improve the long-term prediction accuracy. The clustering results of the lane change duration are used to establish the lane changing models considering the driving behavior, the driving behavior probability function is designed based on the probability of each model. Then the two functions are incorporated into the adaptive transition probability matrix, where the quantitative probabilistic relations between the gap satisfaction probability and the driving behavior probability are established. The adaptive transition probability matrix is then used in the interactive multiple model algorithm. Based on the improved interactive multiple model, the personalized trajectory prediction for the traffic participant is obtained. The effectiveness of the framework is validated by simulation and field experiment.

Non-Conservative Trajectory Planning for Automated Vehicles by Estimating Intentions of Dynamic Obstacles

Motion planning algorithms for urban automated driving must handle uncertainty due to unknown intention and future motion of Dynamic Obstacles (DOs). Considering a single future trajectory for each DO is not adequate, especially in urban frameworks where traffic participants exhibit very different behaviors. However, including multiple candidate trajectories representing different behaviors results in an excess of conservatism. We present a novel combination of the Interactive Multiple Model (IMM) algorithm and Stochastic Model Predictive Control (SMPC) that allows non-conservative safe motion planning in presence of DOs with unknown intention. We introduce a framework based on LQR and IMM to predict multiple candidate future trajectories, each interpreted as a high-level intention that the DO is pursuing, and dynamically estimate their probabilities. Then, the future trajectory of the automated vehicle is iteratively planned in an SMPC fashion, in which collision avoidance constraints are generated for multiple future trajectories of each DO, with a focus on the most likely. Our method improves safe motion planning fully exploiting the benefits of multi-modal predictions of the DOs, avoiding excessive conservatism. Advantages of the proposed method are discussed through simulations in the CARLA environment.

Interacting Multiple Model for Lithium-Ion Battery State of Charge Estimation Based on the Electrochemical Impedance Spectroscopy

In terms of the dynamic changes of battery model parameters in a single-model filtering algorithm, the filter estimation accuracy can be poor, and filtering is scattered due to the different internal state parameters of lithium-ion batteries in different aging states, which affects the state of charge (SOC). In order to address these issues, an Interacting Multiple Model (IMM) algorithm was proposed in this study, which adopted an Unscented Kalman Filter (UKF) to better approximate the nonlinear characteristics of the state equation while better stabilizing the filter and having lower computational requirements. Accordingly, the IMM was used to solve the problem of the accurate estimation of the SOC under the dynamic change of model parameters. Moreover, an electrochemical impedance spectrum was used to establish the electrochemical model, after which the lithium-ion equivalent electrochemical circuit model was established, which improved the complexity problem due to its high accuracy but complicated the calculation of the multi-order equivalent circuit model. By conducting experiments and simulations, the algorithm of IMM-UKF was shown to achieve an effective estimation of the battery SOC, even when the state parameters of lithium-ion batteries were uncertain.

Long Short-Term Memory-Based Neural Networks for Missile Maneuvers Trajectories Prediction⋆

Due to its extensive applications in different contexts, moving target tracking has become a hot topic in the last years, above all in the military field. Specifically, missile tracking research received a great effort, mainly for its importance in terms of security and safety. Herein, traditional solutions, e.g. Interacting Multiple Model (IMM) based on the Kalman estimation theory, achieve good performance under the main restrictive assumption of the a priori knowledge of the target model, so neglecting the unavoidable presence of model uncertainties and limiting the achievable tracking accuracy only by the presence of the measurement noise. With the specific aim of overcoming this narrowness, this work investigates the capability of deep neural networks in predicting the missile maneuvering trajectories in a model-free fashion. The idea is to leverage the Long-Short Term Memory (LSTM) net due to its excellent capability in learning long-term dependencies of temporal information. Two different LSTM-based architectures have been hence designed to predict both position and velocity of a missile using raw and noisy measurements provided by a realistic radar system, exploiting a large database abundant of realistic off-line data. Training results and theoretical derivations are verified through non-trivial scenarios in order to assess the capability of predicting unknown and realistic 3D missile maneuvers. Finally, the proposed approach has been also compared with a performing model-based IMM algorithm, suitably tuned to deal with realistic missile maneuvers, confirming the excellent generalization abilities of the developed data-driven architectures for different datasets.

Road slope estimation based on acceleration adaptive interactive multiple model algorithm for commercial vehicles

Road slope is an important external variable in vehicle dynamic control systems. However, it is a challenging problem to estimate road slope accurately for commercial vehicles due to the coupling problem among the mass, road slope and pitch angle. To solve this problem, a novel road slope estimation scheme with the correction of pitch angle is proposed. First, the coupling problem between road slope and body pitch is analyzed from the perspective of sensor signals. Next, the driving conditions are divided into gentle and strong scenarios, abstracted to the smooth driving model (SDM) and intensive driving model (IDM), respectively. SDM alone cannot guarantee accuracy under intensive scenarios, while IDM alone converges slowly under smooth driving scenarios. The acceleration adaptive interactive multiple model (AAIMM) algorithm is then designed to combine the models and determine which model is the most appropriate under different driving intensities. At last, the sensor-less pitch angle correction strategy based on the suspension deformation model is presented and the particle swarm optimization (PSO) algorithm is used to optimize the suspension stiffness off-line. The simulations and road tests indicate the effectiveness and accuracy of the proposed road slope estimation scheme.

Adaptive Hybrid Robust Filter for Multi-Sensor Relative Navigation System

This paper provides an adaptive hybrid robust filter (AHRF) for multi-sensor relative navigation systems that can be used to support cooperative intelligent transport systems. It is known that Huber’s M-estimation based robust filter and the fault detection and exclusion (FDE) based RAIM filter each has its own drawbacks, depending on the nature of the observation error biases. Based on the interactive multiple model (IMM) framework, our proposed AHRF in this paper can take advantage of both filters in a complementary sense. A new adaptive IMM (AIMM) algorithm with Markov transition probability prediction is proposed to allow AHRF to switch efficiently between the two filters. We consider the relative navigation system with Global Navigation Satellite System (GNSS) and ultra-wideband (UWB) as observations to verify AHRF in three cases of possible failure modes and multipath-induced errors. Our results show that AHRF outperforms both the FDE and robust filter in all cases. AHRF framework can be further adapted to include many other fault-tolerant filters to improve the robustness of multi-sensor relative navigation system even further.

Improved IMM algorithm based on support vector regression for UAV tracking

With the development of technology, the relevant performance of unmanned aerial vehicles (UAVs) has been greatly improved, and various highly maneuverable UAVs have been developed, which puts forward higher requirements on target tracking technology. Strong maneuvering refers to relatively instantaneous and dramatic changes in target acceleration or movement patterns, as well as continuous changes in speed, angle, and acceleration. However, the traditional UAV tracking algorithm model has poor adaptability and large amount of calculation. This paper applies support vector regression (SVR) to the interacting multiple model (IMM) algorithm. The simulation results show that the improved algorithm has higher tracking accuracy for highly maneuverable targets than the original algorithm, and can adjust parameters adaptively, making it more adaptable.

An M-Estimation-Based Improved Interacting Multiple Model for INS/DVL Navigation Method

This paper presents an M-estimation-based Improved Interacting Multiple Model (IIMM) algorithm for inertial navigation system (INS)/Doppler velocity logs (D VL) integrated method to directly apply in complex underwater environment without empirical parameters. Considering the time-varying measurement noise covariance, a variable model structure based on Bayesian estimation law is proposed to adapt to the environment and an adaptive state transition probability matrix is generated to promote the model adaption. Meanwhile, M-estimation-based filter is employed as primary model to save IIMM from the effect of outliers. The performance of the IIMM algorithm is evaluated on simulation, land vehicle, and Yangtze River test, where the state-of-the-art is compared adequately. The robustness simulation test is also performed. It is highlighted that IIMM approach can adapt to actual model rapidly and can resist outliers efficiently. The proposed IIMM method can improve the accuracy and robustness of the navigation system in a severe and unknown environment without increasing the computational load.

Adaptive Dynamic State Estimation of Distribution Network Based on Interacting Multiple Model

With the large-scale access of all kinds of distributed generations (DGs), the operation mode of the distribution network is increasingly diverse and changeable. To monitor the operation of an active distribution network, an adaptive dynamic estimation method is proposed to address the new generation of power system. Considering the features of different types of operation scenario change of distribution network and DGs, the proposed method uses the state deviation index to identify the current operation mode before state estimation. In the adaptive estimation stage, two typical estimators are improved to cope with the typical operation mode and embedded in the interactive multiple model (IMM) algorithm framework. IMM uses the identification results of operation mode to give higher weight to the corresponding estimator and finally outputs the joint estimation results. The proposed estimation method is investigated in an improved IEEE 33-bus system and an actual distribution network in China, which results indicate the proposed method converges more quickly and maintains better accuracy while facing the complex distribution network.

Bearing-only 2D maneuvering target tracking using smart interacting multiple model filter

In this paper, along with reviewing and analyzing the maneuvering target tracking model, the multiple-model Interacting Multiple Model algorithm is used to solve the maneuvering target tracking problem in the presence of measurement noise. In addition, for reliable estimation another method is proposed, which uses higher-order Markov models to describe the system behavior precisely. It means that the previous two models are used to predict the next model of target in order to present a more better algorithm than the first-order IMM algorithm. In this approach, two models are employed. For each model Extended Kalman Filter is used to randomly estimate states of the target. The final estimation of the maneuvering target consists of these two models. Final target estimation is obtained from a weighted sum of all state estimates. In addition, target tracking is presented with two modes for noise measurement: one is an adaptive method and the other is an assignment of an integer amount considering problem circumstances. In the end, the results are compared.

Variational Bayesian Based IMM Robust GPS Navigation Filter

This paper investigates the navigational performance of Global Positioning System (GPS) using the variational Bayesian (VB) based robust filter with interacting multiple model (IMM) adaptation as the navigation processor. The performance of the state estimation for GPS navigation processing using the family of Kalman filter (KF) may be degraded due to the fact that in practical situations the statistics of measurement noise might change. In the proposed algorithm, the adaptivity is achieved by estimating the time-varying noise covariance matrices based on VB learning using the probabilistic approach, where in each update step, both the system state and time-varying measurement noise were recognized as random variables to be estimated. The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning. One of the two major classical adaptive Kalman filter (AKF) approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate (MMAE). The IMM algorithm uses two or more filters to process in parallel, where each filter corresponds to a different dynamic or measurement model. The robust Huber's M-estimation-based extended Kalman filter (HEKF) algorithm integrates both merits of the Huber M-estimation methodology and EKF. The robustness is enhanced by modifying the filter update based on Huber's M-estimation method in the filtering framework. The proposed algorithm, referred to as the interactive multi-model based variational Bayesian HEKF (IMM-VBHEKF), provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors, such as the multipath effect. Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.

A Failure Identification and Recovery Framework for a Planar Reconfigurable Cable Driven Parallel Robot

In cable driven parallel robots (CDPRs), a single cable malfunction usually induces complete failure of the entire robot. However, the lost static workspace (due to failure) can often be recovered through reconfiguration of the cable attachment points on the frame. This capability is introduced by adding kinematic redundancies to the robot in the form of moving linear sliders that are manipulated in a real-time redundancy resolution controller. The presented work combines this controller with an online failure detection framework to develop a complete fault tolerant control scheme for automatic task recovery. This solution provides robustness by combining pose estimation of the end-effector with the failure detection through the application of an Interactive Multiple Model (IMM) algorithm relying only on end-effector information. The failure and pose estimation scheme is then tied into the redundancy resolution approach to produce a seamless automatic task (trajectory) recovery approach for cable failures.