# IMM Filtering Algorithms for a Highly Maneuvering Fighter Aircraft: An Overview
The NCV is a nonmaneuvering motion, whereas nearly constant acceleration (NCA), nearly constant jerk (NCJ), and NCT with an unknown angular velocity are maneuvering motions [1; 8]. The models for NCA and NCJ present linear characteristics when considering the Cartesian co-ordinates of the target state. Conversely, the NCT model introduces nonlinearity into the target state representation if the angular velocity remains unspecified. In general, a target can move with a sequence of nonmaneuvering and maneuvering motions. In scenarios where a target exhibits a variety of movement patterns, the times of change in motion are usually unknown. For such a target, the continuous-valued kinematic state (known as the base state) and the discrete-valued mode (known as the modal state) or dynamic model change with time [8]. This class of problems is known as the hybrid state estimation or the jump Markov state estimation problem [8; 20; 25]. A dynamic model describes the time evolution of the base state by using a stochastic difference equation. The modal state can assume a finite number of possible values and can switch from one mode to another over time. A homogeneous Markov chain with a known transition probability matrix (TPM) describes changes in the modal state [8; 20; 25]. In a hybrid state estimation algorithm, a bank of mode-matched filters is run in parallel, and an algorithm to manage the co-operation among the filters is used. The generalized pseudo-Bayesian (GPB) [8; 25] algorithm and the interacting multiple model (IMM) algorithm were proposed by [PERSON] et al. [26; 27] and are examples of hybrid state estimation algorithms. The \(k\)th-order GPB algorithm is denoted by GPBk and requires \(n_{\rm m}^{k}\) filters, where \(n_{\rm m}\) is the number of models, and \(k\) is the number of sampling periods over which mode switching is considered. In contrast, the IMM algorithm always uses \(n_{\rm m}\) filters, and the performance of the IMM algorithm is comparable to that of the GPB2 algorithm (which uses \(n_{\rm m}^{2}\) filters) at a much reduced computational cost. The computational complexity of the IMM algorithm is nearly linear in the number of models with a small quadratic term. An attractive feature of the IMM algorithm is its modularity [25], which allows it to be used with any filter, such as the KF, EKF, UKF, CKF, etc. The IMM approach has been effectively utilized in a broad spectrum of applications [28; 29; 30; 31; 32; 33; 34; 35; 36; 37]. Comprehensive insights into the algorithm, along with an extensive review, can be found in [8] and [25], respectively. If a single-model filter (e.g., KF, EKF, UKF, or CKF) is used for a maneuvering target, then a high level of process noise will be chosen with a nonmaneuvering motion (e.g., NCV) used to handle maneuvering motion. For this choice, the filter will perform well in the maneuvering segments of the trajectory, but its performance will be poor in the nonmaneuvering segments. If a low level of process noise is chosen, then the filter will perform well in the nonmaneuvering segments, but it will have large errors in the maneuvering segments. On the other hand, the IMM filter will perform well in the nonmaneuvering and maneuvering segments since it probabilistically chooses the motion models. The IMM algorithm also finds application in multi-target tracking (MTT), which refers to the problem of jointly estimating the number of targets and their states from noisy sensor measurements in the presence of a false alarm and a sensor probability of detection that is less than unity [38; 39; 40; 41; 42]. MTT problems occur in both civilian and military domains and arise in air traffic control (ATC), ground surveillance, maritime surveillance, airborne surveillance, space-object tracking, autonomous vehicles, ballistic missile defense, [8; 25; 38; 40; 43; 44; 45], robotics, remote sensing, computer vision, biomedical research, etc. In general, a tracking scenario includes nonmaneuvering and maneuvering targets.