## 4 Tracking  
### Models for Tracking  
Target tracking has always been a hot topic in many application fields, and it is the basic algorithm in navigation systems. The displacement, velocity, acceleration, and other motion characteristics of the maneuvering target are estimated by using the data measured by the sensor. In the 1970s, researchers were interested in target tracking technology [74], which had many military and civilian applications, such as missile defense, ocean surveillance, and so on. In a tracking problem, two aspects are very important: the system models and the estimation method. The former includes the process model and the measurement model. Accurate estimation requires accurate process models. For example, when radar tracks a target, the human action or control command of the driver at any time will make the target turn, dodge and execute other actions in the course of target movement. To obtain enough information about the trajectory tracking performance of the target, it is necessary to use the correct motion model of the maneuvering target to perform the estimation. Some process models have been proposed for the tracking of a maneuvering target. The constant-velocity (CV) models emphasize that accelerations are very small with the so-called white-noise acceleration model. This model assumes that the target acceleration is an independent process (strictly white noise), such as \(w_{c}(t)^{\cdot}N(0,\sigma^{2})\), where \(w_{c}(t)\) is the acceleration noise. The most attractive feature of this model is its simplicity. The second simple model is the so-called constant-acceleration (CA) model or, more precisely, the \"nearly-constant-acceleration model\". This model assumes that the derivative of acceleration is the Gaussion white-noise as \(w_{a}(t)^{\cdot}N(0,\sigma^{2})\), where \(w_{a}(t)\) is the noise of the derivative of acceleration. Since the Singer model was put forward in 1970 [14], researchers have advanced the \"current\" statistical model, and IMM, among other maneuvering target models. The Singer model models target acceleration as a first-order semi-Markovian process with zero mean, which is in essence an a priori model because it does not use online information for the target maneuvering, although it can be made adaptive through an adaptation of some parameters. Because of the complexity of the objectives of an actual track, any a priori model cannot be extremely effective for the diverse acceleration situations of actual target maneuvers. One of the main shortcomings of the Singer model  
Figure 5: Flow diagram of Vision\(+\)IMU integration algorithm. is that the target acceleration has zero mean at any moment. Another shortcoming is that it cannot use online information. An acceleration model, called the current statistical model [15] is, in essence, a Singer model with an adaptive mean--that is, a Singer model modified to have a nonzero mean of the acceleration. In this current model, the model can use online tracking information, and the priori (unconditional) probability density of the acceleration is replaced by a conditional density, (i.e., Rayleigh density). Clearly, this conditional density carries more accurate information and is better able to be used than the a priori density. We note that this conditional Rayleigh assumption was made for the sole purpose of obtaining the variance of the acceleration prediction. Based on those models, there are many modified models for maneuvering target tracking, but all of them need a prior hypothesis. Because the tracking systems are of different types, the prior hypothesis is sometimes inappropriate. In general, we call the Singer model, the current statistical model, or the Jerk model as the'state' model, and they have one common problem, that they all assume the maneuvering target possesses a particular set of movement characteristics.