# Artificial Neural Networks for Navigation Systems: A Review of Recent Research
## 3 Navigation Integration Using the State Estimators
The implementation of the Kalman family of filters needs a precise and logically valid statistical understanding of the process noise and measurement noise. Inadequ understanding of the noise statistics may cause filter divergence and substantially impair KF performance. Relativistic issues will arise if a filter's theoretical operation and its real behavior do not correlate. The assumptions on the statistical database of disruption are violated in various of scenarios in which there are instabilities in the process model and noise characterization, because in many real-world scenarios, the availability of a well-defined model is unattainable because some observations are ignored in the modeling step and one approach for taking them into consideration is to consider an equivalent model influenced by uncertainty. Moreover, there are model assumptions in actual navigational applications that the continuous state-space model is unable to capture. Since the actual vehicle motions are the result of non-linear processes, the linear model contains modeling mistakes. It is necessary to predetermine the system model, the system's beginning conditions, and the noise properties. It frequently happens that little prior knowledge of the operation is accessible. The availability of a well-defined model is inappropriate in particular scenarios in which there are many uncertainties in the proposed system and noise interpretation. Predictions based on disruption statistics are violated due to a number of realistic applications, and some conditions are ignored in the modeling step. It is reasonable to suppose that an adaptive process will dynamically identify the system model uncertainties and modeling errors. Innovation-based adaptive estimating (IAE) and multiple-model-based adaptive estimation (MMAE), such as the interacting multiple models (IMM) [5; 6; 7; 8] algorithm, are the two main approaches to AKFs that have been developed. The IMM algorithm has a configuration in which many model-matched state estimation filters operate in parallel and interact (exchange information) at each sampling period. By modifying the probabilities of each approach, which are utilized as weightings in the aggregate global state estimation, the algorithm performs soft switching between the various modes. The mode-conditionedforecast's covariances as well as the variations between these estimates are taken into account in the covariance matrix linked to this combined estimate. The noise data from the measurement sequence during the filtering process can be removed, and an IAE technique has been devised to estimate the process noise covariance \(\mathrm{Q_{k}}\) and/or measurement noise covariance \(\mathrm{R_{k}}\). A bank of KFs with various parameters operates concurrently in an MMAE approach, and the weights of every sub-filter are aggressively changed in response to fresh assessments. The sub-filter with well-known parameters wins after a thorough study. The MMAE method, however, requires more resources and may not completely account for the true system model. Another drawback is that the parameter estimation method for both IAE and MMAE systems requires a sliding window over the measurement sequence, which causes inaccuracy and delay. Consequently, adaptive filters introduce more sophisticated components in integrated navigation systems. The selection in integrated navigation systems' adaptive filters frequently uses fuzzy logic techniques. Such a selection selects the best sensors or dynamically modifies the noise covariance matrix. Target tracking may be manipulated well using interactive multiple models. Then the more accurate noise covariance matrix was estimated using the IMM technique. When used in an underwater environment, the IMM-adaptive robust cubature Kalman filter technique may successfully address the issues of measurement noise and typical statistical inaccuracy. The technique makes use of VB learning to give a robust tracking capacity for time-varying noise covariance as well as an approximation of the noise strength.