TDOA-Based Target Tracking Filter While Reducing NLOS Errors in Cluttered Environments
Abstract
:1. Introduction
2. Literature Review
3. Preliminary Information
3.1. Time Difference of Arrival (TDOA)
3.2. Kalman Filter (KF)
3.2.1. Prediction
3.2.2. Measurement Update
4. Transmitter Tracking While Decreasing NLOS Error in TDOA Measurements
4.1. System Models
4.2. Definitions and Assumptions
- (A1) Considering unknown, cluttered environments, at least three LOS receivers exist among all receivers. However, these LOS receivers are not known in advance.
- (A2) Considering LOS receivers, the measurement noise in Equation (2) has a Gaussian distribution with zero mean and variance that is not known in advance.
- (A3) The transmitter exists inside a bounded workspace, whose boundary is known in advance.
4.3. Least-Squares Estimation (LSE) for Solving the TDOA Localization
4.4. NLOS Error Reduction Algorithm
- 1
- Let define the set of all receivers. Initially, we set .
- 2
- From , we compute all receiver sets, such that each receiver set has K receivers. The number of total receiver sets is . Let define each receiver set. Using all receivers in each receiver set , one calculates the transmitter estimate utilizing the LSE solution (Equation (18)) in Section 4.3. In addition, we calculate the associated , as defined in Equation (19).
- 3
- Under Equation (20), a reliable estimate has a smaller . Therefore, we find a receiver set with the minimum . Let define the found receiver set.
- 4
- Let define the number of elements in . From , we compute all receiver sets, such that each receiver set has receivers. In this way, we build new receiver sets, . For the new receiver sets, one computes the transmitter estimate utilizing the LSE solution (Equation (18)) in Section 4.3. In addition, one utilizes Equation (19) to derive the associated . Among the new receiver sets, one searches for the set with the minimum . Let define the found receiver set.
- 5
- If becomes 3, then jump to the next step. Else, jump to step [4].
- 6
Exception Handling
4.5. IMM KF
5. MATLAB Simulations
5.1. Monte Carlo (MC) Simulations
5.2. Scenario 1
5.3. Scenario 2
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Kim, J. TDOA-Based Target Tracking Filter While Reducing NLOS Errors in Cluttered Environments. Sensors 2023, 23, 4566. https://doi.org/10.3390/s23094566
Kim J. TDOA-Based Target Tracking Filter While Reducing NLOS Errors in Cluttered Environments. Sensors. 2023; 23(9):4566. https://doi.org/10.3390/s23094566
Chicago/Turabian StyleKim, Jonghoek. 2023. "TDOA-Based Target Tracking Filter While Reducing NLOS Errors in Cluttered Environments" Sensors 23, no. 9: 4566. https://doi.org/10.3390/s23094566