Neural Network Based Recursive Least Square Technique for Indoor Wireless Positioning

Location Based Services (LBS) in the realms of Smart City realizations require accurate real time positioning information of objects and people indoors. Both VLC based and the RF based positioning techniques have been studied in the literature. In RF system, we use Recursive Least Square (RLS) multilateration algorithm to estimate the position of unknown target indoor. The RLS multilateration algorithm is based on the trilateration solution using algebraic method. Solution obtained from the trilateration is used in RLS algorithm and the solution is updated recursively. Since Machine Learning (ML) is one of the widely used approaches to improve the accuracy in indoor positioning, we have used Artificial Neural Network (ANN) to fine tune the simulated distances with Rician noise. Therefore, the proposed technique hybridizes RLS with Artificial Neural Network (ANN) to solve a multilateration problem of different sets of anchor nodes. 

We use MATLABTM for the simulation purpose. While simulating distances, Rician noise is considered for anchor-target distance and, noisy distances are fed into ANN filter. Instead of using directly simulated distances, estimated distances from ANN are used for RLS implementation. Results from the hybrid RLS-ANN are compared with pure RLS, pure least square (LS) and LS-ANN approaches. Hybrid RLS-ANN provides the least Root Mean Square Error (RMSE) among all the techniques and improves the accuracy up to 80% compared to the pure LS multilateration technique. Complexity of the proposed technique is relatively low with significantly increased accuracy. 

We also compare the results with different sets of anchor nodes for RLS implementation. Hybrid RLS-ANN algorithm is used for anchor nodes N = 4 to N = 10. Comparing the results, it has been shown that as the number of anchor nodes increases, the RMSE decreases steadily. RLS multilateration with large number of anchor nodes performs better than LS multilateration. On the other hand, distance error is largely reduced by using ANN training and RLS with ANN estimated distances further improves the accuracy. 

In VLC system, we analyze the impact of SNR on indoor positioning. VLC indoor positioning is analyzed based on SNR distribution on the room indoor. Distance measurement is analyzed with three parameters: angle of incidence, angle of irradiance and transmitter FOV. Since SNR has the direct impact on the VLC indoor distance measurement, a comparative study of the SNR variation with respect to transmitter FOV, receiver FOV, angles of incidence and irradiance is presented, and corresponding distance measurement error is analyzed.