Optimised complexity reduction for maximum likelihood position estimation in spread spectrum navigation receivers

In urban environments, spread spectrum radio navigation is subject to multipath propagation causing multipath errors of tens of metres. Low-complexity high-resolution channel delay estimation is crucial for position estimation in the receivers to mitigate the multipath errors. The main drawback of maximum likelihood (ML) channel delay estimation is the high computational complexity. Thus, recent publications present methods to decrease its computational complexity. These contributions assess the complexity reduction by means of signal subspace energy errors (SSEEs). This assessment of the complexity reduction is incomplete, as the relevant metric, that is, the relationship between complexity reduction and degrading position accuracy in terms of increasing root mean square error (RMSE) lacks. The authors main contribution is the derivation and analysis of this relation. The larger RMSE for complexity-reduced ML estimation algorithms compared to the implementation without complexity reduction consists of an increased noise variance and a non-zero bias. Thus, this contribution associates the SSEE and the RMSE for complexity-reduced ML estimators. Computer simulations confirm the revealed analytical relationships. Furthermore, the authors approach yields a novel method to minimise the increased noise variance of complexity-reduced ML estimation. Thus, the authors algorithms yield a lower RMSE.