Parameter Estimation Using Delay and Multiply Method

The Delay and Multiply method is a parameter estimation technique commonly used in GPS signal acquisition, primarily addressing the joint estimation problem of pseudocode phase and Doppler frequency shift. Its core principle involves performing time delay and multiplication operations on received signals to separate hidden pseudorandom code and carrier information.

In GPS signal processing, each satellite transmits a unique pseudorandom code modulated signal. The receiver needs to simultaneously resolve two key parameters: pseudocode phase offset and Doppler frequency shift (caused by relative motion between satellites and receivers). Implementation steps of the Delay and Multiply method include:

During signal preprocessing, the received intermediate frequency signal undergoes digital sampling to form a discrete time sequence. In code implementation, this typically involves ADC conversion and down-conversion to baseband.

The delay operation creates two signal copies, with one version applying a fixed chip delay (typically half a chip period). This delay must be smaller than the pseudocode's correlation radius. Programmatically, this can be implemented using FIFO buffers or shift registers.

The multiplication stage performs conjugate multiplication between the original signal and delayed signal. This operation eliminates pseudocode modulation components while preserving carrier frequency information. The multiplied signal exhibits distinct single-frequency characteristics. Code implementation requires complex multiplication operations with proper handling of I/Q components.

Spectral analysis phase applies FFT transformation to the multiplication results. Doppler frequency shift can be accurately estimated by detecting spectral peak positions, while peak amplitude reflects pseudocode phase matching degree. Implementation typically uses optimized FFT algorithms with zero-padding for frequency resolution enhancement.

For three-satellite simulation scenarios, synthetic signals with different pseudocodes and Doppler shifts must be generated for each satellite. Parallel processing of these three signal paths verifies the algorithm's capability to distinguish different satellite signals. Practical implementation must consider integer multiple relationships of pseudocode periods to avoid spectral ambiguity issues.

Compared to traditional parallel code phase search methods, this approach significantly reduces computational complexity. However, in low SNR environments, it requires conjunction with techniques like coherent integration to improve detection performance. Modern GPS receivers often employ enhanced schemes such as differential coherent integration to improve acquisition sensitivity.