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How to parameterise the GPS Platforms observation model regularly

Recent innovations in tracking device have introduced ways to enhance precision, availability, and reliability in advanced receivers. These innovations address mitigation of multipath errors, receiver stability, and data reliability under adverse signal conditions. Adverse conditions arise from partial obstructions like canopies and light trees that make satellite signals weak, interference from other communication systems, interference from power lines and transformers, high levels of ionospheric activities that make tracking of L2 signal harder, abrupt motions of the receiver, or momentary signal interruptions like going through a short tunnel that temporarily blocks all satellites.

As already discussed in the parameterisation of the vehicle GPS tracking systems observation model, clock errors and instrumental biases as well as ambiguities are partially over parameterised or linearly correlated. Cancelling the over – parameterised unknowns out of the equation or modelling them first and then keeping them fixed using the a priori method is, generally speaking, equivalent. As long as one knows which parameters should be kept fixed, the a priori information used is true one and is just used as a tool for fixing the parameters to zero. If the model is not parameterised regularly and one does not exactly know which parameters are over-parameterised, then the normal equation will be singular and cannot be solved. Again, using a priori information may make the equation solvable. However, in this case, the a priori information has the meaning of the direct “measures” on the related parameters.

Therefore the a priori information used must be a true and reasonable one; otherwise, the given a priori information will affect the solution in some unreasonable ways. If different a priori information is given, different results will be obtained. Therefore, the a priori information used should be based on true information. Independent Parameterisation of the Observation Model A priori information can be obtained from external surveys or from the experiences of long term data processing that does not use a priori information. A regular (independent) parameterisation of the vehicle GPS locator observation model is a precondition for a stable solution of the normal equation without using a priori information. As mentioned above, to parameterise the model independently or to fix the over parameterised unknowns are equivalent. However, in order to keep some parameters fixed one has to know which parameters are over-parameterised and have to be fixed. Therefore, in any case, one has to know how to parameterise the GPS observation model regularly. Fixing the over-parameterised unknowns after a general parameterisation is equivalent to a direct independent parameterisation. Therefore, the parameterisation of the GPS observation model should be regular.

Independent parameterisation is necessary because of the linear correlation of some parameters. The linear correlation partially merges the different effects together so that these effects cannot be separated exactly from each other. The constant parts of the different effects are nearly impossible to be separated without precise physical models, whereas many model parameters are presented in the Car tracking GPS observation equation and have to be codetermined. The inseparability of the bias effects comes partially from the physics of the surveys and depends on strategy of the surveys. Understanding the inseparability of the bias effects is important for designing surveys. The physical models have to be determined more precisely in order to separate the constant parts of the effects.

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