An Enhanced Received Signal Level Cellular Location Determination Method via Maximum Likelihood and Kalman Filtering

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An Enhanced Received Signal Level Cellular
Location Determination Method via Maximum
Likelihood and Kalman Filtering

• Ioannis G. Papageorgiou
• Charalambos D. Charalambous
• Christos Panayiotou
• University of Cyprus
• WCNC 2005, New Orleans, LA USA
• 13-17 March 2005

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Summary

• Problem statement
• Drivers
• Main obstacles
• Proposed solution
• Advantages
• Assumptions
• Initial Estimate
• Final Estimate
• Conclusions

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Problem Statement I

• Accurately tracking a cell phone
• Other key variables come into play
• Consistency
• TTFF (Time To First Fix)
• Cost (of course)
• and more
• Main Drivers
• Regulatory
• E-911, E-112 mandates
• Commercial

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Problem Statement II

• Main Obstacles to Location Estimation
• Non Line of Sight (NLoS) conditions
• Multipath Propagation
• Dynamicity of user and environment
• Geometric Dilution of Precision

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Proposed Solution I

• A two-step CLD method based on Maximum Likelihood
  and Kalman Filtering Estimation Techniques
• First step
• RSL method in combination with MLE and
  triangulation
• RSL values from Network Measurement Reports (NMR)
  are used
• Time-invariant lognormal propagation model
• Achieves a rough localization

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Proposed Solution II

• Second and Final Step
• Extended Kalman Filtering on instantaneous field
  measurements is used
• The 3D Aulin model used to account for multipath
  propagation and NLoS conditions
• The first-step estimate is incorporated to
  initialize the filter
• A high accuracy is achieved

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Proposed Solution III

• Advantages
• No hardware modifications are needed at the
  network
• Uses current standards and infrastructure
• Assumptions
• Channel knowledge
• Access to the instantaneous received signal

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Initial Estimate I

• NMR values of RSL are used to estimate the
  location, through MLE
• Lognormal Propagation model
• where
• Parameters e,d0,and the variance of X should be
  estimated or selected with care

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Initial Estimate II

• Sample m from all N BSs,
• follows the N-variate Gaussian distribution,
  i.e., where
• is the mean path loss for each BS.
• Assuming iid noise, the likelihood function is
  the product of the individual likelihood functions

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Initial Estimate III

• i.e.,
• Maximizing with respect to and solving
  for using the invariance property of the MLE,
  we get
• which is the MLE for the distance of the n-th BS
  from the MS

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Initial Estimate IV

• Then, we perform triangulation using the least
  squares error method to estimate the location
• where

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Initial Estimate V

• Simulation Setup
• 19(!) cell cluster, BSs equipped with
  omnidirectional antenna and the number of
  arranged users in the central cell is 1000
• The simulated environment is designated by the
  values of d0,sn, en and cell radius Rn.

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Initial Estimate VI

• Number of NMR samples is 20, and the number of
  BSs is 3-7.
• Results for urban (R500m) and suburban (R2500m)
  environments

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Initial Estimate VII

• The FCC mandate is satisfied for urban
  environments only. Inconsistency of the method
• Main error source is triangulation. The error
  increases as the cell radius increases
• Failure as a stand-alone method BUT
• Localizes the problem

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Final Estimate I

• The well-known 3D multipath channel of Aulin is
  incorporated to better account for channel
  impairments

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Final Estimate II

• The electric field at any receiving point
• consists of N plane waves, and is given by
• where
• and n(t) is white Gaussian noise
• IMPORTANT it depends parametrically on the
  location of the receiver, thus it can be utilized
  to estimate it

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Final Estimate III

• Extended Kalman Filtering (EKF) is used to
  estimate the location. The Initial Estimate
  initializes the filter estimate
• The discretized state-space form is
• where xk is the system state and wk,vk, are
  zero-mean independent Gaussian noise processes

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Final Estimate IV

• with covariance ,
• Clearly, h(.) is non-linear, thus EKF is used

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Final Estimate V

• where
• Simulation Setup same as for the Initial
  Estimate but 5 BSs
• Results for the worst case suburban environment
  are depicted
• Presenting the case when the location as well as
  the velocity is unknown, thus the system state is

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Final Estimate VI

• Assuming zero-mean Gaussian acceleration, the
  dynamics of the mobile are given by
• where w1, w2 are white noise processes. In
  discrete time, the dynamics are given by

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Final Estimate VII

• in which f(.) is a linear and A is a 4x4
  identity matrix
• For urban areas we take with Rayleigh
  distributed attenuation. In urban and suburban
  areas we take N between 2-6 with Nakagami
  distributed attenuation

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Final Estimate VIII

• Results for rural areas

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Final Estimate IX
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Conclusions

• Triangulation is an obstacle for location
  estimation
• Stand-alone methods are not consistent
• The algorithmic part of a method is important for
  TTFF
• A method should be robust against channel
  knowledge