A UWB Location Algorithm---Based on Adaptive Kalman Filter

In order to solve the problem of large fluctuations in UWB(Ultra Wide Band) positioning accuracy and solid-state deviations in the positioning results, which are in complex indoor environments, an adaptive Kalman filter method is introduced in the later stage of data processing. This method can better retain data information and obtain better filtering effects when the system noise is complex and measurement information is missing,.Thereby providing better positioning accuracy. The experiment uses AGV trolley equipped with UWB sensors to obtain measurement data, uses traditional Kalman filtering and adaptive Kalman filtering methods to compare the filtering effects of the algorithms. The experimental results show that when the measurement information is missing, compared with the traditional Kalman filter algorithm, the adaptive Kalman filter method is a real-time high-precision indoor positioning algorithm with higher positioning accuracy.


Introduction
With the rapid development in science technology, people are highly demanded on the accuracy of an indoor location. Locations can be estimated by traditional location techniques, such as infrared ray, ultrasonic, RFID(Radio Frequency Identification) and Wi-Fi, it becomes harder to satisfy the application needs in the refining industry because the accuracy of such techniques could be easily impacted by the local environment [1]. By contrast, UWB indoor location is a wireless technique with no carrier, which possesses high-speed transmission, low-power emission, and strong penetrability. Besides, it is based on short-duration pulse and has the advantages of such a technique, bringing favorable location in distance-of-sight transmission [2].
When equipment begins to run, UWB, owing to complex indoor transmission, often locates on a small area instead of a single point. Nowadays, it becomes a hot topic for learners to rectify and smooth locations Literature [3] studies error characteristic in one of UWB measurements---based on round-trip time. It analyzes Non-gaussian noise in RTT measurement and verifies the advantage of the particle filter algorithm. However, it is overly computed given by a restriction in which algorithm itself uses plenty of samples to explore randomly. In order to forecast target location Literature [4] proposes an extended finite impulse response estimator based on UWB ranging information and time delay positioning model but the accuracy depends on the average level.
To better improve the accuracy of UWB location, this paper introduces a new location algorithm that adapts UWB. In addition, a small car--AGV, as sensor carriers, is adapted to verify the effectiveness of algorithm improvement [5]. The above method, combining with indoor environment, can provide better location accuracy, which is realized under systematic noise and inadequate measuring information.

Traditional Kalman filter and Self-adapting Kalman filter
State equation of general linear discrete system can be represented as following one: In this equation, K refers to Kalman gain matrix; P refers to error covariance matrix;Q(k) refers to covariance matrix ofw(k);R(k) refers to covariance matrix ofv(k).
In practical applications, mathematical models and noise estimation, which described characteristics of system dynamics, sometimes are far from accuracy when they are under complex environments as well as other factors [6]. As a result, physics process cannot be reflected directly. Meanwhile, Kalman filtering is a recursive process. With the improving filtering steps, round-off error will be accumulated, which makes filter gain matrix lose its weighting function. Thus, the growing number of measurements magnified both mean value and covariance of evaluated error. The result is that smoothing will become less accurate when it is evaluating. Or worse is that Kalman filter will diverge. In order to control its divergence and improve precision, this paper introduces methods of adaptive Kalman filter[7].
among the rest， k r 、 K R 、 k q and k Q can be gained through statistical estimators of time-varing noise: refers to forgotten factors. In this paper, the vehicle trajectory is filtered. State variables are set as ( ) x k . it uses 4 state variables, that is

Modeling and parameter setting
, in which x represents separately direction displacement, direction velocity, and y-direction displacement, and direction velocity. The initial estimated value of speed is expressed by the observed value [10][11].
Measurement equation is: Correspondingly, variance matrix can be written, which corresponds to the process noise k ω k V .
Besides, in order to obtain estimated value with invariant state by Kalman filter, it has to provide initial value 0 X 0 P from both state variate and mean square value of estimated errors. It